Shuangyan Shan

Zhijing Xu

Speaker Verification Channel Compensation based on DAE-RBM-PLDA

Keywords: Speaker recognition, I-vector, Denoising Autoencoders, Restricted Boltzmann Machine

In the speaker recognition system, a model combining the Deep Neural Network (DNN), Identity Vector (I-Vector) and Probabilistic Linear Discriminant Analysis (PLDA) proved to be very effective. In order to further improve the performance of PLDA recognition model, the Denoising Autoencoder (DAE) and Restricted Boltzmann Machine (RBM) and the combination of them (DAE-RBM) are applied to the channel compensation on PLDA model, the aim is to minimize the effect of the speaker i-vector space channel information. The results of our experiment indicate that the Equal Error Rate (EER) and the minimum Detection Cost Function (minDCF) of DAE-PLDA and RBM-PLDA are significantly reduced compared with the standard PLDA system. The DAE-RBM-PLDA which combined the advantages of them enables system identification performance to be further improved.

Introduction

Speaker recognition is a kind of biometric technology, which is a technique for extracting effective feature information from speaker voice for speaker recognition. The more popular speaker recognition model is based on the Gaussian Mixture Model-Universal Background Model (GMM-UBM) [START_REF] Reynolds | Speaker verification using adapted Gaussian mixture models[END_REF]. Then, Patrick proposed Joint Factor Analysis (JFA) [START_REF] Kenny | et al. A study of interspeaker variability in speaker verification[END_REF], Najim proposed modeling methods such as Identity-Vector (i-vector) [START_REF] Dehak | et al. Front-end factor analysis for speaker verification [J]. Audio,Speech,and Language Processing[END_REF]. The current i-vector has become the most effective technology which is the textindependent speaker recognition, this framework can be divided into three steps: First, using the GMM-UBM to express the speech acoustics feature sequence as a sufficient statistic, and then converted to low-dimensional features vector i-vector, after the i-vector is extracted, the Probabilistic Linear Discriminant Analysis (PLDA) model is used for channel compensation and the vertexes are obtained by comparing the i-vector generation verification scores of the different speech segments.

In recent years, the deep neural network (DNN) has been successfully applied to the field of speech recognition [START_REF] Hinton | Deep neural networks for acoustic modeling in speech recognition: The shared views of four research groups[END_REF]. In the field of speaker recognition, Lei [START_REF] Variani | Deep neural networks for small footprint textdependent speaker verification[END_REF] used DNN to classify phonetic features into different phoneme spaces based on phoneme features, and then extract the acoustic features of different utterances in each space, and propose i-vector based on DNN. This model uses the output of the DNN output layer softmax in the UBM to calculate the various posterior probability, which results in significant performance improvement for the speaker confirmation.

Denoising Autoencoders (DAE) can reconstruct the raw data from the corrupted data by training. The feature of the speaker indicate that i-vector is affected by the influence of the speaker channel information as damaged data. Therefore, channel compensation can be achieved by DAE reconstruction method to obtain a more robust effect, resulting in noise immunity, thereby reducing the channel diversity of the speaker. In [START_REF] Stafylakis | PLDA using Gaussian Restricted Boltzmann Machines with application to Speaker Verification[END_REF], RBM-PLDA-based channel compensation technology is proved to be superior to standard PLDA. RBM reconstructs i-vector by separating the speaker information and channel information, and then applies the factor containing the speaker information to the PLDA side for comparison. Based on the advantages of DAE and RBM, this paper proposes a channel compensation method based on DAE-RBM-PLDA to further reduce the influence of speaker channel diversity.

I-vector-based Speaker Recognition System

GMM I-vector Technology

The i-vector is a compact representation of a GMM supervector, containing both the speaker and channel characteristics of a given speech utterance. The model is based on the mean supervector represented by GMM-UBM. The mean super-vector of a speaker's speech can be decomposed into the following equation:

 T m M   (1)
Where m is the Universal Background Model (UBM), a GMM mean supervector, T is a low-rank matrix defines the total variability space,  is a speaker-and channel- dependent latent variable with standard normal distribution, and its posterior mean is ivector.

In the process of i-vector extraction, we need to use the EM algorithm to estimate the global difference space matrix T , and extract the Baum-Welch statistic. The zeroth- order statistics and the first-order statistics of the speech segment h of the speaker s in the j-th GMM mixed component are as follows:

    t h j x j P s N | ,   (2)      j t t h j m x x j P s F    | , (3)
Where  

         M j t j t j t x j P w x j P w x j P 1 | | | (4)
And then the following calculation can be obtained corresponding i-vector.

 

h T h h F T I W E 1 1       (5)

DNN I-vector Technology

GMM has a strong ability to fit, but its shortcoming is that it cannot effectively model nonlinear or near nonlinear data. Therefore, DNN is applied to acoustic modeling, DNN's multi-layer nonlinear structure makes it a powerful characterization capability, it uses unsupervised generation algorithm for pre-training, and then use the back propagation algorithm for parameter fine tuning. DNN consists of input layer, multiple hidden layer and Softmax output layer. The Softmax layer gives the posterior probability   t x j P | of the bound three-factor state class on the speech frame, which is used as the corresponding Gaussian occupancy rate, substituting the formulas (2) and (3) to estimate the DNN i-vector zero-order statistics and first-order statistics, and then extract i-vcetor according to formula [START_REF] Variani | Deep neural networks for small footprint textdependent speaker verification[END_REF]. DNN-based i-vector extraction process and the identification process are as shown in Figure 1: PLDA is an i-vector-based channel compensation algorithm, i-vector feature contains speaker information and channel information. We only need to extract the speaker information, so channel compensation is needed to remove channel interference. The simplified PLDA proved to be an effective method of channel compensation [START_REF] Garcia-Romero | Analysis of i-vector Length Normalization in Speaker Recognition Systems[END_REF]. The simplified PLDA model is as follows:

sh s sh Z Vy      (6)
Where sh  is the i-vector representing h-th session of s-th speaker,  is the mean of all training data, matrixV describes the subspace of the speaker, characterizes the differences between human beings, s y is the hidden speaker factor, sh z is the residual noise. The above parameters satisfy the following distribution:

  1 , 0 ~N y s (7)   D N z sh , 0 ~ (8)
The purpose of the PLDA training phase is to estimate the parameter

  D V , ,   
required by the model using the EM algorithm based on the speaker's speech data set for a given sample. Identify the score after the model is trained, the ivector which is given the same speaker registration and testing are e  and s  respectively, the formula for calculating the likelihood ratio score is as follows:

Score = ln 𝑃(𝜔 𝑒 , 𝜔 𝑠 |𝐻 0 ) 𝑃(𝜔 𝑒 , 𝜔 𝑠 |𝐻 1 ) (9)
Where 0

H indicates that e  and s  are from the same speaker, and 1 H is from different speakers. Calculate the likelihood ratio of the two Gaussian functions as the final decision for the score.

PLDA Based on DAE and RBM

Denoising Autoencoders (DAE) is a self-coding device by special training. Accept the damaged data as input in the input, and training to predict the original undamaged data as an output of the automatic encoder, to produce anti-noise ability, resulting in a more robust data reconstruction effect. DAE training process is shown in Figure 2.

Introducing a damage process   x y C | , which represents the probability that the given data x will produce a corrupted sample y . The automatic encoder assumes that x is the original input, and the noise reduction automatic encoder uses   y as the damage input with noise, taking x as an output, and self-coding for learning and training. The application of DAE to the speaker recognition system back-end model was first proposed in [START_REF] Novoselov | Non-linear PLDA for i-vector speaker verification[END_REF], and this paper will continue to explore further improve system performance. The i-vector can be regarded as a damaged data which is influenced by the speaker's channel information in this system. The training can be simplified as follows.

In the experiment, the DAE training starts from generative supervised training of the denoising RBM as shown in Figure 3. This RBM has binary hidden layer and Gaussian visible layer, taking a concatenation of two-valued vectors as an input. The first vector   s i is the average over all sessions of this speaker, the second vector   h s i , is an i-vector extracted from the h-th session of s-th speaker. RBM is trained by CD algorithm [START_REF] Hinton | A practical guide to training restricted boltzmann machines[M]//Neural networks: Tricks of the trade[END_REF], weight matrix parametersV ,W are used to initialize the DAE model. After the pre-training model is expanded as shown in Figure 4, this model can be seen as a standard DAE model to rebuild i-vector. The output uses the speaker's average i-vector to reduce the difference in speaker channel information. Then the back propagation algorithm is used to tune the network parameters. The output of the DAE is whitened and length normalizated and it can be validated directly as a standard PLDA model input (DAE-PLDA), the judgment is based on a pre-set threshold.

