Giorgio Morales
email: gmorales@inictel.edu.pe

Itamar Salazar-Reque

Joel Telles
email: jtelles@inictel.edu.pe

Daniel Díaz

Detecting Violent Robberies in CCTV Videos Using Deep Learning

Keywords: Action recognition, convLSTM, Robbery detection

Video surveillance through security cameras has become difficult due to the fact that many systems require manual human inspection for identifying violent or suspicious scenarios, which is practically inefficient. Therefore, the contribution of this paper is twofold: the presentation of a video dataset called UNI-Crime, and the proposal of a violent robbery detection method in CCTV videos using a deep-learning sequence model. Each of the 30 frames of our videos passes through a pre-trained VGG-16 feature extractor; then, all the sequence of features is processed by two convolutional long-short term memory (con-vLSTM) layers; finally, the last hidden state passes through a series of fully-connected layers in order to obtain a single classification result. The method is able to detect a variety of violent robberies (i.e., armed robberies involving firearms or knives, or robberies showing different level of aggressiveness) with an accuracy of 96.69%.

Introduction

Citizen insecurity is one of the most important problems affecting today's people quality of life. This is especially true for developing countries where the problem is exacerbated by the poverty and the lack of opportunities [START_REF]The Global Shapers Survey[END_REF]. Of the different ways in which insecurity manifests itself, robberies are the most frequent. To reduce their rate of occurrence, a common solution is to install both indoor cameras -such as in convenience stores, gas stations, or restaurants -, or outdoor cameras -as the public surveillance cameras on the streets managed by the government. Unfortunately, for this solution to be efficient, many resources must be spent. For instance, indoor cameras are normally used just to record the assault and subsequently to identify the robber; but to use them to warn the police when a robbery is being committed, human inspection is needed. This is the approach in public outdoor cameras, where robbery detection relies on the use of continuously monitored surveillance cameras by security agents. Nevertheless, this is a limited solution due to the small number of agents compared to the number of cameras to be monitored, and to the inherent fatigue caused by this exhausting task.

In this context, the use of artificial intelligence techniques to offer new tools for automatic robbery detection can be of great aid. However, this is a difficult mission since a robbery can happen anywhere in the city, which means that there is a high variety of scenarios that make the solution to this problem a big challenge.

To the best of our knowledge, no studies have been proposed for the automatic detection of robbery. Violence detection, however, do present several previous researches. Some of them used hand-crafted features as in [START_REF] Mabrouk | Spatio-temporal feature using optical flow based distribution for violence detection[END_REF] where the authors proposed DiMOLIF, a new feature, based on STIPs [START_REF] Laptev | On space-time interest points[END_REF] and optical flow, to describe violence in surveillance videos. They used this new feature to classify video clips from two datasets using a SVM classifier obtaining an accuracy of 88% and 85% respectively. Deniz et al [START_REF] Deniz | Fast violence detection in video[END_REF], compute power spectrum of two consecutive frames to detect sudden changes elicited by fast movements to detect violence with an accuracy improvement of up to 12% with respect to the compared methods. It is worth saying that both studies assumed that the actions are fast enough so the difference between frames encoded a violence action. This is not necessarily true for some armed robberies where the criminal can intimidate the victim by holding a gun without a sudden movement. Some other approaches used deep convolutional neural networks (CNN). In [START_REF] Tay | A robust abnormal behavior detection method using convolutional neural network[END_REF], the authors used a 6-layer CNN to classify frame images from videos as normal or abnormal. However, as images were sampled from video sequences there might be a high correlation between samples making the network prone to overfitting. Moreover, as robbery is an action, it will require more than one image to be correctly described. Additionally, the practical use of this approach will require the system to work in every frame which is computationally expensive. In [6], Trajectory-Pooled Deep-Convolutional Descriptors (TDD) were described. They were presented as a new video feature for action recognition that combined the merits of both hand-crafted features (Improved trajectories [START_REF] Wang | Action recognition with improved trajectories[END_REF]) and deep-learned features (two-stream ConvNets [START_REF] Simonyan | Two-stream convolutional networks for action recognition in videos[END_REF]). This was later used in [START_REF] Meng | Trajectory-Pooled Deep Convolutional Networks for Violence Detection in Videos[END_REF] for violence detection with high accuracy. In [START_REF] Zhou | Violent Interaction Detection in Video Based on Deep Learning[END_REF], the authors proposed an image acceleration field calculated from the optical flow field, which serves as an input to a Convolutional Neural Network, called FigthNet. Finally, Sudhakaran et al. [START_REF] Sudhakaran | Learning to detect violent videos using convolutional long short-term memory[END_REF] developed an end-to-end trainable deep neural network for performing violent video classification using convolutional long short term memory (convLSTM) networks.

In this work, we propose an end-to-end trainable sequence model for violent robbery classification similar to that proposed by [START_REF] Sudhakaran | Learning to detect violent videos using convolutional long short-term memory[END_REF]. We no longer have to design hand-crafted features and feed them into a classifier; instead, the input of our model is a sequence of 30 RGB frames extracted from the CCTV videos of our dataset. The first part of our architecture is the feature extractor, which process each frame using a pre-trained CNN, such as VGG16 or NASNetMobile.

The second part is the sequence network; it is composed of convLSTM layers, which can encode the spatio-temporal changes of the processed features. We tried different configurations and selected the best network, achieving a classification accuracy of 96,69% in our validation dataset.

Proposed Method

UNI-Crime Dataset

One of the difficulties of training an optimal model for robbery detection is the lack of a proper public dataset. Namely, some common problems are the small number of samples, the poor diversity of scenarios, or the absence of spontaneity in simulated scenes [START_REF] Hassner | Violent flows: Real-time detection of violent crowd behavior[END_REF][START_REF] Nievas | Violence detection in video using computer vision techniques[END_REF][START_REF] Li | Anomaly detection and localization in crowded scenes[END_REF]. Nevertheless, the main problem is that almost none of the previous datasets contains scenes of robberies recorded by CCTV cameras, which is what we aim to detect. On the other hand, the UCF-Crime dataset [START_REF] Sultani | Real-world Anomaly Detection in Surveillance Videos[END_REF] contains 1900 CCTV videos of normal actions, robberies, abuse, explosions, among other anomalies. However, those videos have different duration and frame rates; what is more, many of them are edited videos that contain multi-camera view, which is not useful for analyzing the continuity of an action, or present advertisements at the beginning or at the end.

For those reasons, we decided to construct the UNI-Crime dataset [16] based on the UCF-Crime dataset. For this, we discarded those multi-camera and repeated videos. Due to the fact that some videos are too long (three minutes or more) and others too short (20 seconds), we standardized the duration of our videos to 10 seconds. To do this, we trim each 10 useful seconds of the videos and classify them as robbery or non-robbery; by doing so, we can get multiple scenes of both classes from a single video, which strengthen our model, since it is less prone to overfitting. We also re-sized all the videos to 256 × 256 pixels and standardized the frame rate to 3 frames per second; that is, 30 frames per video, in order to avoid redundant information. In addition, we downloaded extra videos from Youtube, mainly from robberies or normal actions at stores. In the end, we collected 1421 videos: 1001 of non-robbery and 420 of robbery. A sample of frames from the dataset is shown in Fig. 1.

Neural Network Training

We propose a sequence model for end-to-end robbery detection. The architecture of the model is divided in two parts: the feature extractor, and the recurrent network. We tried the pre-trained VGG16 [START_REF] Simonyan | Very Deep Convolutional Networks for Large-Scale Image Recognition[END_REF] and NASNetMobile [START_REF] Zoph | Learning Transferable Architectures for Scalable Image Recognition[END_REF] networks as feature extractors, and the Convolutional LSTM network (convLSTM) [START_REF] Shi | Convolutional LSTM Network: A Machine Learning Approach for Precipitation Nowcasting[END_REF] as the recurrent network. We give further details about these structures below:

ConvLSTM The Long-Short Term Memory (LSTM) network [START_REF] Hochreiter | Long short-term memory[END_REF] is a recurrent end-to-end architecture which is capable of efficiently encoding long and short temporal changes of a sequence thanks to the memory cells it presents. Recently, LSTM networks have been widely used for different purposes such as speech recognition, natural language processing (NLP) or even human action recognition [START_REF] Salehinejad | Recent Advances in Recurrent Neural Networks[END_REF]. However, a standard LSTM network discards most of the spatial information due to it vectorizes all incoming data. Therefore, the Convolutional Long-Short Term Memory (convLSTM) network [START_REF] Shi | Convolutional LSTM Network: A Machine Learning Approach for Precipitation Nowcasting[END_REF] was proposed in order to preserve both the spatial and temporal information. The equations that govern a single LSTM unit are as follows:

Γ <t> f = σ(W f x * x <t> + W f a * a <t-1> + b f ), (1)
Γ <t> u = σ(W ux * x <t> + W ua * a <t-1> + b u ), (2)
c<t> = tanh(W cx * x <t> + W ca * a <t-1> + b c ), (3)
c <t> = Γ <t> f • c <t-1> + Γ <t> u • c<t> , (4)
Γ <t> o = σ(W ox * x <t> + W oa * a <t-1> + b o ), (5)
a <t> = Γ <t> o • tanh(c <t> ), (6)
where x <t> is the two-dimensional input at time t; Γ <t> f , Γ <t> u , Γ <t> o are the outputs of the forget, update and output gates, respectively; c <t> is the cell state; c<t> is the candidate for replacing the previous cell state; a <t> is the hidden state; and W f x , W f a , W ux , W ua , W ox , and W oa are two-dimensional convolutional filters.

VGG16 Also called OxfordNet, is a convolutional neural network that is trained on ImageNet [START_REF] Deng | ImageNet: A Large-Scale Hierarchical Image Database[END_REF]. Table 1 shows the performance of the model on the ImageNet validation dataset. The network is 16 layers deep and it exclusively uses 3 × 3 convolutional filters. It is commonly used as a high-level feature extractor for tasks such as saliency detection [START_REF] Lee | Deep Saliency with Encoded Low Level Distance Map and High Level Features[END_REF], action recognition [START_REF] Lan | Deep Local Video Feature for Action Recognition[END_REF][START_REF] Li | VideoLSTM Convolves, Attends and Flows for Action Recognition[END_REF] or semantic segmentation [START_REF] Liu | Faster R-CNN for Robust Pedestrian Detection Using Semantic Segmentation Network[END_REF]. Hence, we consider the convolutional features from the last pooling layer.