RBM is an undirected model consisting of a random layer of visible neurons and a layer of hidden neuron. It can act on the PLDA channel compensation side, the hidden layer is decomposed by the speaker information factor and the channel information factor, as shown in Figure 5. We use the similar algorithm [START_REF] Stafylakis | PLDA using Gaussian Restricted Boltzmann Machines with application to Speaker Verification[END_REF] to carry out training, the difference is that it is consistent with the hidden layer values for the previous DAE pretraining, where the hidden layer uses binary values and subjects to the Gaussian Bernoulli distribution. In the recognition phase, the visible layer inputs the i-vector of the speaker and the speaker's speech containing the speaker information at the output as input of the PLDA model (RBM-PLDA) is used to score the comparison. From the above analysis we can see the effective feature extraction principle based on DAE and RBM . Use DAE and RBM mixed method, the first layer is the DAE, after the whitening and length normalization as RBM input, RBM and standard PLDA is combined to form a discriminant model, recorded as DAE-RBM-PLDA. The block diagram for the system is shown in Figure 6.

Experiments and Results

In this paper, DAC13 is used as experimental phonetic database, and the Equal Error Rate (EER) and minimum Detection Cost Function (DCF) are used as performance evaluation indexes.

In the UBM i-vector system, MFCC and the one-dimensional energy and its first and second order differences, which are total 39-dimensional MFCC features. Voice frame length is 25ms, frame shift is 10ms. In the DNN i-vector system, DNN speaker features are 40-dimensional Filter Bank features and its first and second order differences, which are total 120-dimensional. DNN has 5 hidden layers, each layer includes 2048 nodes. We first compared the performance of the standard PLDA model in the UBM i-vector and DNN i-vector systems. Experiments show that the recognition performance of DNN system is significantly improved by comparing with GMM-UBM system. DNN i-vector PLDA is the baseline system, the performance comparison is shown in Figure 7 and Table 1. and the minimum detection cost function of DAE-PLDA and RBM-PLDA back-end channel compensation model with deep learning model are significantly lower than those of standard PLDA model system. The performance improvement of the DAE-RBM-PLDA model is more obvious than the baseline system, which is 15.1% higher than the baseline system, which verified the effectiveness of the channel compensation method.

Conclusions

In this paper, we proposed the speaker verification channel compensation method based on DAE-RBM-PLDA, the method is combining the advantages of DAE and RBM. This method first performs RBM pre-training and initializes the DAE model with the ivector processed by whitening and length normalization. The output of DAE is the average i-vector of over all sessions of the speaker, so it reduced the influence of the speaker channel information. And then combined with the RBM, the output i-vector of DAE is used as the input of RBM, hidden layer reconstruction separates speaker information and speaker channel information, select the speaker information needed for the experiment to perform the final likelihood ratio score of the back-end PLDA, further reducing the channel diversity of the speaker. The speaker confirmation experiment on the DAC13 dataset shows that the DAE-RBM-PLDA model, which combines the advantages of both DAE and RBM, can effectively improve the recognition rate.

  the posterior probability of generating the t x in the Gaussian mixture component j in the UBM model:

Fig. 1 .

 1 Fig.1. DNN-based Speaker Identification System Flow Chart

Fig. 2 .Fig. 3 .

 23 Fig.2. DAE Structure Schematic Diagram

Fig. 4 .Fig. 5 .

 45 Fig.4. DAE

Fig. 6 .

 6 Fig.6. PLDA, DAE-PLDA, RBM-PLDA, DAE-RBM-PLDA Process

Fig. 7 .

 7 Fig.7. Model Performance Line Chart

Table 1 .

 1 PLDA, DAE-PLDA, RBM-PLDA, DAE-RBM-PLDA Performance Comparison

	4
	3
	2
	1
	0
	1	2	3	4	5
		EER	DCF
	System	Back-end Model	EER,%	minDCF
	1 UBM	PLDA	4.49		1.432
	2 DNN	PLDA	3.32		1.275
	3 DNN	DAE-PLDA	2.79		0.863
	4 DNN	RBM-PLDA	2.91		0.954
	5 DNN	DAE-RBM-PLDA	2.82		0.913
	From the experimental results of Table 1, it can be seen that the equal error rate

Acknowledgment

This study was funded by the National Natural Science Foundation of China (Grant No.61404083).


Qian Qian
email: qianqian_yn@126.com

Xiaoting Wang

Miao Song

Feng Wang

Gazes induce similar sequential effects as arrows in a target discrimination task

Keywords: Attention orienting, Cueing effect, Sequence effect, Memory retrieval

Symbolic cueing paradigm has been widely used to investigate the attention orienting induced by centrally-presented gaze or arrow cues. Previous studies have found a sequence effect in this paradigm when arrows are used as central cues and simple detection tasks are included. The present study investigated the universality of the sequence effect with gaze cues and in discrimination tasks. It was found that sequence effects are not limited to specific cue types or specific tasks, and the sequence effect can even generalize across different cue types (from gaze to arrow, or from arrow to gaze). In addition, the sequence effect is not influenced by the repetition and switch of target identities (along with response keys). The results suggest that sequential processing is a common mechanism in attention orienting systems, and support the automatic retrieval hypothesis more than the strategy adjustment account.

Introduction

Orienting of attention refers to the ability for our attention system to be able to select pertinent input for further processing according to external cues [START_REF] Posner | Orienting of attention[END_REF]. It has been found that perception of a pointing arrow is enough to shift our attention to the pointed location reflexively [START_REF] Hommel | Symbolic control of visual attention[END_REF]. Besides arrows, another people's gaze can also shift attention even when these symbolic cues are uninformative for our task in hand [START_REF] Frischen | Gaze cueing of attention: Visual attention, social cognition, and individual differences[END_REF]. In a typical study of the symbolic cueing, observers were presented with a centrally-presented symbolic cue (e.g., a gaze or an arrow) indicating left or right, and after a certain time interval (stimulus onset asynchrony (SOA)) were instructed to respond to the appearance of a target to the left or right of the central cue. Although observers were told that the direction of the central cue did not predict where the target would occur, reaction time (RT) was reliably faster when the cue direction was toward (i.e., valid trials), rather than away from (i.e., invalid trials), the target. This facilitation of RT between valid and invalid trials is referred to as cueing effect, which is considered to be evidence of attention orienting.

Several recent studies [START_REF] Jongen | Sequence effects in a spatial cueing task: Endogenous orienting is sensitive to orienting in the preceding trial[END_REF][START_REF] Gómez | Sequential P3 effects in a Posner's spatial cueing paradigm: trial-by-trial learning of the predictive value of the cue[END_REF] reported a sequence effect in symbolic cueing paradigm. That is, when using a predictive central arrow cue (i.e., the ratio of valid trials among all trials were 80%), the cueing effect in one trial is significant smaller when the previous trial is an invalid trial than when it is a valid trial. Since the cues of these studies successfully predict the target locations in most of the trials, the sequence effect has been attributed to the continuous updating of the predictive value that participants assign to the spatial cue. In other words, participants adapt their utilization of the cue depending on whether it is correctly or wrongly directed their attention on the previous trial. On the contrary, another explanation about the sequence effect observed in these studies is automatic memory processes in which information of previous trials is automatically retrieved from memory to facilitate performance on current trials. For example, when the previous trial type (valid or invalid) is consistent with the current trial type, performance will be facilitated, whereas when the previous and current trial types differ, performance is slowed due to the conflict between the two trial types. This automatic retrieval hypothesis is in line with the view from peripheral cueing studies [START_REF] Dodd | The effect of previous trial type on inhibition of return[END_REF] and further supported by the results of [START_REF] Qian | Sequence effects by non-predictive arrow cues[END_REF], in which the sequence effect was still found when the arrow cues did not predict the target location and the participants were explicitly asked to ignore the arrow cues.