NASNet It is a product of Google's AutoML project, whose aim is to automate the design of machine learning models. In [START_REF] Zoph | Learning Transferable Architectures for Scalable Image Recognition[END_REF] they proposed a novel search method so that AutoML could find the best layer or combination of layers (like those present in ResNet [START_REF] He | Deep residual learning for image recognition[END_REF] or Inception [START_REF] Szegedy | Going deeper with convolutions[END_REF][START_REF] Szegedy | Inceptionv4, Inception-Resnet and the impact of residual connections on learning[END_REF] models) which can then be stacked many times in a flexible manner to create a final network. One of the networks derived from the large NASNet, trained on the ImageNet and COCO datasets, is called NASNetMobile, which achieved better performance than equivalently-sized state-of-the-art models for mobile platforms [START_REF] Howard | Mobilenets: Efficient convolutional neural networks for mobile vision applications[END_REF][START_REF] Zhang | Shufflenet: An extremely efficient convolutional neural network for mobile devices[END_REF]. Proposed Architecture Fig. 2 illustrates the general architecture of the network for detecting violent robberies. Its input is a sequence of 30 frames of 224 × 224 × 3 pixels. Contrary to previous works such as [START_REF] Simonyan | Two-stream convolutional networks for action recognition in videos[END_REF] or [START_REF] Sudhakaran | Learning to detect violent videos using convolutional long short-term memory[END_REF], we do not use optical flow images or the difference between adjacent frames as inputs because of two reasons: First, some armed robberies does not necessarily involve rapid changes in the scene; instead, a robber could threat a person holding a gun without sudden movements. Second, we want to keep as much spatial information as we can and let the convLSTM to encode the spatial changes. Each frame passes through a convolutional feature extractor, which could be derived from a pre-trained VGG16 or NASNet network. These high-level features are processed using the convLSTM layers. The last convLSTM layer is a manyto-one layer. Finally, the hidden state of the last convLSTM unit is processed by three fully-connected layers in order to obtain a single classification result.

We tried different network architectures but show in Table 2 only the five architectures that achieved the greatest performances. The first one, ROBN et1, uses the first 13 layers of the pre-trained VGG16 network as feature extractor and two LSTM layers (as shown in Fig. 2). The second one, ROBN et2, uses the first 253 layers of the pre-trained NASNetMobile network (i.e. until the activation 74 layer whose output is 28 × 28 × 88) as feature extractor and one LSTM layer. The third one, ROBN et3, uses the same feature extractor as ROBN et2 and two LSTM layers. The fourth one, ROBN et4, uses the first 769 layers of the pre-trained NASNetMobile network (i.e. until the last convolutional layer, activation 188, whose output is 7 × 7 × 1056) as feature extractor and one LSTM layer. The fifth one, ROBN et5, uses the same feature extractor as ROBN et4 and two LSTM layers.

Results

Since the UNI-Crime dataset contains 256 × 256 -pixel videos and the input size of both the VGG16 and NASNetMobile networks is 224×224, we applied random cropping four times to each video; two of the cropped videos were horizontally flipped. In this way, we applied data augmentation techniques and got a dataset of 5684 videos. We divided 85% of the dataset to create the training set, and 15% to create the validation set.

The training algorithm was implemented using Python 3.6 on a PC with Intel i7-8700 at 3.7 GHz CPU, 64GB RAM and a NVIDIA GeForce GTX 1080 Ti GPU. The proposed CNN was trained during 120 epochs using an Adam optimizer [START_REF] Kingma | Adam: A method for stochastic optimization[END_REF] with a learning rate of 0.001, a momentum term β 1 of 0.9, a momentum term β 2 of 0.999 and a mini-batch size of 8. Furthermore, we added a 10% dropout rate before the fully-connected layers to prevent overfitting. Figure 3 shows the evolution of network accuracy and loss over training time of all the networks. Table 4 compares the performance of the five networks in terms of classification accuracy from the validation set.

From Table 4 we chose ROBN et1 as the best network, as it presented the highest classification accuracy value and the lowest cost when evaluating in the validation set (Figure 4). What is more, ROBN et1 is nearly 1.3% more accurate when compared to the second best accuracy and it presents 80,703,104 less parameters. Furthermore, we observe in Figure 3 that only ROBN et1 shows a little difference between the training and validation values over the training time, meaning that it prevents overfitting problems and has better performance than the other networks when it comes to predicting new samples outside the training set. Finally, in Table 4 we compared our results with those achieved using the method of [START_REF] Sudhakaran | Learning to detect violent videos using convolutional long short-term memory[END_REF] with the UNI-Crime dataset. Although their training accuracy is slightly higher than ours, our validation accuracy is higher than theirs by more than five percentage points. This fact supports our preference of using RGB inputs instead of optical flow inputs. [START_REF] Sudhakaran | Learning to detect violent videos using convolutional long short-term memory[END_REF] 99.63 91.25

Conclusion

In this paper, we have presented an efficient end-to-end trainable deep neural network to tackle the problem of violent robbery detection in CCTV videos. We presented a dataset that encompasses both normal and robbery scenarios. What is more, some of the normal videos contained in our dataset correspond to moments before or after the robbery, which ensures that our method can discern between normal and robbery events even in the same environment.

The proposed method is able to encode both the spatial and temporal changes using convolutional LSTM layers that receive a sequence of features extracted by a pre-trained CNN from the original video frames. The classification accuracy evaluated in the validation dataset achieves a value of 96.69%. Although this is a promising result, further improvements need to be done in order to offer a scalable and marketable product, such as severely increasing the number of videos and scenarios of the dataset, reducing the computational cost, among others.

Fig. 1 .

 1 Fig. 1. Sample frames from the UNI-Crime dataset. (a)(b) Robbery samples. (c)(d) Non-robbery samples.

Fig. 2 .

 2 Fig. 2. The proposed network architecture using two convLSTM layers and the first 13 layers of the VGG16 network as feature extractor.

Fig. 3 .

 3 Fig. 3. Comparison of metrics evolution over training time of all networks. (a) Epochs vs. Accuracy. (b) Epochs vs. Loss.

Fig. 4 .

 4 Fig. 4. Metrics evolution over training time of ROBNet1. (a) Epochs vs. Accuracy. (b) Epochs vs. Loss.

Table 1 .

 1 Models performance on the Imagenet validation dataset.

	Network	Top-1 Accuracy (%) Top-5 Accuracy (%) Parameters
	VGG16	0.713	0.901	138,357,544
	NASNetMobile	0.744	0.919	5,326,716

Table 2 .

 2 Parameters of the proposed network architectures.

	Network Feature Extractor	#convLSTM #Filters #Filters Layers Layer 1 Layer 2
	ROBNet1	VGG16 (13 layers)	2	128	64
	ROBNet2 NASNet (253 layers)	1	128	-
	ROBNet3 NASNet (253 layers)	2	128	64
	ROBNet4 NASNet (769 layers)	1	128	-
	ROBNet5 NASNet (769 layers)	2	128	64

Table 3 .

 3 Metrics Comparison of Different Robbery Detection Networks

	Network ACC Parameters
	ROBNet1	96.698	20,906,095
	ROBNet2	95.401	101,609,199
	ROBNet3	94.103	88,025,199
	ROBNet4	93.514	11,989,743
	ROBNet5	92.453	6,927,471

Table 4 .

 4 Metrics Comparison of Different Robbery Detection Networks

	Network	Training ACC (%) Validation ACC (%)
	ROBNet1	99.46	96.69
	Sudhakaran


Pradeep Hewage
email: hewagep@edgehill.ac.uk

Ardhendu Behera
email: beheraa@edgehill.ac.uk

Marcello Trovati
email: marcello.trovati@edgehill.ac.uk

Ella Pereira
email: pereirae@edgehill.ac.uk

Long-Short Term Memory for an Effective Short-Term Weather Forecasting Model Using Surface Weather Data

Keywords: Long Short-Term Memory, Numerical Weather Prediction, WRF, Surface Weather Parameters, time-series data analysis

Numerical Weather Prediction (NWP) requires considerable computer power to solve complex mathematical equations to obtain a forecast based on current weather conditions. In this article, we propose a lightweight data-driven weather forecasting model by exploring state-of-the-art deep learning techniques based on Artificial Neural Network (ANN). Weather information is captured by time-series data and thus, we explore the latest Long Short-Term Memory (LSTM) layered model, which is a specialised form of Recurrent Neural Network (RNN) for weather prediction. The aim of this research is to develop and evaluate a short-term weather forecasting model using the LSTM and evaluate the accuracy compared to the well-established Weather Research and Forecasting (WRF) NWP model. The proposed deep model consists of stacked LSTM layers that uses surface weather parameters over a given period of time for weather forecasting. The model is experimented with different number of LSTM layers, optimisers, and learning rates and optimised for effective short-term weather predictions. Our experiment shows that the proposed lightweight model produces better results compared to the well-known and complex WRF model, demonstrating its potential for efficient and accurate short-term weather forecasting.

Introduction

Weather forecasting refers to the scientific process of predicting the state of the atmosphere based on specific time frames and locations [START_REF] Hayati | Application of Artificial Neural Networks for Temperature Forecasting[END_REF]. Numerical Weather Prediction (NWP) utilises computer algorithms to provide a forecast based on current weather conditions by solving large systems of non-linear mathematical equations, which are based on specific mathematical models [START_REF] Lynch | The emergence of numerical weather prediction: Richardson's dream[END_REF]. Meteorology adopted a more quantitative approach with the advance of technology and computer science, and forecast models became more accessible to researchers, forecasters, and other stakeholders. Many NWP systems were developed in recent years, such as Weather Research and Forecasting (WRF) model, where increasing high performance computing power has facilitated the enhancement and the introduction of regional or limited area models [START_REF] Oana | Use of Genetic Algorithms in Numerical Weather Prediction[END_REF]. As a consequence, the WRF model became the world's most-used atmospheric NWP model due to its higher resolution rate, accuracy, open source nature, community support, and wide variety of usability within different domains [START_REF]WRF Model Users Site[END_REF], [START_REF] Powers | The Weather Research and Forecasting Model: Overview, System Efforts, and Future Directions[END_REF].

According to [START_REF] Hayati | Application of Artificial Neural Networks for Temperature Forecasting[END_REF], data-driven computer modelling systems can be utilised to reduce the computational power of NWPs. In particular, Artificial Neural Network (ANN) can be used for this purpose due to their adaptive nature and learning capabilities based on prior knowledge. This feature makes the ANN techniques very appealing in application domains for solving highly nonlinear phenomena. Recurrent Neural Networks (RNN) and deep learning have attracted considerable attention due to their superior performance [START_REF] Jozefowicz | An Empirical Exploration of Recurrent Network Architectures[END_REF]. Deep learning allows stacked neural networks and includes several layers as part of overall composition known as nodes. The computation takes place at the node level, since it allows the combination of data input through a set of weights. Subsequently, the activation function gets established on the basis of input-weight products while signal progresses take place in the network [START_REF] Hinton | Reducing the Dimensionality of Data with Neural Networks[END_REF].