In symbolic cueing studies, arrow and gaze cues are two representative attentional cues. However, so far as we know, the sequence effect of symbolic cueing is investigated only with arrow cues and only in a simple detection task [START_REF] Jongen | Sequence effects in a spatial cueing task: Endogenous orienting is sensitive to orienting in the preceding trial[END_REF], [START_REF] Qian | Sequence effects by non-predictive arrow cues[END_REF]. Therefore, there still have some questions for the sequence effect. First, whether sequence effects can be found in other cueing tasks. For example, a simple detection task only need participants to press one key whenever they detect the targets, but a discrimination task will ask participants to choose response keys according to the target identities. In the simple detection task, there are only one target and one response , but in the discrimination task, target identities and responses either repeated or switched between consecutive trials. We still don't know whether sequence effects exist in a discrimination task, and whether the change of target identities and responses between trials influences the sequence effect; Second, whether or not gaze cues induce sequence effects, this question is important because it can help to answer the question whether or not sequential processes in human attention orienting systems are common mechanisms responding to central symbolic cues; Third, if sequential processes are common mechanisms, whether or not the sequence processes of symbolic cueing can generalize across different cue types (e.g., from gaze to arrow cues), and whether there are differences between them.

In experiment 1, sequence effects were tested with a central gaze cue. If sequence effects are common mechanisms in symbolic cueing, significant sequence effects should also be observed in gaze cue condition. In addition, different from previous studies, a discrimination task, instead of a simple detection task, was used to test the flexibility of the sequence effect. If sequence effects are robust phenomenon in symbolic cueing, significant sequence effects should also be observed with a discrimination task. Considering that in the previous study [START_REF] Qian | Sequence effects by non-predictive arrow cues[END_REF], significant sequence effects were only found when the SOA of previous trials was relatively long, we expect that sequence effects of gaze cueing are significant, but only for long SOA conditions.

Another advantage for choosing a discrimination task instead of a simple detection task is that there are two kinds of targets, and participants need to press different buttons to respond to the different targets. Therefore, target identities and its corresponding responses will either repeated or switched between consecutive trials. By using a simple detection task, previous study [START_REF] Qian | Sequence effects by non-predictive arrow cues[END_REF] found a significant influence of target location alternation on sequence effects in arrow cueing. However, because participants only need to press one specific button to respond to the appearance of one specific target in a simple detection task, whether the sequence effect is also influenced by the repetition and switch of target identities (along with its corresponding responses) is still unknown. With a discrimination task, we can investigate how target locations and target identities affect sequence effects.

Experiment 2 was aimed to compare the sequence effects induced by gaze and arrow cues. During the experimental trials, gaze and arrow cues were randomly mixed to form four kinds of cue sequence conditions between consecutive trials: gaze-gaze sequence, gaze-arrow sequence, arrow-gaze sequence, and arrow-arrow sequence. This experimental design had several advantages. First, the sequence effects induced by gaze and arrow cues could be compared directly by comparing the magnitude of sequence effects between gaze-gaze sequence and arrow-arrow sequence conditions. Different from arrow cues, cueing effects by gazes are based on mechanisms specialized for gaze perception [START_REF] Qian | Gaze cueing as a function of perceived gaze direction[END_REF]. The biological-significance of the gaze cues should make it more meaningful and important for participants. Therefore, according to strategy adjustment account, participants may adapt their utilization of the gaze cues more strongly than arrow cues, leading to an enhanced sequence effect in gaze cueing. However, an automatic retrieval hypothesis will predict similar sequence effects for both gaze and arrow cues.

Second, the experimental design allowed us to investigate whether the sequence effect could generalize across cue types. According to the strategy adjustment account, sequence effects are originated from continuous updating of the predictive value that participants assign to the cue. Therefore, the change of cue types between consecutive trials should eliminate the sequential processing, because the last cue is new for participants and there is no reason for participants to update the predictive value of a new cue. On the contrary, an automatic retrieval hypothesis will predict undistinguishable sequence effects for four kinds of cue sequence conditions.

2

Experiment 1

Participants

A total of 33 students (with a mean age of 23 years, range 19 to 27 years, 13 females) consented to participate in this experiment. All participants were right-handed and reported normal or corrected-to-normal vision. All participants were naive as to the purpose of the experiment.

Apparatus and Stimuli

The stimuli were presented on a LCD display operating at a 75 Hz frame rate. The participants were seated approximately 60 cm away from the screen in a dimly-lit room.

A cross, subtending 1º , was placed at the center of the screen as a fixation point. Face photographs were included as central cues. The central stimulus was a photograph of a female face, about 4゜ wide and 7゜ height, displayed in eight-bit grayscale. The face photograph was manipulated to produce the left-gaze and right-gaze cues by cutting out the pupil/iris area of each eye and pasting it into the left and right corner of each eye, respectively, using Photoshop CS2 software. The target stimulus was a capital letter ('X' or 'O') measuring 1º wide, 1º high, and was presented 15º away from the fixation point on the left or right side.

Design and Procedure

The cue-target SOAs were 100 ms and 600 ms. On each trial, cue direction, target location, and SOA duration were selected randomly and equally. Therefore, the cue validity was 50%. For each participant, there were six blocks with 80 trials each. Including 20 training trials, there were in total 500 trials for each participant.

Participants were instructed to keep fixating on the center of the screen. First, a fixation cross appeared at the center of the screen for 1000 ms, and then the cue stimulus appeared. After a certain cue-target SOA, a target letter 'X' or 'O' appeared either at left or right until participants had responded or 1500 ms had elapsed. The cue stimulus was still remained on the screen after the appearance of the target. Participants were instructed to respond to the identity of the target letters by pressing the 'UP' key with their middle finger of the right hand or the 'DOWN' key with their index finger of the right hand, the mapping between the responses and the target letters were counter-balanced across the participants. Participants were also informed that the central stimuli did not predict the location in which target would appear, and that they should try to ignore the central cues.

Results

The participants missed or responded to a wrong target at about 2.6% of the all trials. Anticipations (RT of less than 100 ms) and outliers (RT over 1000 ms) were classified as errors and were excluded from analysis. After that, responses with RTs exceeding plus or minus two standard deviations of each participant's mean RT on each single cell of the design were also removed as errors. As a result, about 8.4% of all trials were removed as errors. The error rates did not vary systematically and no signs of any speedaccuracy trade-off were observed. The mean RTs under different conditions can be seen in Fig. 1. A four-way ANOVA with previous SOA (pre-100 ms and pre-600 ms), SOA (100 ms and 500 ms), previous cue validity (pre-valid and pre-invalid), and cue validity (valid and invalid) as within-participants factors was conducted on the RTs. There was a significant main effect of previous SOA, F(1, 32) = 9.122, p < .005, with RTs becoming slower as the previous SOA was increased. The main effect of SOA was also significant, F(1, 32) = 30.589, p < .0001, with RTs becoming shorter as the current SOA was increased. The interaction between previous SOA and previous cue validity was significant, F(1, 32) = 9.096, p < .005. This interaction was qualified by a significant previous SOA × current SOA × previous cue validity × cue validity interaction, F(1, 32) =4.200, p < .049. Further tests revealed that the previous cue validity × cue validity interaction (indicating the sequence effects) were only significant when both the previous and current SOAs were 600 ms, F(1, 32) = 6.787, p < .014, but not for other combinations of previous and current SOAs (ps > .4). The average sequence effects (calculated by cueing effects of pre-valid trials minus cueing effects of pre-invalid trials) for different SOA conditions are 0.3 ms (pre100-100), -3.2 ms (pre100-600), -6.1 ms (pre600-100), and 16.7 ms (pre600-600). No other effects or interactions reached significance.

In order to investigate the influence of target locations and target identities on the sequence effects, a four-way ANOVA with target location (repeated and switched), target identity (repeated and switched), previous cue validity (pre-valid and pre-invalid), and cue validity (valid and invalid) as within-participants factors was conducted on the RTs. The main effects of target location and target identity were both significant, F(1, 32) = 15.044, p < .0001, and F(1, 32) = 37.151, p < .0001, respectively. The interaction between target location and target identity was also significant, F(1, 32) = 200.270, p < .0001, reflecting that alternation of target identity between trials slowed RTs only when target location repeats between trials. The interaction between target location and previous cue validity was significant, F(1, 32) = 12.734, p < .001. No other effects or interactions reached significance.