Figure 1 depicts a general overview of the proposed research. More specifically, the proposed weather prediction model is defined on the Long Short-Term memory (LSTM), a specialised form of the RNN, for weather prediction. The performance of the proposed model is subsequently compared to the well-established WRF model to assess and evaluate its computational efficiency and accuracy.

Weather Research and Forecasting Model

The Weather Research and Forecasting (WRF) model was developed by Norwegian physicist Vilhelm Bjerknes and applied various thermodynamic equations so that numerical weather-based predictions can be made mainly through different vertical levels [START_REF] Stensrud | Parameterization schemes: keys to understanding numerical weather prediction models[END_REF]. The primary role of the WRF was to carry out analysis focusing on climate time scale via linking physics data between land, atmosphere and ocean. The WRF model became the world's most-used atmospheric model since its initial public release was in the year 2000 [START_REF] Powers | The Weather Research and Forecasting Model: Overview, System Efforts, and Future Directions[END_REF].

The WRF model needs to run in two different modes to extract time-series data. Firstly, historical weather data are collected and subsequently, predicted weather data is identified for evaluation purposes. GRIdded Binary (GRIB) data are a concise data format commonly used in meteorology to store historical and forecast weather data [START_REF] Skamarock | A Description of the Advanced Research WRF Version 3[END_REF], [START_REF] Noaa | Reading GRIB Files[END_REF]. Global Forecast System (GFS) GRIB data provides 0.25 degrees resolution and available to download every three hours freely [START_REF] Commerce | NCEP GFS 0.25 Degree Global Forecast Grids Historical Archive[END_REF]. Therefore, the GFS three hourly data are selected for this project, with a horizontal resolution set to 27km.

One of the primary challenges in the WRF is its requirement for massive computational power to solve the equations that describe the atmosphere. Furthermore, atmospheric processes are associated with highly chaotic dynamical systems, which causes a limited model accuracy. As a consequence, the model forecast capabilities are less reliable as the difference between current time and the forecast time increases [START_REF] Hayati | Application of Artificial Neural Networks for Temperature Forecasting[END_REF], [START_REF] Baboo | An Efficient Weather Forecasting System using Artificial Neural Network[END_REF]. In addition, the WRF is a large and complex model with different versions and applications, which lead to the need for greater understanding of the model, its implementation and the different option associated with its execution [START_REF] Powers | The Weather Research and Forecasting Model: Overview, System Efforts, and Future Directions[END_REF]. The GFS 0.25 degrees dataset is the freely available highest resolution dataset for the WRF model. This allows the user to forecast weather data at a horizontal resolution about 27km [START_REF] Noaa | Reading GRIB Files[END_REF], [START_REF] Commerce | NCEP GFS 0.25 Degree Global Forecast Grids Historical Archive[END_REF]. This implies that the user can predict data with increased accuracy up to 27km. The model calculates the lesser resolution data based on results obtained. Thus, the model provides better results for long-range forecast and not for a selected geographical region, such as a farm, school, places of interest, and so on [START_REF] Powers | The Weather Research and Forecasting Model: Overview, System Efforts, and Future Directions[END_REF], [START_REF] Skamarock | A Description of the Advanced Research WRF Version 3[END_REF], [START_REF] Routray | Impact of Satellite Radiance Data on Simulations of Bay of Bengal Tropical Cyclones Using the WRF-3DVAR Modeling System[END_REF].

This article proposes a novel lightweight weather prediction model that could run on a standalone PC for accurate short-term weather prediction and could easily be deployed in a selected geographical region. As depicted in Figure 2, the proposed model is based on state-of-the-art deep learning techniques that use Artificial Neural Network (ANN) and modern LSTM layers.

Proposed Deep Model using Long Short-Term Memory (LSTM) Network

The approach discussed in this work is based on temporal weather data to identify the patterns and produces weather predictions. As discussed above, we use the state-of-theart Long Short-Term Memory (LSTM), which is a specialised form of Recurrent Neural Network (RNN) and it is widely applied to handle temporal data. The key concepts of the LSTM have the ability to learn long-term dependencies by incorporating memory units. These memory units allow the network to learn, forget previously hidden states, and update hidden states [START_REF] Jozefowicz | An Empirical Exploration of Recurrent Network Architectures[END_REF], [START_REF] Hinton | Reducing the Dimensionality of Data with Neural Networks[END_REF], [START_REF] Gulli | Deep Learning with Keras[END_REF]. Figure 2a shows the proposed lightweight model consisting of stacked LSTM layers for weather forecasting using surface weather parameters. Table 1 describes the surface weather parameters, which are used as the input parameters. The model provides outputs, which are the predicted weather parameters Figure 2b shows the LSTM memory architecture used in our model. More specifically, the proposed model has the input vector 𝑥 𝑡 = [p1, p2, p3… p10] at a given timestep𝑡, which consists of 10 different (p1, p2 ... p10) weather parameters. In the given time 𝑡, the model is updated the memory cells for long-term 𝑐 𝑡-1 and short-term ℎ 𝑡-1 recall from the previous timestep 𝑡 -1 via:

𝑖 𝑡 =
The notations of equation 1 are: 𝑤 * -weight matrices, 𝑏 * -biases, ⊙element-wise vector product, 𝑖 𝑡 -input gate and 𝑗 𝑡 -input moderation gate contributing to memory, 𝑓 𝑡forget gate, and 𝑜 𝑡 -output gate as a multiplier between memory gates. To allow the LSTM to make complex decisions over a short period of time, there are two types of hidden states, namely 𝑐 𝑡 and ℎ 𝑡 [START_REF] Jozefowicz | An Empirical Exploration of Recurrent Network Architectures[END_REF], [START_REF] Behera | Context-driven Multi-stream LSTM (M-LSTM) for Recognizing Fine-Grained Activity of Drivers[END_REF]. The LSTM has the ability to selectively consider its current inputs or forgets its previous memory by switching the gates 𝑖 𝑡 and 𝑓 𝑡 . Similarly, the output gate 𝑜 𝑡 learns how much memory cell 𝑐 𝑡 needs to be transferred to the hidden state ℎ 𝑡 . Compared to the RNN, these additional memory cells give the ability to learn enormously complex and long-term temporal dynamics with the LSTM. We use Keras to implement the proposed model using LSTM [START_REF] Gulli | Deep Learning with Keras[END_REF], [START_REF] Keras | Home -Keras Documentation[END_REF], [START_REF] Krizhevsky | ImageNet Classification with Deep Convolutional Neural Networks[END_REF]. For monitoring and forecasting purposes, the surface weather parameters are observed and reported in [18]. The surface parameters of wind direction and wind speed can be calculated from the WRF surface variables 𝑈 10 and 𝑉 10 [START_REF]WRF Model Users Site[END_REF]. Table 1 shows the surface weather parameters which are utilised in this research. The XLAT-Reference Latitude and XLONG-Reference Longitude parameters are used with each data point for the location identification.

Data Collection and preparation

As described in Sections 2 and 4.1, the GRIB data is used to run the WRF model and extract data for the 12 weather parameters for the period of January 2018 to May 2018. This is used as the training dataset to train the proposed models. Similarly, the June 2018 data is extracted to test the network. This is used to test different trained AI models to identify the best model for forecasting. The July 2018 dataset is also extracted as the evaluation dataset set which is used as the ground truth to compare perdition from the best model. The WRF model is being run in forecast mode using the same format GRIB data for the month of July 2018 to evaluate the overall model (WRF prediction).

The training data set has been normalised to keep each value in between -1 and 1 and the same maximum and minimum variable values are used to normalise the testing data set and the evaluation data set. Then apply the sliding window method for each dataset based on seven days data to train and next 3 hours data as the model's output. The capacity of the final training dataset became 6.5GB and the testing dataset 0.27GB.

Proposed model with optimal number of LSTM layers

Several different configurations have been utilised to train and test the proposed models. Figure 2a depicts the general architecture of the proposed model. Each layer consists of a number of nodes. Optimises are generally used in deep learning networks to minimise a given cost function by updating the model parameters such as weights and bias values. For better learning, it is often useful to reduce learning rates as the training progresses when training a deep network. This can be achieved by using adaptive learning rate methods [START_REF] Gulli | Deep Learning with Keras[END_REF]. Therefore, the fixed learning rate and adaptive learning rate methods have been explored to train the proposed deep models. The proposed model is evaluated using two different types, namely multi-input multi-output (MIMO) and multi-input single-output (MISO). In the MIMO, all 10 variables are fed into the network, which are expected to predict the same 10 variables as the output. In contrast, in the MISO approach, all 10 variables are fed into the network with a single variable output. In the MIMO, only one model is required for weather forecasting involving 10 different variables. Whereas, in the MISO, 10 different models are required as each of them is trained to predict a particular weather parameter with all 10 variables as input. Figure 3 depicts the basic arrangement of the MIMO and the MISO. The both MIMO and MISO classifications are utilised within these experiments.

The most common metrics for evaluating regression models include Mean Squared Error (MSE), Mean Absolute Error (MAE), Root Mean Squared Error (RMSE) and Explained Variance (EV) [START_REF]Metrics -Keras Documentation[END_REF]. In this work, we use the MSE to evaluate the models. As described in Section 4.3, there are different deep learning models, which are trained with different optimisers, different learning rates and regressions (MIMO and MISO). These models are evaluated using the June 2018 data to select the best model or a model with the lease MSE, which can be used as a tool for future forecasting. The selected best model is used to forecast the weather parameters for the July 2018 data (Model Prediction) and the model predicted values are evaluated with respect to the ground truth. Similarly, the WRF model has been run in forecast mode using the same format GRIB data for the month of July 2018 (WRF Prediction). These WRF predicted values are evaluated with respect to the ground truth. Finally, we compare the model prediction and WRF perdition to determine the possibility to use a deep learning model for weather forecasting.

5

Results and discussion

As described in Section 4.4, deep learning models are trained with different configurations and controls. The results are subsequently evaluated via the Mean Squared Error (MSE). This is used to assess the least error model and after comparing all evaluation reports. The least MSE for the MIMO is identified in the configuration with three LSTM layers, with the respective number of nodes 128, 512, and 256. We use the SGD optimizer with fixed learning rate of 0.01 to optimize the MSE regression loss function.

The model is trained for 230 epochs for optimum performance. The best values for each variable for the MISO are found in different configurations with different optimisers. Figure 4 graphically represents the comparison of MSE in each variable for both MIMO and MISO. As per Figure 4, there is no significant difference between MSE values for each variable between the MIMO and the MISO. These differences are less than 0.04 for each variable. These error figures are significantly smaller, and the MISO requires 10 different models for the prediction of 10 different weather parameters. Therefore, we consider the MIMO model since it is much more efficient (only one model to run) than running 10 different models of MISO. As described in section 4.3, the July 2018 weather data are utilised to get weather prediction using the same format described in section 4.2. Similarly, the WRF model is run in forecast mode using the July 2018 data to compare results. Both WRF and model predicted values are compared with respect to the ground truth and calculated the MSE. Table 3 represents the MSE comparison values for each variable.