The results of experiment 1 showed that significant sequence effects can be found in a discrimination task with gaze cues. Furthermore, similar to the finding of previous study [START_REF] Qian | Sequence effects by non-predictive arrow cues[END_REF], sequence effects were only significant under relatively long SOA conditions. However, contrary to the previous study [START_REF] Qian | Sequence effects by non-predictive arrow cues[END_REF], no significant influence of target location (or target identity) on the sequence effect was found. This is probably because that the sequence effects are not significant in most of trials when previous or current SOAs are short. An investigation that only involves the pre600-600 SOA condition will be infeasible for the small trial numbers. Therefore, the influence of target location and target identity will be investigated again in experiment 2.

3

Experiment 2

Participants

A total of 36 students (with a mean age of 23 years, range 19 to 27 years, 15 females) consented to participate in this experiment. All participants were right-handed and reported normal or corrected-to-normal vision. All participants were naive as to the purpose of the experiment.

Apparatus and Stimuli

The apparatus and the stimuli were the same as that in experiment 1 except that an arrow cue was included. For arrow cues, the central fixation stimulus was a horizontal line centered on the screen, 3゜ in length. An arrow head and an arrow tail appeared at the ends of the central line, both pointing left or both pointing right. The length of an arrow, from the tip of the arrow head to the ends of the tail, was 4゜.

Design and Procedure

A relatively long SOA (600 ms) was used to ensure the capability of the design to induce sequence effects. On each trial, cue type (gaze cue or arrow cue), cue direction, and target location were selected randomly and equally. There were eight blocks with 80 trials each. Including 20 training trials, there were in total 660 trials for each participant. The procedure was the same as that in experiment 1.

Results

The participants missed or responded to wrong targets at an average of about 2.1% of all trials. Anticipations (RT of less than 100 ms) and outliers (RT over 1000 ms) were classified as errors and were excluded from analysis. After that, responses with RTs exceeding plus or minus two standard deviations of the participant's mean RT on each single cell of the design were also removed as errors. As a result, about 7.5% of all trials were removed as errors. The error rates did not vary systematically and no signs of any speed-accuracy trade-off were observed.

A four-way ANOVA with previous cue type (pre-gaze or pre-arrow), cue type (gaze or arrow), previous cue validity (pre-valid and pre-invalid), and cue validity (valid and invalid) as within-participants factors was conducted on the RTs. There was a significant main effect of cue validity, F(1, 35) = 50.446, p < .0001, demonstrating the cueing effect, and a significant interaction between previous validity and cue validity, F(1, 35) = 14.06, p < .001, indicating the significant sequence effect. As for the influence of cue types, the interaction between previous cue type and previous cue validity was significant, F(1, 35) = 8.265, p < .007, reflecting that RTs were shorter for pre-valid than for pre-invalid condition when the previous cue was an arrow, but this tendency was reversed when the previous cue was a gaze. The interaction between previous cue type and cue validity was also significant, F(1, 35) = 4.548, p < .04, indicating that cueing effects were larger for pre-arrow condition than for pre-gaze condition. No other factors or interactions were significant. The average sequence effects for different cue sequence conditions are 11.1 ms (arrow-face sequence), 10.6 ms (arrow-arrow), 7.1 ms (face-arrow), and 7.2 ms (face-face). Paired-samples t tests confirmed that the magnitude of these four sequence effects is not significantly different from each other (ps > .59). The mean RTs under different cue sequence conditions can be seen in Fig. 2. Similar to the experiment 1, a four-way ANOVA with target location (repeated and switched), target identity (repeated and switched), previous cue validity (pre-valid and pre-invalid), and cue validity (valid and invalid) as within-participants factors was conducted on the RTs. The main effects of target location and target identity were both significant, F(1, 35) = 31.779, p < .0001, and F(1, 35) = 35.923, p < .0001, respectively. Similar to that in experiment 1, the interaction between target location and target identity was significant, F(1, 35) = 121.552, p < .0001, demonstrating that alternation of target identity between trials slowed RTs only when target location repeats between trials. The interaction between target location and previous cue validity was also significant, F(1, 35) = 25.232, p < .0001. In addition, there was a significant main effect of cue validity, F(1, 35) = 41.302, p < .0001, demonstrating the cueing effect, and a significant interaction between previous validity and cue validity, F(1, 35) = 12.774, p < .001, indicating the sequence effect. Importantly, the target location × previous cue validity × cue validity interaction were marginally significant, F(1, 35) = 3.989, p = .054, replicating the influence of target locations on the sequence effect that was observed in the previous study. No other effects or interactions reached significance.

In all, significant sequence effects were found for all four combination conditions of two cue types. In addition, although the influence of target locations on the sequence effect was replicated, no significant influence of target identity alternation was found.

Discussion

The present study investigated the sequence effects (i.e., trial-by-trial influence) induced by gaze and arrow cues in cueing paradigm. In experiment 1, participants were asked to discriminate targets in a gaze cueing task, and it was found that gaze cues induced significant sequence effects in long SOA conditions. In addition, sequence effects were not influenced by the repetition and switch of target identities and its corresponding responses. When gaze and arrow cues were intermixed in experiment 2, the four combination conditions of cue types induced significant and similar sequence effects. In addition, though the influence of target locations on the sequence effects that was reported previously [START_REF] Qian | Sequence effects by non-predictive arrow cues[END_REF] was replicated, no significant influence of target identities was found.

Results from experiment 1 extend our knowledge about the sequence effects for the following aspects. First, sequence effects still exist when gazes are used as central cues. This finding suggests that sequential processing is a common phenomenon in symbolic cueing paradigm and is not limited to specific cue types, such as arrows.

Second, the appearance of sequence effects does not depend on specific task demands. So far as we know, all previous studies used the simple detection task to test the sequence effects. Before this study, it remains unknown whether or not the sequence effects can be found with different tasks.

Third, both experiment 1 and experiment 2 found that overall RTs were slowed down by the alternation of target identities (at least when target location repeated between trials), probably because participants need time to choose a different valid response key for a changed target. However, sequence effects were not influenced by the repetition and switch of target identities (along with its responses). From a memory perspective, there may be two major phases for the sequence processes: initial encoding phase in previous trials and later retrieval phase in current trials. In the former phase, the spatial organization information between cue directions and target locations needs to be encoded into memory; in the later phase, the information will be retrieved from memory to affect performance. Current results may reflect some memory mechanisms during the sequential processing. That is, the target identity information is not encoded and retrieved between trials.

Sequence effects by gaze and arrow cues were directly compared in experiment 2. Gaze and arrow cues were intermixed in a within-block design. Such design resulted four kinds of cue sequence conditions between consecutive trials: gaze-gaze sequence, gaze-arrow sequence, arrow-gaze sequence, arrow-arrow sequence. Interestingly, sequence effects are significant for all sequence conditions despite the alternation of cue types. That means gaze cues induce the same amount of sequence effects as arrow cues, and the sequence effect can generalize across different cue types (from gaze to arrow, or from arrow to gaze). This finding supports the automatic retrieval hypothesis and suggests that sequence effects induced by gaze and arrow cues are processed in the same system, probably the so-called implicit memory system in human brain [START_REF] Maljkovic | Priming of pop-out: III. A short-term implicit memory system beneficial for rapid target selection[END_REF][START_REF] Kristjá Nsson | Rapid learning in attention shifts: A review[END_REF].

In all, the present study investigated the sequence effect in gaze cueing paradigm. Similar to the previous findings from arrow cueing, significant sequence effects were found. The results extend our knowledge by showing that sequence effects in cueing paradigm are not limited to a specific cue type or a specific task, and suggest that sequential processing is a common mechanism in attention orienting systems.

Fig. 1 .

 1 Fig. 1. Mean reaction times (RTs) under different previous and current cue validities and SOAs in Experiment 1.

Fig. 2 .

 2 Fig. 2. Mean reaction times (RTs) under different previous and current cue validities and different combination of cue types between trials in Experiment 2.

Acknowledgments. This research is supported by the NSFC (31300938, 61462053, and 61403251), and the Yunnan NSFC(2016FB107).


Yingying Xu
email: s_yingyingxu@163.com

Zhihua Cui
email: zhihua.cui@hotmail.com

Lifang Wang

Discrete Cuckoo Search with Local Search for Max-cut Problem

Keywords: Max-cut problem, discrete cuckoo search algorithm, local search strategy

Max-cut problem is a well-known NP-hard problem, in this paper, a hybrid meta-heuristic algorithm is designed to solve it. In this algorithm, the discrete cuckoo search is employed to find the approximate satisfied solution, while the local optimal solution is used to further improve the performance. To test the validity, three other algorithms are used to compare, simulation results show our modification is effective.

Introduction

Max-cut problem is a well-known NP-hard graph problem. For a graph ( , ) G V E  , {1, 2,..., n} V  is vertex set and E is the ordered set of undirected edges. Let ij w be the weight associated with edge{ , } i j E  , then max-cut problem is to find an optimal partition 12 ( , ) VV [START_REF] Grillo | Application of particle swarm optimisation with backward calculation to solve a fuzzy multi-objective supply chain master planning model[END_REF] VV  , 12 V V V ), so that the total weights of the edges crossing different subsets is maximized, in other words, the objective function can be represented as: [START_REF] Grillo | Application of particle swarm optimisation with backward calculation to solve a fuzzy multi-objective supply chain master planning model[END_REF]

, 1 2 ij ij ij i V j V i j xx ww       (1)
where

  1, 1 ( 1, 2, , ) i x i n    , 1 i x  represents 1 i
xV  , as well as 1

i x  denotes 2 i xV  .
During the past years, many algorithms have been designed to solve it, including exact algorithm, approximate algorithm and heuristic algorithm [START_REF] Xia | An efficient Lagrangian smoothing heuristic for Max-Cut[END_REF][START_REF] Marti | Advanced Scatter Search for the Max-Cut Problem[END_REF]. Heuristic algorithm [START_REF] Wang | A new metaheuristic optimization algorithm motivated by elephant herding behavior[END_REF][START_REF] Bilbao | On the application of multiobjective harmony search heuristics to the predictive deployment of firefighting aircrafts: a realistic case study[END_REF][START_REF] Rajakumar | A survey on nature inspired metaheuristic algorithms with its domain specifications[END_REF] is an umbrella for all population-based stochastic optimization algorithm inspired by heuristic information [START_REF] Xiao | Emergent computation of complex systems: a comprehensive review[END_REF], such as ant colony optimization [START_REF] Dorigo | Special section on ant colony optimization[END_REF][START_REF] Stodola | Applying the ant colony optimisation algorithm to the capacitated multi-depot vehicle routing problem[END_REF], fruit fly optimization [START_REF] Zhang | Optimising web service composition based on differential fruit fly optimisation algorithm[END_REF], particle swarm optimization [START_REF] Eberhart | Special issue on particle swarm optimization[END_REF][START_REF] Adewumi | On the performance of particle swarm optimisation with(out) some control parameters for global optimisation[END_REF][START_REF] Grillo | Application of particle swarm optimisation with backward calculation to solve a fuzzy multi-objective supply chain master planning model[END_REF], artificial bee colony [START_REF] Lv | Improved multi-strategy artificial bee colony algorithm[END_REF][START_REF] Sun | Artificial bee colony algorithm with improved special centre[END_REF][START_REF] Lu | Artificial bee colony with bidirectional search[END_REF][START_REF] Yu | A new multi-population-based artificial bee colony for numerical optimization[END_REF], social emotional optimisation algorithm [START_REF] Guo | Enhanced social emotional optimisation algorithm with elite multi-parent crossover[END_REF], firefly algorithm [START_REF] Wang | Firefly algorithm with neighborhood attraction[END_REF][START_REF] Wang | Firefly algorithm with random attraction[END_REF][START_REF] Yu | An improved firefly algorithm based on probabilistic attraction[END_REF][START_REF] Nasiri | History-driven firefly algorithm for optimisation in dynamic and uncertain environments[END_REF][START_REF] Fister | A comprehensive review of firefly algorithms[END_REF] and bat algorithm [START_REF] Yang | Bat algorithm: a novel approach for global engineering optimization[END_REF][START_REF] Cai | Improved bat algorithm with optimal forage strategy and random disturbance strategy[END_REF][START_REF] Xue | Optimal parameter settings for bat algorithm[END_REF].

For max-cut problem, Laguna et al. [START_REF] Laguna | Hybridizing the cross-entropy method: an application to the max-cut problem[END_REF] designed a hybrid version of cross entropy method, while Lin [START_REF] Lin | A discrete dynamic convexized method for the max-cut problem[END_REF] proposed a discrete dynamic convexized method. Festa et al. [START_REF] Festa | Randomized heuristics for the MAX-CUT problem[END_REF] investigated several heuristics derived from greedy randomized adaptive search procedure and variable neighborhood search. In 2007, Wang [START_REF] Wang | A Memetic Algorithm with Genetic Particle Swarm Optimization and Neural Network for Maximum Cut Problems[END_REF] proposed a hybrid algorithm combining with chaotic discrete Hopfield neural network and genetic particle swarm optimization, while in 2011, Wang [START_REF] Wang | Combining tabu Hopfield network and estimation of distribution for unconstrained binary quadratic programming problem[END_REF] designed another combination with tabu Hopfield neural network and estimation of distribution algorithm. Inspired by this work, Lin [START_REF] Lin | An Integrated Method Based on PSO and EDA for the Max-Cut Problem[END_REF] designed an integrated method combined with particle swarm optimization and estimation of distribution algorithm, and a local search strategy is employed to improve the accuracy. Shylo [START_REF] Shylo | Solving the maxcut problem by the global equilibrium search[END_REF] also employed global equilibrium search algorithms and tabu search to improve the accuracy.

In this paper, we propose a new heuristic algorithm to combining the cuckoo search algorithm and local search strategy, and apply it to solve max-cut problem. The rest of this paper is organized as follows: In Section 2, the details of our proposed hybrid algorithm are presented, as well as the simulation results are reported in Section 3.

2

Hybrid Algorithm

Discrete Cuckoo Search Algorithm

Cuckoo search algorithm was proposed in 2009 [START_REF] Yang | Cuckoo search via Levy flights[END_REF], up to now, many variants are proposed to improve the performance [START_REF] Cui | A novel oriented cuckoo search algorithm to improve DV-hop performance for cyber-physical systems[END_REF][START_REF] Zhang | Hybrid multi-objective cuckoo search with dynamical local search[END_REF][START_REF] Li | DV-hop localisation algorithm with DDICS[END_REF]. However, max-cut problem is a combination problem, and a discrete cuckoo search algorithm is designed to solve it.

In this discrete version, the position movement will use the following strategies [START_REF] Feng | Binary cuckoo search algorithm[END_REF]:

Strategy 1: 1 , () ( ) 1, m m ijk ijk x rand Sig Step x other          (2) where ( ) 1/ (1 exp( )) Sig Step Step    (3)
Strategy 2:

1 1, () ( ) , m m ijk ijk rand Sig Step x x other         (4)
where

( ) 1 2 / (1 exp( )) Sig Step Step     (5) Strategy 3: 1 1, () ( ) , m m ijk ijk rand Sig Step x x other         (6)
where

( ) 2 / (1 exp( )) 1 Sig Step Step     (7)
The most difference among three strategy is the sigma function () sig step , and jump path step is a random number with Levy distribution, to provide a deep insight, the Eq. ( 3), Eq.( 5) and Eq.( 7) are plotted in Fig. 1-Fig. 3.

Local Search Strategy

For any partition 12 ( , ) VV , if the vertex j is moved from the current partition to an- other subset, the gain index j g is defined as follows:

        12 21 1 , , , , 2 , , , , ,
,

jk jk j k E k V j k E k V j jk jk j k E k V j k E k V w w j V g w w j V                   (
If ( 0 sel  ) If sel >30 1 sel = 1 3 sel  ; Else 1 sel = sel ;
Move the vertices of 1 sel , which are selected sequentially from sorted result.

Evaluate the fitness End End

Proposed Hybrid Algorithm

Our modification is a hybrid meta-heuristic method combining a discrete cuckoo search algorithm and local search strategy. The discrete cuckoo search is employed to find the approximate satisfied solution, while the local optimal solution is used to further improve the performance for the obtained approximate satisfied solution. Furthermore, to avoid the premature convergence, a mutation strategy is also employed to avoid the premature convergence. The pseudocode of our hybrid algorithm is listed in Algorithm 3. For each cuckoo, the mutation operation will randomly take 0.1% vertices to flip. We find that the algorithm will be improved after adding the mutation operation.