When comparing the Table 3 figures, the proposed deep model provides comparatively best results in eight occasions out of 10. The WRF model provides the best results for the Snow and Soil Moisture (SMOIS) variables. In both occasions, these error figures are quite small. For example, MSE for the variable snow is 0.0168574 kg/m 2 . This is quite a small and therefore, negligible. Similarly, the SMOIS has got a minimal and negligible error value.

Conclusion and Future Work

In this paper, we demonstrate that the proposed lightweight deep model can be utilised for short-term weather forecasting. The model outperformed the state-of-the-art WRF model. The proposed model could run on a standalone computer unit and it could easily be deployed in a selected geographical region. Furthermore, the proposed model is able to overcome some challenges within the WRF model, such as the understanding of the model and its installation, as well as its running and portability. In particular, the deep model is portable and can be easily installed into a Python environment for an effective results [START_REF] Skamarock | A Description of the Advanced Research WRF Version 3[END_REF], [START_REF] Gulli | Deep Learning with Keras[END_REF]. This process is highly efficient compared to the WRF model. This research is carried out using ten different surface weather parameters and an increased number of inputs would probably lead to enhanced results. However, it will increase the model complexity requiring a large number of parameters to estimate. Furthermore, January to May weather data is utilised to train the deep model and the increase in the size of training dataset could help towards an improved results in a deep learning network [START_REF] Gulli | Deep Learning with Keras[END_REF]. Besides, we used the MIMO approach within this research to predict weather data. Figure 4 shows that the MISO approach produces better MSE values compared to the MIMO. Therefore, there is a huge potential that the MISO approach will increase the accuracy of the results even this method is less efficient compared to the MIMO. These are our future experimentation.

Fig. 1 .

 1 Fig. 1. Overview of the research (Data, processes, and dataflow show in green rectangles, blue rounded rectangles, and arrows respectively)

Fig. 2 .

 2 Fig. 2. a) Proposed layered LSTM and b) LSTM memory cell used for this research a) Proposed Weather Prediction Model

Fig. 3 .

 3 Fig. 3. Further classifications-MIMO and MISO a) MIMO layout b) MISO layout

Fig. 4 .

 4 Fig. 4. Comparison of MIMO and MISO

  tanh(𝑤 𝑥𝑖 𝑥 𝑡 + 𝑤 ℎ𝑖 ℎ 𝑡-1 + 𝑏 𝑖 ) 𝑗 𝑡 = sigm(𝑤 𝑥𝑗 𝑥 𝑡 + 𝑤 ℎ𝑖 ℎ 𝑡-1 + 𝑏 𝑗 ) 𝑓 𝑡 = sigm(𝑤 𝑥𝑓 𝑥 𝑡 + 𝑤 ℎ𝑓 ℎ 𝑡-1 + 𝑏 𝑓 ) 𝑜 𝑡 = tanh(𝑤 𝑥𝑜 𝑥 𝑡 + 𝑤 ℎ𝑜 ℎ 𝑡-1 + 𝑏 𝑜 ) 𝑐 𝑡 = 𝑐 𝑡-1 ⊙ 𝑓 𝑡 + 𝑖 𝑡 ⊙ 𝑗 𝑡 ℎ 𝑡 = tanh(𝑐 𝑡 ) ⊙ 𝑜 𝑡

Table 1 .

 1 Surface weather parameters (10 identified variables used by our model)

	Variable	Description	Measuring Unit
	TSK	Skin temperature or surface temperature	o K
	PSFC	Surface pressure	Pa
	U10	X component of wind at 10m	m/s
	V10	Y component of wind at 10m	m/s
	Q2	2-meter specific humidity	Kg/Kg
	Rainc	Convective rain (Accumulated precipitation)	mm
	Rainnc	Non-convective rain	mm
	Snow	Snow water equivalent	Kg/m 2
	TSLB	Soil temperature	o K
	SMOIS	Soil Moisture	m 3 /m 3

Table 2 .

 2 Comparison of models (Less MSE is

	better)
	Parame-	MSE
	ter	WRF Model	Deep Model
	TSK	4.0209727	2.7882845
	PSFC	227869.02	123881.22
	U10	10.540705	5.327054
	V10	12.0824	4.6248293
	Q2	1.11172e -6	7.716598e -7
	Rainc	15.942339	0.11341145
	Rainnc	18.627722	0.83847433
	Snow	0.0 0.016857434
	TSLB	8.140333	2.6088953
	SMOIS	8.52319e -5 2.4246839e -5


Fabio Fassetti
email: f.fassetti@dimes.unical.it

Ilaria Fassetti
email: ilaria.fassetti@gmail.com

Simona Nisticò
email: s.nistico@dimes.unical.it

Learning and Detecting Stuttering Disorders

Keywords: Deep learning, audio classication, stuttering

Stuttering is a widespread speech disorder involving about the 5% of the population and the 2.5% of children under the age of 5. Much work in literature studies causes, mechanisms and epidemiology and much work is devoted to illustrate treatments, prognosis and how to diagnose stutter. Relevantly, a stuttering evaluation requires the skills of a multi-dimensional team. An expert speech-language therapist conduct a precise evaluation with a series of tests, observations, and interviews. During an evaluation, a speech language therapist perceive, record and transcribe the number and types of speech disuencies that a person produces in dierent situations. Stuttering is very variable in the number of repeated syllables/words and in the secondary aspects that alter the clinical picture. This work wants to help in the dicult task of evaluating the stuttering and recognize the occurrencies of disuency episodes like repetitions and prolongations of sounds, syllables, words or phrases silent pauses, hesitations or blocks before speech. In particular, we propose a deep-learning based approach able at automatically detecting diuent production point in the speech helping in early classication of the problems providing the number of disuencies and time intervals where the disuencies occur. A deep learner is built to preliminarly valuate audio fragments. However, the scenario at hand contains some peculiarities making the detection challenging. Indeed, (i) fragments too short lead to uneective classication since a too short audio fragment is not able to capture the stuttering episode; and (ii) fragments too long lead to uneective classication since stuttering episode can have a very small duration and, then, the much uent speaking contained in the fragment masks the disuence. So, we design an ad-hoc segment classier that, exploiting the output of a deep learner working with non too short fragments, classies each small segment composing an audio fragment by estimating the probability of containing a disuence.

Introduction

Stuttering is a communication disorder where the smooth ow of speech is disrupted. It begins during childhood and, in some cases, lasts throughout life. This dysuency may interfere with the ability to be clear and understood. The eort to learn to speak and the normal stress of the evolutionary growth can trigger in the child language manifestations characterized by brief repetitions, hesitations and prolongations of sounds that characterize both the early stuttering and the normal disuency. About 5% of the child population experience a period of stuttering that lasts 6 months or more. A lot of Children of those who start stuttering will have a remission of the disorder in late childhood. Most of the risk for stuttering onset is over by age 5, earlier than has been previously thought, with a male-to-female ratio near onset smaller than what has been thought [START_REF] Yairi | Epidemiology of stuttering: 21st century advances[END_REF].

There is strong clinical evidence that more of 60% of the treated stuttering children have a stuttering relative in the family. Children who start stuttering before 42 months have a greater chance of overcoming and solving the problem.

Physiological and normal developmental disuencies are dicult to dierentiate from the rst signs of eective stuttering. But if the subject stutters for more than 6 months, it is dicult to solve the problem spontaneously. Signs of chronicity in older children (e.g., 6-or 7-year-olds) who had stuttered for two years may not be quite the same as those in 2-to 4-year-olds who have short stuttering histories [START_REF] Yairi | Predictive factors of persistence and recovery: Pathways of childhood stuttering[END_REF]. It is important to remember that stuttering is not caused by nervousness nor is it related to personality or intellectual capabilities.

Despite not demonstrating more severe stuttering, socially anxious adults who stutter demonstrate more psychological diculties and have a more negative view of their speech [START_REF] Iverach | Comparison of adults who stutter with and without social anxiety disorder[END_REF]. Parents have not done anything that may have caused their son's stuttering even if they feel responsible in some way! Exist also an idiopathic stuttering that is caused by a possible deciency in motor inhibition in children who stutter [START_REF] Markett | Impaired motor inhibition in adults who stutter -evidence from speech-free stop-signal reaction time tasks[END_REF].

Stuttering is characterized by an abnormally high number of disuencies, abnormally long disuencies, and physical tension that is often evident during speech [START_REF] Tichenor | Speaker and observer perceptions of physical tension during stuttering[END_REF]. Some signs of stuttering are [START_REF] Weir | Developmental dysuency: Early intervention is key[END_REF]: repetitions of whole words (e.g., We, we, we went) repetitions of parts of words (e.g., Be-be-because) prolongation or stretching of sounds (e.g., Ssssssee) silent blocks (getting stuck on a word or tense hesitations)

The child with severe stuttering often shows physical symptoms of stress, especially the increase in muscle tension, and tries to hide his stuttering and avoids speaking and exposing himself to linguistic situations. Although severe stuttering is more common in older children, it may, nevertheless, start at any age, between 1.5 years and 7 years. This person can exhibit behaviors associated with stuttering: blinking, looking away, or muscle tension in the buccal or other parts of the face. Moreover, part of the tension and of the impact can be perceived in a strong increase of the vocal tone or of the intonation (increase of the vocal frequency) during the repetitions or during the extensions. The subject with severe stuttering can resort to extraverbal sounds, interjections, such as um, uh, well. . . at the beginning of a word in which he expects to stutter. Especially moderate to severe stuttering had a negative impact on overall quality of life [START_REF] Koedoot | Quality of life in adults who stutter[END_REF].

This work aims at contributing in stuttering recognition by helping therapists and patients in detecting episodes of disuency. Technically speaking, we propose a system that fed with an input audio outputs the time interval related to stuttering phenomena. The system consists in several phases, the two main ones are devoted to classify.

The rest of the paper is organized as follows. Section 2 presents the basic notions exploited in this work; Section 3 introduces the architecture of our technique; Section 4 details the proposed technique and the main phases it requires; Section 5 describes the experimental campaign we perform to validate our technique; Section 6 draws the conclusions.