Algorithm 3 Cuckoo search with Local search Begin

For the graph, initialise population pop , and record the best solution gbest ; Find the approximate satisfied solution by the discrete cuckoo search (refer to Alg.1);

Where (Stop condition is not verified) the local strategy (refer to Alg.2) is employed to improve the quality of the solution;

If a particle

x in a group is not improved in two consec- utive searches, a mutation strategy is employed to avoid the premature convergence; End End

Performance Evolution

To test the performance of our proposed hybrid algorithm, G-set graph benchmarks are employed, and compared with the following algorithms:

• Hybridizing the cross-entropy method (HCE, in briefly) [START_REF] Laguna | Hybridizing the cross-entropy method: an application to the max-cut problem[END_REF] The program is implemented with MATLAB. In this set of instances, the number of vertex range from 800 to 3000. the control factor r p is 0.3, the probability a p are both set to 0.5, the total generation is 500.

For chosen benchmarks, each instance will run 50 times, Table 1 provides the optimal value achieved by the three algorithms and our proposed algorithm. The last line noted as " / / " w t l is the comparison results between our proposed DCSLS and its competitors. "w/t/l" represents our algorithm wins in w functions, ties in t functions, and loses in l functions. It means DCSLS is better than HCE for six functions, while only worse than HCE for three functions. DCSLS are superior than DHNN-EDA and LNA for six functions too, while DHNN-EDA and LNA only better than DCSLS with two and three functions, respectively. In one word, DCSLS achieves the best performance when compared with HCE, DHNN-EDA and LNA. To provide a deep comparison, two non-parametric statistics tests: Friedman test and Wilcoxon test, are employed to show the differences among these four algorithms. In Tab.2, the ranking value is: DCSLS<HCE<DHNN-EDA<LNA, DCSLS maintains the lowest ranking, it means the performance of DCSLS is more better. Tab.3 implies there is significantly difference between DCSLS and DHNN-EDA.

Conclusion

In this paper, a new hybrid algorithm combining with discrete cuckoo search and local search strategy is designed. The cuckoo update manner of discrete cuckoo search is the same as [START_REF] Feng | Binary cuckoo search algorithm[END_REF], while the local search strategy is designed. Simulation results show our modification achieves the best performance when compared with other three algorithms.

Acknowledgments

Fig. 1 .Fig. 2 .Fig. 3 .

 123 Fig. 1. Illustration for Eq.(3) Fig. 2. Illustration for Eq.(5)

9 1

 9 Update the nest position for each cuckoo by strategy 1;

	Else
		If		Step 	0
				Update each cuckoo with strategy 2;
		Else
				Update each cuckoo with strategy 3;
		End
	End
	Evaluate the objective fitness for each cuckoo;
	If	rand	()		r p
		Re-update the position of corresponding cuckoo with
	formulas:
		x	t	1  	x	t		() t t R p x     
			jk			jk	gk	uk
		Evaluate the new cuckoos' finesses;
	End
	Record the best position
	End
	Output the best position
	End

  With this manner, the following local search strategy is introduced:

				8)
	Gain	0
		Algorithm 2 Local Search Strategy
		Begin
		Use formula (8) to calculate the gain of each vertex
		Descending all gains
		Count the number (	sel ) of vertices with	0 g  is satisfied
				j

j g  means the vertex j should be moved with a lower objective function.

Table 1 :

 1 Comparison of the results

	In-stances	best	HCE	DHNN-EDA	LNA	DCSLS
	G1	11624	11584	11614	11490	11607
	G2	11620	11595	11599	11505	11599
	G3	11622	11574	11617	11511	11605
	G11	564	552	494	560	530
	G12	556	542	476	546	528
	G13	582	564	520	572	552
	G14	3064	3030	3027	3023	3035
	G15	3050	3012	2988	2996	3016
	G16	3052	3015	3001	2994	3018
	// w t l		6/0/3	6/1/2	6/0/3

Table 2 :

 2 Friedman test

Table 3 :

 3 Wilcoxon test

.

  This research is supported by the Natural Science Foundation of Shanxi Province under No. 201601D011045.

		Rank-	DCSLS vs	P-Value
		Value	HCE	0.594
	HCE	2.33	LNA	0.192
	DCSLS	1.94	DHNN-EDA	0.050
	LNA	2.89
	DHNN-EDA	2.83


Esteban Arias Caracas

Daniel Fernando

Mendoza López

Paulo Alonso Gaona-García

Jhon Francined

Herrera Cubides

Enrique Carlos

Montenegro-Marín

Daniel Fernando Mendoza
email: dfmendozal@correo.udistrital.edu.co

Esteban Arias Caracas

Daniel Fernando Mendoza López

Paulo Alonso Gaona-García

Jhon Francined Herrera
email: jfherrerac@udistrital.edu.co

Carlos Enrique Montenegro Marín

Evaluation of the Linked Open Data Quality Based on a Fuzzy Logic Model

Keywords: Linked open data, Fuzzy logic, Quality measurement

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Linked Open Data has been one of the most recent changes in information in recent years, specifically the way in which data is published, distributed and consumed [START_REF] Hu | Proceedings of the 16th International Conference on Information Integration and Web-based Applications & Services -iiWAS[END_REF]. These data can easily be uploaded and updated by any type of organization, be it individuals, small groups of people, educational organizations, social networking sites and even government agencies [START_REF] Bonatti | Robust and Scalable Linked Data Reasoning Incorporating Provenance and Trust Annotations[END_REF]. Due to this large number of people, which can upload data to the Web, this model has grown exponentially, from 12 datasets in 2007, to approximately 300 in September 2011, and 9,960 datasets in 2016 [START_REF] Auer | LODStats -9960 datasets[END_REF], taking into account that this number is accumulated from the data catalogs: data.gov, publicdata.eu and datahub.io [START_REF] Ermilov | The Data Web Census Dataset[END_REF]; three of the main collections of datasets available to the public. This growth in Linked Open Data requires methods or tools that can handle this data, to make it "secure, stable, fast and accurate; in other words, have a better quality," [START_REF] Thakkar | Are Linked Datasets fit for Open-domain Question Answering? A Quality Assessment[END_REF]. However, quality is a very complex concept; defining what is good quality or not is very subjective and cannot be defined in one way or by a simple judgment [START_REF] Bonatti | Robust and Scalable Linked Data Reasoning Incorporating Provenance and Trust Annotations[END_REF][START_REF] Debattista | Luzzu-A Methodology and Framework for Linked Data Quality Assessment[END_REF].

For this reason, many researchers have been looking for methods to complement the quality of the data and administer them for later evaluation. Some of these researchers have created software that can evaluate quality with mathematical procedures, such the quality measurement software, "Luzzu" [START_REF] Debattista | Luzzu-A Methodology and Framework for Linked Data Quality Assessment[END_REF]. However, much of these results are extracted from classical or conventional mathematical models. This causes the calculated quality to possess a certain degree of uncertainty. Therefore, a formulated problem is generated: How to calculate the quality of Linked Open Data in a more precise way, with a considerable amount of quality variables to take into account?

As a new solution to the previous problem, modeling based on fuzzy logic is a solution that can provide the measurement of quality, taking into account the tolerance of intermediate values between conventional evaluators [START_REF] Hellmann | Fuzzy Logic Introduction[END_REF]. To cover the complexity of quality, it has approached the classification of quality through dimensions [START_REF] Zaveri | Quality Assessment Methodologies for Linked Open Data A Systematic Literature Review and Conceptual Framework[END_REF]. The proposed model covers 2 dimensions, of which four aspects will be represented in order to evaluate the quality of the linked open data, which will help to show the capacity of the fuzzy logic model when supporting a large number of quality aspects, and obtain a more accurate approximation of quality.

2

Theoretical Background and Related Work

Quality Dimensions

Datasets can be analyzed and classified through different dimensions, which can be contextual, trustworthy, intrinsic, among others [START_REF] Zaveri | Quality Assessment Methodologies for Linked Open Data A Systematic Literature Review and Conceptual Framework[END_REF]. These dimensions are classifications of groups of different variables or data quality measurement values or variables. For this model, the trust and accessibility dimensions were the most appropriate approaches to analyze the model. The reason why these dimensions were chosen resides in the importance of each dimension can generate and the relationship between factors linked to the opinion of the client and linked to the functionality of the data set. The combination of both factors can arrive at a closer approximation to correctly measure the quality of the data, as well as to build the model as comprehensible to the user as possible.