Preliminaries

In this section we report some preliminary notions. The input audio le is quite clean since we assume that the therapist acquire the registration of the patient in a safe environment. From the input wav le we obtain feature vectors by considering spectrograms [START_REF] Ingemann | Speech recognition through spectrogram matching[END_REF] and Mel frequency cepstral coecients [START_REF] Davis | Readings in speech recognition[END_REF]. [START_REF] Ingemann | Speech recognition through spectrogram matching[END_REF] The proposed Architecture

The proposed architecture consists in several phases. For the sake of clarity, we introduce them next to provide a general overview. Each phase is detailed in the following section. The main ow is reported in Figure 1. CLEANING PHASE. This phase consists in cleaning the input audio le. Even if, as before stated, we assume that the input audio le is quite clean, without background sounds that could compromise quality, this phase is needed to clean the input audio le from intervals during which the patient does not speak. Also, during this phase the input le is normalized in terms of volume, and sampling frequency. See Section 4.1 for details. AUDIO FRAGMENTATION PHASE. This phase consists in splitting the input le in fragments having length f len and overlapped of ε seconds as detailed in Section 4.2. FEATURE EXTRACTION PHASE. This phase consists in extracting features from raw audio fragments and represent a critical part of the architecture. Each fragment is transformed in a numeric vector as detailed in Section 4.3.

FRAGMENT CLASSIFICATION PHASE. This phase represents, with the succeeding classication phase, the core of our architecture. Here, a trained deep learner assigns each fragments to the class of uent or disuent with a certain probability. Details on this are reported in Section 4.4.

SEGMENT CLASSIFICATION PHASE. This phase is, with the previous learning phase, the core of the architecture. Here, a probabilistic model allows the classication of each segment composing a fragment, exploiting the overlapping of the fragments and taking as input the probabilities of belonging to the uent or disuent class computed by the previous phase. Details are provided in Section 4.5.

Detection Technique

In this Section we describe the proposed technique providing details about all the phases above introduced.

Noise Removal

The input audio le is assumed to be clean from background sounds that could compromise audio quality. However, there can be several time intervals during which the patient does not speak. These intervals cannot be completely removed since, in many cases, the silence is symptomatic of a disuence. Thus, in this phase the system recognizes these intervals and reduces each of them so that its duration is large enough to guarantee that at least one fragment captures the segment just before the noise interval and the segment just after the noise interval. Note that, this operation is performed also for the audio les employed to train the system. To perform this operation, we trained a learner able to discriminate between spoken and no-spoken fragments. This learner is simple and highly accurated since the classes are well-separated.

Audio File Preparation

With the aim of obtaining classiable fragments of the input audio le we recover to a xed-size sliding window approach. Indeed, in order for the learner to correctly work, fragments cannot be too long, otherwise stuttering phenomena would be obfuscated by uent speech, and cannot be too short since we need fragments of at least some seconds, how can be intuitively understood. Indeed, also a human, to recognize a stuttered phoneme, needs to hear at least for the interval covering the stuttering phenomenon that has a great variability but is, in general, wider than the duration of a segment. On the other hand, if there were not overlapping, the stuttering phenomenon could be split in two adjacent intervals and, then, not recognized. In other words, we need that at least one fragment contains all the stuttering phenomenon if this is shorter than the duration of a fragment, that a fragment and its adjacent ones cover all the stuttering phenomenon otherwise.

Let S be the input audio stream and let d be its duration in seconds. Choosen a fragment length in seconds, denoted as f len , and an overlap size in seconds, denoted as ε, and letting n = f len ε be the number of segments per fragment,

n s = d ε
be the total number of segments,

n f = n s -(n -1)
be the total number of fragments, then, S is sectioned in n f fragments of equal size f len and overlapped of ε seconds. Each fragment is composed by n segments and, thus, S can be considered as partitioned in n s segments and each segment, due to the overlap, belongs to n distinct fragments as illustrated in Figure 2.

S s1 s2 s3 s4 s5 s6 s7 s8 s9 s10 s11 s12 s13 s14 s15 • • • sn s | d | | f len | ε ε ε ε ε f1 s1 s2 s3

• • • fn

f • • •

Feature Extraction

From each audio fragment, we need to build a numeric vector representing audio features. In particular, we compute spectrograms [START_REF] Ingemann | Speech recognition through spectrogram matching[END_REF] and Mel frequency cepstral coecients [START_REF] Davis | Readings in speech recognition[END_REF].

Fragment Classication

As for the fragments classication, we adopt a deep-learning based classier.

The learning phase through a deep learner provides the fragment f i , i ∈ [0 . . . n f ] (see Figure 2) with a classication π ℓ i stating for the probability that the fragment f i belongs to the class labeled ℓ, with ℓ ∈ {uent, disuent}.

Segment Classication

The classication described in the previous section provides for each fragment f i , i ∈ [0 . . . n f ] the probability π ℓ i to belong to a certain class labeled ℓ. Nevertheless, each segment s i , i ∈ [0 . . . n s ] (see Figure 2) has to be classied in order to detect the time intervals of uent speaking and the time intervals of disuent speaking.

Consider, for example, the scenario where each fragment consists in 5 segments and a time interval I with a c 2 voice has a duration of 3 segments. There are, then, 7 overlapped fragments covering I as illustrated in Figure 3. )]

| class c1 || class c2 || class c1 | S s1 s2 s3 s4 s5 s7 s8 s9 s10 s11 s12 s13 s14
denote the fragment starting from the segment s i , then s i belongs to the set of fragments {f max(1,i-n+1) , . . . , f i }, which are employed to evaluate the trend of classication when s i appears, and does not belong to the succeeding set of fragments {f min(i+1,ns) , . . . , f min(i+n-1,ns) }, containing some segments of fragment f i . Thus, these fragments share with f i some segments excepting s i and are, roughly speaking, employed to evaluate the trend of classication when s i disappears.

As described in Section 4.4, the learning phase through a deep learner provides the fragment f i with a classication π ℓ i stating for the probability that the fragment f i belongs to the class labeled ℓ.

In order to exploit the overlap to improve segment classication, we aim at evaluating the contribution that the i-th segment gives to the classication.

Case 1: valuating the eect of the i-th segment when it appears. The segment s i rstly appears as n-th segment of the fragment f i-n+1 . Then, consider fragment f i-n as referring fragment (s i has not yet been seen) and let

φ ℓ i (j) = π ℓ i-n+j π ℓ i-n , ∀j ∈ [1, n ′ ), for each label ℓ
with n ′ ≤ n is a parameter representing how many contributions are to be taken into account. In this case, we denote π ℓ ref = π ℓ i-n and π ℓ curr = π ℓ i-n+j .

Case 2: valuating the eect of the i-th segment when it disappears. The segment s i rstly disappears for the fragment f i+1 . Then, consider fragment f i+j as referring fragment (s i is not seen) and let

φ ℓ i (j) = π ℓ i π ℓ i+j , ∀j ∈ [1, n ′ ), ∀k ∈ {0, 1}
with n ′ ≤ n is a parameter representing how many contributions are to be taken into account. In this case, we denote π ℓ curr = π ℓ i and π ℓ ref = π ℓ i+j .

We, rstly, compute the probability to observe a ratio smaller than φ ℓ i (j)

F (φ ℓ i (j), λ) = 1 -e -λ•φ ℓ i (j) , with λ = ε • j f len .
We use an exponential distribution since when f i belongs to a class labeled ℓ, π ℓ i is high, then we want to capture that the ratio is lowered with high probability and further raised with low probability. Also, the dependence of λ from j allows us to alleviate the exponential trend. The idea is that the more j is high, the more the change in the ratio can be high. In other words, it is quite improbable that a single segment can drastically change the ratio. Whereas, when j is high, more segments are taken into accounts and then the change can be high.

How much this value exceeds the no-change case, namely φ k i (j) = 1, is employed as weight for π ℓ curr

g ℓ i (j) = F ( φ ℓ i (j), λ ) F (1, λ) • π ℓ curr .
In order to normalize this value in a vote ranging from 0 to 1, we apply an exponential kernel function to it:

h ℓ i (j) = 1 -e -λ•g ℓ i (j) , with λ = - log(1 -π ℓ curr ) π ℓ curr so that, if φ ℓ i (j) = 1 then h ℓ i (j)
coincides with π ℓ curr .To combine votes h j i , we compute the weighted arithmetic mean, where the weights are related to the probability that observing π ℓ curr given π ℓ ref is due to chance. This probability follows a gamma distribution with parameters k and θ and

f Γ (x) = 1 Γ (k) • θ k • x k-1 • e -x θ , F Γ (x) = 1 Γ (k) • γ ( k, x θ ) are,
(1 -π ℓ curr ) given (1 -π ℓ ref ).
To compute F Γ , we valuate k and θ by xing the value x (say t this value) maximizing the gamma probability density function and the value x such that the probability of observing x is equal to the probability of observing a value distant 4 standard deviations from the mean. In particular, we determine k and θ with the following constraints: (i) the maximum is when π ℓ curr = π ℓ ref , then t = π ℓ ref ; and (ii), due to the fact that π ℓ curr is at most 1, we want that 1 is at 4 standard deviations from the mean. The following theorem accounts for the computation of these parameters.

Theorem 1 (Parameters k and θ of F Γ ). The value of parameters θ and k of F Γ such that the maximum is in a generic point t < 1 and that 1 is at 4 standard deviation from the mean are

k = ( 2 + √ 4 + w • (w -1) w -1 ) 2 with w = -W -1 ( - 1 t • e 1 t ) (1)
where W is the Lambert function and

θ = t k -1 .
(

Proof. The rst constraint can be imposed by computing the rst derivative of f (x) and evaluating it in t.

∂ f ∂ x = 1 Γ (k) • θ k • (k -1) • x k-2 • e -x θ + 1 Γ (k) • θ k • x k-1 • -1 θ • e -x θ which is equal to 0 in t when ∂ f ∂ x t = 0 ⇒ 1 Γ (k) • θ k • (k -1) • t k-2 • e -t θ + 1 Γ (k) • θ k • t k-1 • -1 θ • e -t θ = 0 ⇒ (k -1) - t θ ⇒ θ = t k -1 .
As for parameter k, since the mean is kθ and the standard deviation is θ √ k we have to solve the following equation:

f (1) = f ( kθ + 4θ √ k
) and, thus,

1 Γ (k) • θ k • e -1 θ = 1 Γ (k) • θ k • (kθ + 4θ √ k) k-1 • e -kθ+4θ √ k θ ⇒ e -1 θ = (kθ + 4θ √ k) k-1 • e -kθ+4θ √ k θ ⇒ - 1 θ = (k -1) log (kθ + 4θ √ k) - kθ + 4θ √ k θ ⇒ -1 = θ(k -1) log (kθ + 4θ √ k) -(kθ + 4θ √ k).
By substituting Equation ( 2) we obtain

-1 = t log kt + 4t √ k (k -1) - kt + 4t √ k k -1 by setting w = k + 4 √ k k -1 (3) we obtain wt -1 t = log wt ⇒ e w-1 t = wt
which can be solved by exploiting the Lambert function W , thus obtaining w = -W -1

( 1 t • e -1 t
) .