But each dimension has different values or variables to work with. As an example, intrinsic dimensions classify variables such as accuracy, consistency or conciseness [START_REF] Zaveri | Quality Assessment Methodologies for Linked Open Data A Systematic Literature Review and Conceptual Framework[END_REF]. These dimensions can be defined differently for each author, however, they share similar approaches and characteristics. For this model, it is defined by the values of Response Time, Scalability, Trustworthiness and Timeliness.

The classification of each concept to its respective dimension results in the grouping of the response time and scalability in the dimensions of accessibility and the Trustworthiness and Timeliness in the confidence dimension.

Fuzzy Logic

The need to specify the fuzzy logic as the model to work was justified by the importance of changing the paradigm of mathematical results during studies during the last years.

In classical mathematical concepts, variables can only be represented in 0 or 1, true or false, among others. In the measurement of quality, this type of results is ambiguous, since quality cannot exist or not exist. It is a value that can be partially good or partially bad, partially true or partially false [START_REF] Alena | Application of Fuzzy Principles in Evaluating Quality of Manufacturing Process[END_REF]. Quality, for example, is something that cannot be described in a classic model of good or bad so easily; leads to ambiguous results and inaccurate results, but Fuzzy Logic, considering that it uses rules that define quality in segments and results that can be represented in more than two ways or variables, can adequately define a better approximation of the Data Quality evaluation.

Related Work

It is worth noting that both the fuzzy logic, which is the model used, and the open data are quite recent concepts and both have a very strong affinity, as well as a greater use during the last years [START_REF] Dernoncourt | Introduction to fuzzy logic[END_REF]. Due to this reason, there are very few previous works similar to the one in this article. The union of these two concepts arises from their compatibility and innovation. The representation of the rules that define the quality in segments of more than two answers can adequately define a better approximation of the evaluation of Data Quality, without the need of great requirements both for its main design and its portability, thus allowing to add more quality variables and more dimensions to work, for later calculation of quality more accurately.

The most outstanding work to take into account is the one by Daniel Lewis and Trevor Martin about the use of fuzzy logic for the analysis of ontologies and vocabularies within of Linked Open Data [START_REF] Lewis | Managing Vagueness with Fuzzy in Hierarchical Big Data1[END_REF]. Mainly the fuzzy logic model to use in this article is the traditional one, while they demonstrated their investigation with the approximation X-μ, and the fact that the focus is on ontologies of linked open data, when this model seeks to create a new approach to a quality measurement of linked open data. Similarly, there are previously developed frameworks that seek to solve the aforementioned problems, the most similar to the case of this article is the "Luzzu" software. Its main objective is "to be scalable, extensible, interoperable and customizable" [START_REF] Debattista | Luzzu-A Methodology and Framework for Linked Data Quality Assessment[END_REF]. This framework works through the selection of quality metrics to be used within a default dataset or a SPARQL Endpoint. The Luzzu framework uses many more aspects of quality, with a capacity of 22 aspects of quality or metrics, related through nine dimensions of quality [START_REF] Debattista | Luzzu-A Methodology and Framework for Linked Data Quality Assessment[END_REF].

The Proposed Methodology

As a modeling of the methodology, it was decided to use a quasi-experimental empirical study, which allows estimating the impact of the different aspects of quality to obtain a global quality, without the use of random variables in the process, as shown in Fig. 1. As a population the dataset of opendata.cz is taken into account, which has its own RDF Query Language (SPARQL) Endpoint, by which query type queries are carried out. As a sample, 100 datasets were taken associated with the main dataset opendata.cz, located in the Czech Republic. The SPARQL Endpoint corresponding to the opendata.cz dataset was used as instruments for data collection, and a JSON file for its subsequent analysis within the model was obtained as a result of a query to this endpoint. As a model analysis plan, it has been decided to compare quality values between the two cases raised for the visualization of the effect of more or less variables included within the fuzzy logic model. In turn, it was decided to show the comparative graphs between both cases for the values resulting from the evaluated quality, at the same time to visualize by means of tables statistical tests such as the deviation and the standard error.

Type of Investigation

The modeling for the evaluation of data quality in Linked Open Data can be built with a fuzzy logic approach, defining whether the quality is low, medium or high. Due to the represented model that uses a centroid method, since the need to improve previous models of data quality with a considerable number of inputs or quality criteria, allows us to obtain a percentage approximation value. As a percentage that is represented between a range and this truth value is more extended than the classical mathematical values of 0 and 1, the established ranges represent values of real life, such as low, medium or high (Fig. 2).

Fig. 2. Structure graph of fuzzy logic, Source: Own elaboration

The fuzzy logic model requires the evaluation of each of the four quality measurement channels, also known as the background of the model, through a series of rules, to then evaluate the output to determine if the quality of the data is high, medium or low. Two cases are evaluated: for the first case all four aspects are taken and the quality is measured with them. In the second case, 2 of the aspects are taken and redefined in their worst possible values and evaluate the quality of the data in a similar way to the first case. The main objective of these cases is to evaluate and compare the results considering that one case has many more factors than the other, and therefore is more accurate [START_REF] Zaveri | Quality Assessment Methodologies for Linked Open Data A Systematic Literature Review and Conceptual Framework[END_REF].

The first entry to evaluate is the Response Time, in which it can be calculated using the capacity in which the analyzed dataset is available and can respond to requests, because it is defined as "a data set can work well only if It is available and has a low response time" [START_REF] Zaveri | Linked Data Quality Assessment and its Application to Societal Progress Measurement[END_REF]. As a model definition within a range between 0 and 1, the response time is 1 if a response is received when requesting internal data from each dataset and the value is 0 otherwise. (Fig. 3). The second input to be measured in the model is scalability. Scalability measures the ability to respond to multiple users or requests at the same time [START_REF] Zaveri | Quality Assessment Methodologies for Linked Open Data A Systematic Literature Review and Conceptual Framework[END_REF]. The evaluation of this concept is taken by the concept of concurrency that supports the service that exposes the endpoint. As a methodology, it is measured by one and four users towards each of the datasets, performing a simulation in which each of these users makes a query towards the endpoint at the same time. After this, the average server response time is calculated for each user case and then applied a division between each average time of one and four users. This response variable will be expressed within a range [0,1], in which the value 0 is considered the lowest possible scalability and 1, the highest.

The relationship between the average time and the generation of the formula was based on the formula of the Timeliness assessment model of Olaf Hartig [START_REF] Hartig | Using Web Data Provenance for Quality Assessment[END_REF]. In his work, due to the similarity and the evaluation method used, which allowed to verify mathematically in a range, adaptable to this model of fuzzy logic.

The third entry to analyze in the model is Trustworthiness. The reliability allows to evaluate if the information and the data are classified as true and correct within the The fourth entry of the model is Timeliness. This concept defines the moment in which the datasets were updated or modified for the last time. As a measurement, Timeliness is defined in an interval [0,1] in which 0 represents uncertainty and the result 1 represents certainty.

Each case of the fuzzy logic model has three specific rules, one defining each possible case of quality within each dimension. It is necessary to clarify that, the output value called Quality within each rule for each dataset is according to the dimension in which the rule is classified, but not to the global quality. This is for the purpose of measuring global quality taking into account all the proposed rules and not only one or two that are met, at the same time to associate each aspect with its related ones and not to mix them, since comparing non-related metrics does not have a lot of logic. According to figure 3 and thanks to the software MATLAB and the tool Fuzzy Logic Toolbox, the rules for the Accessibility Dimension (from number 1 to number 6) and the rules for the Trust Dimension (from number 7 to number 10) are: It is necessary to emphasize that the relationship that has the response time and the scalability shown in Fig. 4, is mainly the performance that both variables specify when evaluating the dataset. Scalability successively measures the response time of each dataset, so the result of the response time will directly affect the scalability result. The relationship that maintains Trustworthiness and Timeliness sown in Fig. 4, is mainly from the internal analysis of each dataset. Both Trustworthiness and Timeliness take internal data from the dataset as date of creation, authors, dataset of origin, among others, which internally define the confidence dimension for obtaining the quality of the data.

Regarding the output result, the model will take into account the generated rules and produce an interval percentage between 0% and 100%, 0% representing the worst possible quality and 100% representing the best possible quality.