From Equation (3), we have

k = ( 2 + √ 4 + w • (w -1) w -1 ) 2
and, then, the theorem is proved.

Once F Γ is fully determined, the weight of each vote h j i is

ν ℓ i (j) = { 1 -F ( h ℓ i (j) ) if π ℓ curr <= π ℓ ref F ( h ℓ i (j) ) otherwise (4)
and, then, we estimate the probability of each segment to belong to a class through the following equation:

p ℓ i = ∑ j ν ℓ i (j) • h ℓ i (j) ∑ j ν ℓ i (j) . ( 5
)
5 Experiments

In this section we present test conducted to prove the eectiveness of our method.

In particular, in order to validate the accuracy of the technique, we perform two In particular, for each combination, we considered 50 random male voice audio les of 5 seconds. For each of them, say f m , we randomly select a female voice audio le f f , we randomly picked a fragment from f f having random duration d ∈ [0.5, 2] seconds, we randomly chose a starting point x in f m and substituted d seconds of f m starting from x with the fragment extracted from f f . Figures 4 report the receiver operating characteristic (ROC) curves [START_REF]Encyclopedia of Machine Learning[END_REF] for the case ε = 0.2, obtained by cumulatively considering all actual labels and all the scores assigned to each segment by the proposed technique. Conversely, Tables 4c report the mean area under the ROC curve (AUC) [START_REF]Encyclopedia of Machine Learning[END_REF] (on the left) and the execution time (on the right) for each combination.

The accuracy of the proposed technique is very high. As expected, the shorter is the overlap the higher is the accuracy but, also, the higher is the execution time. In particular, the execution time is inversely proportional to the overlap since halving the overlap implies doubling the number of fragments to be analyzed. Also, note that shorter fragments performs better. white ε = 0.1 ε = 0.2 ε = 0.5 f len = 1 0.98392 0.97489 0.97509 f len = 1.5 0.97350 0.96457 0.96477 pink ε = 0.1 ε = 0.2 ε = 0.5 f len = 1 0.98513 0.97944 0.97835 f len = 1.5 0.97604 0.97160 0.97052 (c) Fig. 5: Robustness of the technique Stuttering episode detection. In this Section we discuss the eectiveness of the technique as far as the capability of recognizing disuencies is concerned. In order to train the network we exploit the publicly available set of recordings of stuttering speakers, aged from 5 years to 47 years, reported in [START_REF] Howell | Eectiveness of frequency shifted feedback at reducing disuency for linguistically easy, and dicult, sections of speech (original audio recordings included)[END_REF]. The dataset consists in 152 audio les in wav format with a length ranging from ≈ 65 sec to ≈ 1028 sec with a mean length of ≈ 166 sec. Domain experts prepare the datasets by listening and manually selecting time intervals where stuttering episodes occur.

Results are accounted for in Figure 6.

Conclusions

The paper presents a technique to detect stuttering phenomena in audio les.

The method employs a deep learning based classier together with an ad-hoc segment classier managing the output of the former classier. The technique is able to eectively individuate stuttering episodes also having short duration and the experiments conrm that the approach is promising.

  Fig. 1: Methodology Flow

Fig. 2 :

 2 Fig. 2: Example of Audio Fragmentation with n = 5.

Fig. 3 :

 3 Fig. 3: Example of challenging segment classication.

Fig. 4 :

 4 Fig. 4: Accuracy of the technique

Figure 5

 5 Figure5report the results associated with the test of robustness to the noise. In particular, for each combination of those previously depicted, we add to the input le white noise and pink noise. Tables on the right report the AUC associated with white and pink noise. The results are encouraging since they show a good robustness to the noise of our technique. We do not report execution time since they are almost the same as the previous case.

Fig. 6 :

 6 Fig. 6: Eectiveness of the technique

  respectively, the probability density function and the cumulative density function. Since the Gamma distribution is asymmetric and since both π ℓ ref ∈ [0, 1] and π ℓ curr ∈ [0, 1], in comparing π ℓ curr and π ℓ ref we adopt the following strategy: if π ℓ ref is smaller than 0.5 then we compute the probability of observing a value more extreme than π ℓ curr given π ℓ ref , otherwise, if π ℓ ref is greater than 0.5 then we compute the probability of observing a value more extreme than


Stamatis Karlos
email: stkarlos@upatras.gr

Kanas
email: vaskanas@upatras.gr

Nikos Fazakis
email: fazakis@ece.upat-ras.gr

Christos Aridas

Sotiris Kotsiantis

Investigating the benefits of exploiting incremental learners under Active Learning scheme

Keywords: Incremental learners, Active Learning scheme, Stochastic Gradient Descent, Query strategy, unlabeled data

This paper examines the efficacy of incrementally updateable learners under the Active Learning concept, a well-known iterative semi-supervised scheme where the initially collected instances, usually a few, are augmented by the combined actions of both the chosen base learner and the human factor. Instead of exploiting conventional batch-mode learners and refining them at the end of each iteration, we introduce the use of incremental ones, so as to apply favorable query strategies and detect the most informative instances before they are provided to the human factor for annotating them. Our assumption about the benefits of this kind of combination into a suitable framework is verified by the achieved classification accuracy against the baseline strategy of Random Sampling and the corresponding learning behavior of the batch-mode approaches over numerous benchmark datasets, under the pool-based scenario. The measured time reveals also a faster response of the proposed framework, since each constructed classification model into the core of Active Learning concept is built partially, updating the existing information without ignoring the already processed data. Finally, all the conducted comparisons are presented along with the appropriate statistical testing processes, so as to verify our claim.

Introduction

Today, more and more applications from various scientific domains produce large volumes of data, changing the needs of current predictive mechanisms that mainly stem from the Machine Learning (ML) field. Since time and memory constitute the two main factors that highly define the performance of intelligent algorithms, especially when they tackle with problems over the era of Big Data, data scientists and ML/data engineers have to prioritize the structure of new predictive tools according to these specifications [START_REF] Domingos | Mining High-Speed Data Streams[END_REF]. Incremental learning is the answer of the ML community to such kind of issues, where the principal idea is to update an existing or a previously built learning model by exploiting the newly available data, reducing the total time demands while possibly producing less accurate models [START_REF] Pratama | An Incremental Classifier from Data Streams[END_REF]. Besides the simple approach, according to which vast amounts of labeled data (L) are provided or are reaching into data streams, a more realistic scenario has to cope with the shortage of L, in contrast with high enough volumes of unlabeled data (U). One representative reason why this may happen is the fact that in several real-world applications (e.g. in medicine tasks or in long-term experiments) the final state of the target variable may demand large time periods to be verified or to converge. Another reason is the inherit complexity of the data. In case of text-mining and nature language processing, numerous articles, chapters and posts on social media are freely available through web. However because of the complex structure that may characterize these sourcessuch as the complicated or unexplored semantic meanings on languages other than Englishneither the automated solutions produce always decent learning results nor the choice of manually scanning by human entities could be time efficient [START_REF] Mahmoud | Semi-Supervised Keyword Spotting in Arabic Speech Using Self-Training Ensembles[END_REF].

In order to handle this phenomenon, a new kind of algorithms has been raised, often called as Semi-Supervised Learning (SSL) or, even more generic, as Partially-Supervised Learning (PSL), where the former category is contained into the latter [START_REF] Schwenker | Pattern classification and clustering: A review of partially supervised learning approaches[END_REF]. The ambition of PSL algorithms is to exploit the existing labeled instances (li) along with the collected unlabeled examples (ui) and construct a model that maps the unknown instances with the target variable better than the corresponding model, which is based exclusively on the L subset. One main division among PSL algorithms depends on the way that the corresponding ui are getting labeled before they are merged into the L subset, so as to contribute over the increase of the predictive performance of the whole algorithm. While in SSL algorithms this process is automated usually by a base learner, Active Learning (AL) algorithms are differentiated since a human oracle is inserted into the learning process and is responsible for assigning the selected by a criterion ui with accurate enough decisions [START_REF] Aggarwal | Active Learning: A Survey[END_REF]. Although in several domains, only human experts could be exploited, it has been studied and generally verified that the decisions of numerous simple-users tend to converge over these produced by the human specialists in domains like sound/music signal categorization [START_REF] Zhang | Advanced Data Expoitation in Speech Analysis[END_REF]. This means that a large aspect of applications could be satisfied through AL approaches without consuming much humans' expert effort, a fact that might convert this kind of solution into a non-affordable one.

Our ambition in this work is to investigate the benefits of exploiting incremental learners (IncL) under a simple AL scheme that follows pool-based scenario. Thus, IncL would be responsible for detecting the most suitable ui, as well as for exporting the final decisions. The main rivals here are both the AL method whose query strategy coincides with a random selection of ui and the supervised scenario, where the same base learner has been trained based on the full dataset incrementally, as well as the same approaches trained under batch-mode operation. The amount of the initial L plays a crucial role producing per each different value a new variant of each exported algorithm from the proposed framework. More comments are presented in the corresponding paragraph.

To sum up, in Section 2, a number of related works are presented briefly, regarding mainly recent publications over incremental learning task and secondly with AL. Section 3 contains a description of the selected optimizer that injects the desired asset of incrementally update over underlying linear classifiers along with the necessary information about the proposed AL framework, while Section 4 includes more technical information, as well as information about the examined datasets and the conducted experiments. Finally, this work finishes with the conclusory Section that discusses the posed ambitions and highlights future work.

2

Related work

Incremental learning

Incremental learning refers to online learning strategies applicable to real-life streaming scenarios [START_REF] Hoens | Learning from streaming data with concept drift and imbalance: an overview[END_REF] with limited memory resources. So far, IncL is widely used ranging from Big Data and Internet of Things technology [START_REF] Hoens | Learning from streaming data with concept drift and imbalance: an overview[END_REF] to outlier detection for surveillance systems. One of the most popular areas in IncL is image/video data processing. Typical case scenarios are object detection [START_REF] Dou | Moving object detection based on incremental learning low rank representation and spatial constraint[END_REF] and recognition [START_REF] Bai | An incremental structured part model for object recognition[END_REF], image segmentation [START_REF] Tasar | Incremental Learning for Semantic Segmentation of Large-Scale Remote Sensing Data[END_REF] and classification [START_REF] Ristin | Incremental Learning of Random Forests for Large-Scale Image Classification[END_REF], surveillance [START_REF] Shin | Incremental learning method for cyber intelligence, surveillance, and reconnaissance in closed military network using converged IT techniques[END_REF], visual tracking [START_REF] Dou | Robust visual tracking based on incremental discriminative projective non-negative matrix factorization[END_REF] and prediction [START_REF] Wibisono | Traffic big data prediction and visualization using Fast Incremental Model Trees-Drift Detection (FIMT-DD)[END_REF].