4

The Infrastructure of the Implemented Model

The capture of the data (or the population to be taken into account in the research) was done through the SPARQL Endpoint of the data set "opendata.cz", known for its interest in "building an open data infrastructure that allows access to public data in the Czech Republic" [START_REF] Nečaský | [END_REF]. Within Endpoint, the number of data sets that the SPARQL query displays is 100, taking it as the investigative sample of the process. It is necessary to emphasize that the approach used requires both the internal data of the SPARQL query and external data, taken mainly to measure the values of Response Time and Scalability within the framework. The SPARQL query used in the test model obtains the metadata results: the dataset title, the dataset description, the dataset creator (important for the Trustworthiness analysis), the dataset's contributors (important for the analysis of the Trustworthiness), the date of creation and modification of the dataset (important for the analysis of Timeliness), these grouped within a JSON file for later addition to the model. These are designed for the standards of the Semantic Web of RDF and the Vocabularies dcterms (Dublin Core Terms) and foaf (Friend Of A Friend).

The analysis of the data is done through Anaconda Framework, driven by the Python programming language, which allows to evaluate the data of a JavaScript Object Notation (JSON), which is a light interchangeable structured result of data generated by SPARQL Endpoints through the open server VIRTUOSO. As a note, the SPARQL query that obtains information shows the associated datasets, defining their relationship, point of origin and internal data such as the dataset author or the creation date of the dataset [START_REF] Ermilov | The Data Web Census Dataset[END_REF]. Mechanically, both the response time and the scalability are calculated by making requests based on HTTP / 1.1 of the SPARQL query, to obtain response times and calculate an average.

After obtaining the main data, the model proceeds to use controllers and evaluators defined for each antecedent as part of the structure in its programming, each with its specific function; the controllers allow the JSON data to be extracted and divided into segments, defined by the four dimensions of the quality of the data, and the evaluators execute the operations on the data to prepare them for processing in the model. Within the fuzzy logic model, the entries are updated and proceeds to compare the results with the 6 previously defined rules, and allow to obtain an output result per dataset.

Results

The data collection was successful for the 100 datasets to be analyzed, obtained in a JSON file as a result. To show results not extensive to the reader, only four sample datasets from the list of 100 datasets obtained from the SPARQL Endpoint of the dataset "opendata.cz" are shown in this section.

For the Response Time case, the average response time calculated as 43.73ms was compared to each time calculated. This procedure was executed approximately 50 times more and then the average of those times was obtained, in which it gave the result of 48.32 ms. It was possible to verify that each of the datasets analyzed within the study gave results within the JSON of the given request, that is, no null values or no response were obtained from the datasets, so the response time value for each of these datasets is 1. In the case of Scalability, the procedure to follow was a SPARQL request to extract internal data from each dataset, used within the cases of Trustworthiness and Timeliness. This process was executed an amount of 50 times more, obtaining as a result response times for one and four users separately, for a total added of 250 times. As a next step, each of the four user times were added, obtaining data from a single response time group, which were then compared with a user's data, using the average time of both groups. With this, the formula proposed above is applied and the average scalability result equals 0.900363599953. As a reference, this value is between a range of [0,1]. In the case of Trustworthiness, the natural way to measure this case is to take the author and values of each dataset and evaluate if these data are present (without null value). However, due to the empirical status of the study for the 100 sample datasets, the Trustworthiness was statically evaluated as 1, considering that all datasets contain authors and contributors verified by Datahub, a platform designed by the Open Knowledge Foundation.

In the case of Timeliness, the date of each dataset was taken into account as regards its creation and last modification. In order to specify and generalize the calculation of this factor, only the current year of this article (2017) was taken into account to compare both dates. As a result, you get a range between 0 and 1 per data set.

Taking into account the analysis plan previously proposed in the Methodology section, as a first step we studied the standard deviation and the error of the results of the model both for the quality cases and for the Response Time and Scalability due to the use of its average values to execute the model. The standard deviation of both quality cases is quite small, which can define the high precision of the calculated data, due to the low dispersion range between the mean and the values obtained [START_REF] Datastar | How to Interpret Standard Deviation and Standard Error in Survey Research[END_REF]. It is worth noting that Case 2 has a larger Standard Deviation because taking only Timeliness and Response Time as factors that fluctuate the result, but all other variables are still present within the same values as Case 1, so a correlation between both cases exists and has similar standard deviation results, and, therefore, defining a high precision in the output results of the fuzzy logic model.

At the same time, the addition of the standard error confirms the fact that the sample of the data taken does not have a high discrepancy. Specifically, with the result of the quality in case 1, which contains all four quality variables, it is important to know that this discrepancy decreases, and thus allows recognizing that the model can support a greater number of quality variables without fluctuation much discrepancy found (Fig 6 and7). In relation to the results of the quality of the results for both cases, it is observed that the first case has a higher percentage than the second case due to having a better score in two of the dimension values, however, it is observed that both cases have peaks that mean higher quality. The main reason for this phenomenon is that Timeliness and Response Time fluctuate the results. In a real scenario, the peaks are represented by values that do not have a high Timeliness, proven by not having the best possible value in the interval, 1.

In the comparison of the Luzzu framework, although the modeling of both frameworks are different, it can be seen that their growth in terms of processing and speed based on the execution time of the models are linear. However, it is noted that the fuzzy logic model has a faster amount of time executed for the processing in comparison to Luzzu, making it have a better performance. As an added value to this model, although it uses formulas similar to those of this model for the calculation of data [START_REF] Debattista | Luzzu-A Methodology and Framework for Linked Data Quality Assessment[END_REF][START_REF] Zaveri | Linked Data Quality Assessment and its Application to Societal Progress Measurement[END_REF], Luzzu uses classic modeling to process data in a percentage way, without the advantages that fuzzy logic generates to obtain a more precise result, such as the establishment of rules according to dimensions.

Conclusion and Discussion

Linked Open Data has been growing exponentially in recent years, and will continue to grow more and more due to the full capacity for everyone to publish data on the web freely to share information. However, that only makes quality more and more important towards the future. An approach through fuzzy logic is a solution that has many advantages, such as the ability to mathematically define quality and focus on it deeply, rather than classical mathematical approaches. However, as an example, its full potential has not been proven; in this case, the same endpoint was evaluated, which means that quality aspects were similar, apart from facts such as the need to add more and more quality dimensions and, therefore, the use of more rules and operations. Another aspect that this model must consider is a greater inclusion of the user in the evaluation of quality; due to the need to evaluate the model personally and with the help of feedback, allowing the model to be even more precise. In turn, as seen in the comparison with other recent frameworks, there are limitations both of this fuzzy logic model, and of these frameworks, which can be mitigated or complemented. It is possible to find results that allow us to verify the main functionality of this concept, that is, in the definition of relative results, instead of absolutes, as in the case of "if it has quality or does not have quality "scenario.

In summary, the key contribution of the fuzzy logic model is the capacity of the quality calculation of Linked Open Data, related within the datasets, in a precise and controlled manner with a large number of variables and dimensions of quality to measure. As future work, we mainly seek to add a greater number of dimensions to achieve a global quality of the data, while adapting this model to other research techniques within the LOD field with different means and alternatives, according to the evolution of these data.

Fig. 3 .

 3 Fig. 3. Fuzzy logic model for the first case, response time. Source: Own elaboration

  user of them. The Trustworthiness is measured in an interval [-1,1] that considers -1 as absolute distrust and 1 as absolute confidence.

Fig. 4 .

 4 Fig. 4. Fuzzy logic model for the first case, response time. Source: Own elaboration

Fig. 5 .

 5 Fig. 5. Infrastructure of the Implemented Model. Source: Own elaboration

Fig. 6 .

 6 Fig. 6. Graph of the Quality the Results, First Case. Source: Own.

Fig. 7 .

 7 Fig. 7. Graph of the Quality of the Results, Second Case. Source: Own.

Table 1 .

 1 Examples of results of response times, Source: Own.

	Dataset Name	Calculated Response Time
	Czech municipalities	48.1128183467
	Job applicants in regions of Czech Republic	47.8042141867
	Institutional research plans	49.1565653333
	R&D Programmes	47.9116424533

Table 2 .

 2 Examples of scalability results. Source. Own elaboration

	Dataset Name	Calculated	Scalability
		Result
	Czech municipalities	0.917890563599
	Job applicants in regions of Czech Republic	0.891315467557
	Institutional research plans	0.937077953964
	R&D Programmes	0.921803070866