Moreover, the inherit nature of data in robotics make online learning an appropriate approach for mining the streaming signals [START_REF] Wang | Learning From Adaptive Neural Dynamic Surface Control of Strict-Feedback Systems[END_REF]. In another study [START_REF] Zhang | Adaptive incremental learning of image semantics with application to social robot[END_REF] an incremental image semantics learning framework is proposed. The proposed framework aims to learn image semantics from scratch (without a priory knowledge) and enrich the knowledge incrementally with human-robot interactions based on a teaching-and-learning procedure. Khan et al [START_REF] Khan | IBuILD: Incremental bag of Binary words for appearance based loop closure detection[END_REF] present a mechanism to build a consistent topological map for self-localization robotics applications. The proposed appearance-based loop closure detection mechanism builds a binary vocabulary consisting of visual words in an online, incremental manner by tracking features between consecutive video frames to incorporate pose invariance. In another relevant study [START_REF] Saveriano | Incremental kinesthetic teaching of end-effector and null-space motion primitives[END_REF], authors propose a new method to incrementally learn end-effector and null-space motions via kinesthetic teaching allowing the robot to execute complex tasks and to adapt its behavior to dynamic environments. The authors combine IncL with a customized multi-priority kinematic controller to guarantee a smooth human-robot interaction. Another rapidly emerging domain, which utilizes this concept, is robotic automotive [START_REF] Thrun | Sebastian: Toward robotic cars[END_REF].

Active learning

However, all of the above applications require lots of labelled data and usually data labelling is difficult, time-consuming, and/or expensive to obtain. Active learning systems attempt to overcome the labeling bottleneck by asking queries in the form of ui to be labeled by an oracle, aiming to significantly reduce the cardinality of L subset that is needed. Active learning is still being heavily researched, under either more theoretical approaches or more experimental ones. The last years, several attempts have been made to combine AL with Deep Learning (DL) concept, especially targeting specific applications that demand much computational power. Hence, ML researchers have begun searching the benefits of using CNNs and LSTMs and how to improve their efficiency when are applied along with AL frame-works [START_REF] Shen | Deep Active Learning for Named Entity Recognition[END_REF][START_REF] Sener | Active Learning for Convolutional Neural Networks: A Core-Set Approach[END_REF]. There is also research being done on implementing Generative Adversarial Networks (GANs) into the this kind of tasks [START_REF] Liu | Generative Adversarial Active Learning for Unsupervised Outlier Detection[END_REF]. With the increasing interest into deep reinforcement learning, researchers are trying to reframe AL as such a problem [START_REF] Fang | Learning how to Active Learn: A Deep Reinforcement Learning Approach[END_REF]. Also, there are papers which try to learn AL strategies via a meta-learning setting [START_REF] Contardo | A Meta-Learning Approach to One-Step Active-Learning[END_REF]. This does not mean that products of ML or more simple probabilistic base learners have been ignored by the corresponding community. On the contrary, a recent demonstration examines the chance of achieving fast and non-myopic AL strategy in context of binary classification datasets [START_REF] Krempl | Optimised probabilistic active learning (OPAL): For fast, non-myopic, cost-sensitive active classification[END_REF].

Proposed Framework

In order to conduct our investigation, a series of properties have to be defined for formulating the corresponding framework, under which our experiments will be executed.

To be more specific, the base learner that is used in the core of the proposed framework is based on regularized linear models manipulated by Stochastic Gradient Descent (SGD) learning [START_REF] Zhang | Solving Large Scale Linear Prediction Problems Using Stochastic Gradient Descent Algorithms[END_REF]. A more in-depth analysis follows subsequently, into this Section. The same learner is used into both the selected Query strategy of AL framework and the stage of building the final classifier, after having augmented the L subset during each one of the k executed iterations. As it concerns the Query strategy, Uncertainty Sampling (UncS) approach has been selected in the context of this work, favoring the integration of the AL framework with probabilistic classifiers and boosting also the time response of each produced approach [START_REF] Settles | Active Learning[END_REF], [START_REF] Sharma | Evidence-based uncertainty sampling for active learning[END_REF]. Analog to the metric that is applied into the UncS approach, a number of variants can be produced. Finally, the human factor is replaced by an ideal oracle (H oracle ) that exports always the correct decision about the label of each asked instance, playing the role of annotator.

The last generic parameter that has to be set is the Labeled Ratio valueusually depicted as Rand measured in percentage values. This factor defines the amount of the initially li in comparison with the total amount of both li and ui. Its formula is:

R (%) = cardinality(L) / (cardinality(L) + cardinality(U))

(

It is prominent that by acting under small R values, only a small part of the totally available information is provided initially to the AL framework. Hence, the predictions of the base learner are based on poor L subsets that may not reveal useful insights of the specific problem that is tackled, harnessing the achievement of accurate classification behaviors. Thus, the quadruple that defines each product of the proposed framework consists of the base learner, the specific metric of UncS, the number of iterations and the Labeled Ratio value. Its notation hereinafter would be (base-cl, UncSmetric, k, R). The obtained learning behavior of such an algorithm, according to our assumptions, would depict the ability of the selected base learner to operate efficiently under a fast and confident Query strategy to choose among a pool of ui, over which will be trained incrementally for k iterations, before exporting a final classifier, based initially on an amount of labeled instances that is defined by R parameter. Gradient descent (GD) is by far the most popular optimization strategy, used in ML and DL at the moment. It is an optimization algorithm, based on a convex function, that tweaks its parameters iteratively to minimize a given cost function to its local minimum. In a simple supervised learning setup, each training example is composed of an arbitrary input x and a scalar output y in the form (x, y). For our ML model, we choose a family G of functions such as 𝑦 ≅ 𝑔 𝑤 (𝑥) + 𝑏, with w being a weighted vector and b an intercept term, which is necessary for obtaining better fit. Consequently, our goal is to minimize a cost function 𝛹(𝑦 ̂, 𝑦) = 𝛹(𝑔 𝑤 (𝑥), 𝑦) that measures the cost of predicting 𝑦 ̂ given the actual outcome 𝑦 (or yactual) averaged on the training examples n. In other words, we seek to find a solution to the following problem:

𝐸 𝑛 (𝑓 𝑤 , 𝑤) = 1 𝑛 ∑ 𝑙(𝑓 𝑤 (𝑥 𝑗 ), 𝑦 𝑗 ) 𝑛 𝑗=1 + 𝛼𝑅𝑒𝑔(𝑤) (2)
The cost function (𝐸 𝑛 ) of Eq. 2 depends mainly on loss function (l) and the regularization term 𝑅𝑒𝑔(𝑤). The multiplicative constant α refers to a non-negative hyperparameter. Following the original GD process, the minimization of Eq. 2 is taking place updating the next two formulas per each iteration t:

𝑤 𝑡+1 = 𝑤 𝑡 -𝜂 ( 1 𝑛 ∑ 𝛻 𝑤 𝑙(𝑓 𝑤 (𝑥 𝑗 ), 𝑦 𝑗 ) 𝑛 𝑗=1 + 𝑎𝛻 𝑤 𝑅𝑒𝑔(𝑤)) (3)
where the positive scalar η is called the learning rate or step size. In order, for the algorithm, to achieve linear convergence sufficient regularity assumptions should be made, while the initial estimate w0 should be close enough to the optimum and the gain η sufficiently small. It is important to highlight that the evaluation of n derivatives is required at each step. So, the per-iteration computational cost scales linearly with the training data set size n, making the algorithm inapplicable to huge datasets. Thus, the stochastic (SGD) version of the algorithm is used instead, which offers a lighter-weight solution. More specifically, at each iteration, the SDG randomly picks an example and calculates the gradient for this specific example:

𝑤 𝑡+1 = 𝑤 𝑡 -𝜂 𝑡 (𝛻 𝑤 𝑙(𝑓 𝑤 (𝑥 𝑡 ), 𝑦 𝑡 ) + 𝑎𝛻 𝑤 𝑅𝑒𝑔(𝑤))

In other words, SGD approximates the actual gradient using only one data point, saving a lot of time compared to summing over all data. SGD often converges much faster compared to GD but the error function is not as well minimized as in the case of GD. However, in most cases, the close approximation calculated by SGD for the parameter values are enough because they reach the optimal values and keep oscillating there. Another advantage of SGD is its ability to process the incoming data online in a deployed system, since no memory of the previous randomly chosen examples is necessary. In such a situation, the SGD directly optimizes the expected risk, since the examples are randomly drawn from the ground truth distribution [START_REF] Tsuruoka | Stochastic Gradient Descent Training for L1regularized Log-linear Models with Cumulative Penalty[END_REF].

As it concerns 𝑅𝑒𝑔(𝑤) term, three different choices are generally used in the literature: l1 norm that favors sparse solutions, l2 norm that is the most usual met and elastic net (elnet), that is formatted by a convex combination of the previous two norms and offers sparsity with better stabilization than simple l1 norm [START_REF] Zou | Regularization and variable selection via the Elastic Net[END_REF]. Before introducing the proposed framework through suitable pseudocode, we have to define the amount of the ui examples that should be mined per iteration. Although many approaches prefer to mine only one example per time, leading probably to more accurate actively trained classifier but clearly demanding much more computational resources because of the large amount of iterations that should be executed under a specific budget plan (B), a heuristic method is applied here: the questioned quantity of mined instances per iteration is computed by dividing the initial size of L subset with the number of executed iterations k. Thus, after k steps, the finally augmented training set will enumerate to the double number of instances. Additionally, since each ui is defined by a pair of (xf x 1, y), where the scalar y value is not known, the assumed human oracle is defined as a function such that H oracle : R f → yactual, where f parameter denotes the dimensionality of each dataset. The corresponding pseudocode follows here:

Incremental Active Learning Framework based on SGD(loss function, reg)

Experimental Procedure and Results

In order to verify the efficacy of the proposed AL framework, 19 binary datasets have been selected by UCI dataset. Their details are described in Table 1, along with the corresponding cardinality of initial training set (L 0 ) for all the selected R-based scenarios: 5%, 15% and 25%. Moving further, all the conducted experiments are implemented using the libact library [START_REF] Yang | libact: Poolbased Active Learning in Python[END_REF] that supports AL pool-based approaches via well-known python libraries [START_REF] Buitinck | API design for machine learning software: experiences from the scikit-learn project[END_REF]. Thus, 3 different metrics have been inserted into Query Strategy of the proposed framework: Smallest Margin (sm), Least Confident (lc) and Entropy (ent), apart from Random Sampling (random) variant, which constitutes the baseline strategy of AL concept. Moreover, each Supervised approach is included into our comparisons, so as to verify both the relative improvement and the corresponding importance of the implemented algorithms per both R-based case and operation mode. Regarding the base learners that would be combined with SGD optimizer, 6 different approaches are presented here. This means that 2 different choices of base-cl parameter were made, along with all the 3 regularization terms that were referred. To be more specific, and at the same time following the notation of scikit-learn library [START_REF] Buitinck | API design for machine learning software: experiences from the scikit-learn project[END_REF], the corresponding loss functions, using their default properties, are:  base-cl = 'log', which implements the well-known Logistic Regression learner, whose output is filtered appropriately so as to be used in classification tasks [START_REF] Harrell | Regression Modeling Strategies[END_REF],  base-cl = 'mhuber' (or 'modified huber'), which implements a smoothed hinge loss function that is equivalent to quadratically smoothed Support Vector Machine (SVM) with gamma parameter equals to 2, offering robust behavior to outliers.

To begin with, a comparison of the time response of the exploited IncL against their corresponding batch-mode variants is presented. Thus, all the 12 supervised algorithms, either incrementally updated or operating under batch-mode, are measured regarding their execution time during 10-fold cross validation (10-CV) procedure, along with two approaches that are based on the well-known Naive Bayes (NB) algorithm, so as to compare the exploited learners with algorithms that are popular for their simplicity and support also incremental update. Because of lack of space, only a sample of the produced results will be presented here. An appropriate link with the full volume of our results is provided in the end of this Section. From the depicted results, it is observed a speed-up of at least 20% for the incremental SGD-based learners, while their time performance is comparable with the MNB. Similar kind of improvement is also met into the proposed framework. A quad-core machine (Intel Core Q9300, 2.50 GHz, 8GB RAM) was used. As it concerns the classification accuracy that was scored by the selected algorithms, the number of iterations has been fixed equal to 15. This value has been selected via empirical process. However, its tuning could provide better results, compromising the spent human effort and the available B. The next Table presents only the averaged accuracies over the 19 selected datasets, so as to compare the achieved accuracy per actively trained classifier against random strategy and the corresponding supervised variant that uses the whole dataset. The format of the next Table enables the direct comparison of IncL and batch-based approaches. The accuracy of the best performed metric per R-based scenario and same base-learner, independently of its operation mode, is highlighted in bold format. Only two R-scenarios have been included in Table 2.

It is evident that the incrementally based algorithms obtain a superior learning behavior against the conventional batch-mode operating approaches, since in all cases they outperformed the latter approaches. For providing a more detailed insight of the obtained results concerning the produced AL algorithms of the proposed framework, we notice that: in all the 90 1-vs-1 comparison between IncL and batch-based learner the former prevailed, sm metric was ranked as the best metric in 13 out of 18 cases, UncS strategy outperformed random sampling in 33 out of 54 cases, while the Supervised approaches were also outreached 22 times, regarding the incremental scenario. Keeping in mind that the proposed algorithms consume less computational resources, it seems that this kind of combination leads to more remarkable ML tools, regarding both the aspects of accuracy and time efficacy. The statistical verification of the produced results is visualized through CD diagrams. According to this method, appropriate rankings are provided to a post-hoc test, in our case the Bonferroni-Dunn, computed by Friedman statistical test, and corresponding critical differences are computed for significance level equal to 0.05 [START_REF] Hastie | The Elements of Statistical Learning[END_REF]. Every algorithm that is connected via a horizontal line to another one, depicts that their learning behavior did not present significant difference.

For obtaining a more explanatory view of these comparisons, a series of violin plots has been selected to highlight the differences of the IncL and batch-mode algorithms. Through this tactic, the distribution of the scored classification accuracies is visualized, along with the average and the quartile values. In figure 3, the corresponding algorithms that use 'elnet' regularization term are presented. The complete results are provided in https://github.com/terry07/ke80537.

Conclusions and future work

This work constitutes a primal product of our research in involving IncL under SSL schemes so as to compensate the iterative character of the latter, by exploiting the beneficial refinement assets of the former, regarding the base learner. Our results over a wide range of binary datasets prove the remarkable classification accuracy that was achieved in case of AL concept, based on 3 amounts of labeled examples and relying on an ideal human oracle for annotation stage. The common factor over all these experiments was the use of SGD method that injects its incremental property over the linear learners that are applied. Three different regularization terms were also used, creating The next steps are oriented towards both the examination of multiclass datasets and binary datasets that come from more specific tasks, like intrusion detections that suffers from distribution drifting [START_REF] Xiang | Incremental semi-supervised kernel construction with self-organizing incremental neural network and application in intrusion detection[END_REF] or text classification [START_REF] Lin | Semi-supervised collective extraction of opinion target and opinion word from online reviews based on active labeling[END_REF]. Furthermore, a larger variety of AL query strategies could be applied, exploiting either more sophisticated ML techniques [START_REF] Akusok | Advanced Query Strategies for Active Learning with Extreme Learning Machine[END_REF] or margin-based queries that perform robustness over noisy input data [START_REF] Wang | Noise-adaptive Margin-based Active Learning for Multidimensional Data[END_REF]. Moreover, the scheme of ALBL (Active Learning By Learning) [START_REF] Hsu | Active Learning by Learning[END_REF] could be a really promising solution, where a number of AL strategies are evaluated through a metalearning stage. Finally, combination of SSL and AL strategies seems a powerful combination [START_REF] Zhao | Safe semi-supervised classification algorithm combined with active learning sampling strategy[END_REF], reducing heavily human effort, since only a small number of iterations could be selected to ask feedback, while the incremental asset could be retained.

Fig. 1 .

 1 Fig. 1. Pseudocode of the proposed Incremental Active Learning framework

Fig. 2 .

 2 Fig. 2. A CD diagram for mhuber-based learners and 'elnet' as regularization term for R = 25%.

Fig. 2 .

 2 Fig. 2. A violin plot of log-based learners and 'elnet' as regularization term for R = 5%.

Table 1 .

 1 Table captions should be placed above the tables.

	Dataset	Instances	Features	L's cardinality for R = 5% -15% -25%
	bands	365	20	16 -49 -82
	breast-cancer	286	49	13 -39 -64
	bupa	345	7	16 -47 -78
	chess	3196	39	144 -431 -719
	colic	368	472	17 -50 -83
	credit-a	690	44	31 -93 -155
	credit-g	1000	62	45 -135 -225
	heart-statlog	270	14	12 -36 -61
	heart	270	14	12 -36 -61
	housevotes	232	17	10 -31 -52
	kr-vs-kp	3196	41	144 -431 -719
	mammographic	830	6	37 -112 -187
	monk-2	432	7	19 -58 -97
	pima	768	9	35 -104 -173
	saheart	462	10	21 -62 -104
	sick	3772	34	170 -509 -849
	tic-tac-toe	958	28	43 -129 -216
	vote	435	17	20 -59 -98
	wdbc	569	31	26 -77 -128

Table 2 .

 2 Execution time of Incremental and Batch-mode supervised classifiers for 10-CV.

	Dataset	SGD(mhuber, l1)	SGD(mhuber, l2)	SGD(mhuber, elnet)	Multinomial NB
		IncL	Batch	IncL	Batch	IncL	Batch	IncL	Batch
	bands	0.184	0.169	0.274	0.519	0.279	0.241	0.332	0.176
	breast-cancer	0.224	0.225	0.526	0.197	0.147	0.277	0.217	0.225
	bupa	0.206	0.235	0.366	0.401	0.465	0.457	0.253	0.179
	chess	1.414	1.448	0.847	0.788	0.676	3.862	1.685	3.773
	colic	0.409	0.306	0.221	0.182	0.418	0.486	0.223	0.936
	credit-a	0.277	0.387	0.249	0.714	0.288	0.644	0.276	0.385
	credit-g	0.570	1.825	0.351	1.480	1.118	0.927	0.783	0.811
	heart-statlog	0.156	0.689	0.590	0.281	0.354	0.250	0.169	0.485
	heart	0.141	0.152	0.149	0.244	0.221	0.285	0.234	0.217
	housevotes	0.150	0.147	0.210	0.429	0.135	0.164	0.292	0.234
	kr-vs-kp	0.895	1.482	0.683	1.310	2.883	3.033	1.123	1.880
	mammographic	0.250	0.170	0.336	0.490	0.142	0.213	0.167	0.183
	monk-2	0.126	0.206	0.139	0.316	0.156	0.164	0.158	0.156
	pima	0.229	0.324	0.178	0.291	0.172	0.963	0.318	0.546
	saheart	0.161	0.253	0.214	0.286	0.227	0.263	0.516	0.382
	sick	2.939	2.363	1.239	1.901	2.601	1.948	1.156	1.525
	tic-tac-toe	0.477	0.474	0.383	0.406	0.761	0.705	0.399	0.572
	vote	0.167	0.271	0.276	0.747	0.408	0.698	0.210	0.304
	wdbc	0.299	0.733	0.382	0.253	0.785	0.401	0.401	0.441
	Total time (sec)	9.148	11.859	7.613	11.235	12.236	15.981	8.912 13.410

Table 3 .

 3 Classification accuracy of Incremental and Batch-mode algorithms for 10-CV.

		R = 5% lc	ent	sm	random	R = 25% lc ent	sm	random	Super
	SGDinc(mhuber,l1)	71.36	72.98	73.95	73.82	79.42	78.71	79.32	78.10	77.89
	SGDbatch(mhuber,l1)	66.90	67.41	68.87	67.49	74.26	73.33	72.36	73.44	72.12
	SGDinc(mhuber,l2)	70.91	72.07	73.24	72.85	77.59	77.91	78.76	76.22	75.23
	SGDbatch(mhuber,l2)	65.58	66.55	68.23	66.22	71.78	71.56	73.24	72.61	71.33
	SGDinc(mhuber,elnet)	70.66	72.87	74.12	73.69	77.42	77.93	78.28	77.41	75.64
	SGDbatch(mhuber,elnet)	66.81	66.88	66.99	67.05	72.13	72.10	72.01	73.84	70.82
	SGDinc(log,l1)	72.47	74.02	74.62	74.91	78.14	79.56	79.88	80.24	77.34
	SGDbatch(log,l1)	67.37	68.69	68.37	67.08	73.55	73.80	73.11	72.78	72.02
	SGDinc(log,l2)	71.81	72.93	74.35	73.88	77.71	77.82	78.52	77.30	75.29
	SGDbatch(log,l2)	67.45	66.15	66.09	67.00	72.41	71.92	72.64	72.56	71.96
	SGDinc(log,elnet)	72.01	73.21	74.97	73.21	78.24	78.61	77.86	78.02	75.09
	SGDbatch(log,elnet)	67.49	67.57	67.38	66.89	72.44	72.21	73.29	73.43	71.89

Acknowledgements

This research is implemented through the Operational Program Human Resources Development, Education and Lifelong Learning and is co-financed by the European Union (European Social Fund) and Greek national funds.