Anastasios Rigos
email: a.rigos@aegean.gr

George E Tsekouras

Antonios Chatzipavlis
email: a.chatzipavlis@marine.aegean.gr

Adonis F Velegrakis

Modeling Beach Rotation Using a Novel Legendre Polynomial Feedforward Neural Network Trained by Nonlinear Constrained Optimization

Keywords: Beach rotation, feedforward neural network, Legendre polynomials, perched beach, nonlinear constrained optimization

A Legendre polynomial feedforward neural network is proposed to model/predict beach rotation. The study area is the reef-fronted Ammoudara beach, located at the northern coastline of Crete Island (Greece). Specialized experimental devices were deployed to generate a set of input-output data concerning the inshore bathymetry, the wave conditions and the shoreline position. The presence of the fronting beachrock reef (parallel to the shoreline) increases complexity and imposes high non-linear effects. The use of Legendre polynomials enables the network to capture data non-linearities. However, in order to maintain specific functional requirements, the connection weights must be confined within a pre-determined domain of values; it turns out that the network's training process constitutes a constrained nonlinear programming problem, solved by the barrier method. The performance of the network is compared to other two neural-based approaches. Simulations show that the proposed network achieves a superior performance, which could be improved if an additional wave parameter (wave direction) was to be included in the input variables.

Introduction

Beach rotation refers to the realignment of the beach shoreline due mainly to lateral (alongshore) sediment movement caused by shifts in incident wave energy [START_REF] Thomas | A Centurial Record of Beach Rotation[END_REF]. The phenomenon is controlled by the wave-coastal morphology interaction that can result in large localized changes in shoreline position (retreat or advance) and, thus, in changes of the beach planform which, however, may not lead to long term sediment loss or gain; beaches often return to their initial planform with the changes being often seasonal [START_REF] Thomas | Mesoscale Morphological Change, Beach Rotation and Storm Climate Influences along a Macrotidal Embayed Beach[END_REF][START_REF] Ranasinghe | The Southern Oscillation Index, Wave Climate and Beach Rotation[END_REF][START_REF] Klein | Seasonal-term Beach Rotation Processes in Distinct Headland Bay Systems[END_REF]. Although beach rotation has been considered/modeled as an alongshore sediment transport process, recent research suggests a more complex beach response to wave energy, whereby alongshore variability in cross-shore sediment fluxes may also be significant [START_REF] Thomas | Mesoscale Morphological Change, Beach Rotation and Storm Climate Influences along a Macrotidal Embayed Beach[END_REF][START_REF] Harley | New insights into embayed beach rotation: The importance of wave exposure and cross-shore processes[END_REF]. Beach rotation processes are expected to be more complicated in the case of perched beaches i.e. beaches that are fronted by natural or artificial reefs [START_REF] Gallop | The influence of lime-stone reefs on storm erosion and recovery of a perched beach[END_REF], as the sediment dynamics and morhodynamics of these beaches are controlled also by the reef's depth and morphology. Wave transformation and breaking over the reef can induce high non-linear effects [START_REF] Gallop | The influence of coastal reefs on spatial variability in seasonal sand fluxes[END_REF][START_REF] Velegrakis | Shoreline variability of an urban beach fronted by a beachrock reef from video imagery[END_REF]. As a result, the standard modeling methodologies require complex mathematical structures with extremely high computational costs [START_REF] Ranasinghe | The Southern Oscillation Index, Wave Climate and Beach Rotation[END_REF][START_REF] Klein | Seasonal-term Beach Rotation Processes in Distinct Headland Bay Systems[END_REF][START_REF] Harley | New insights into embayed beach rotation: The importance of wave exposure and cross-shore processes[END_REF][START_REF] Lowe | Morphological constraints to wave-driven circulation in coastal reef-lagoon systems: A numerical study[END_REF].

On the other hand, polynomial functions are in the position to effectively model data nonlinearities [START_REF] Rigos | A Chebyshev polynomial radial basis function neural network for automated shoreline extraction from coastal imagery[END_REF]. Polynomial neural networks utilize polynomials to represent the nodes' activation functions and, thus, increase modeling capabilities. Ma and Khorasani [START_REF] Ma | Constructive feedforward neural networks using Hermite polynomial activation functions[END_REF] incorporated into the network's structure Hermite polynomials, where the corresponding parameters were optimized in terms of an adaptive learning scheme. Lee and Jeng [START_REF] Lee | The Chebyshev-polynomials-based unified model neural networks for function approximation[END_REF] used tensor products to develop a Chebysev polynomial type network, whereas Patra et al. [START_REF] Patra | Nonlinear channel equalization for wireless communication systems using Legendre neural networks[END_REF] performed nonlinear channel equalization for wireless communication systems in terms of a Legendre polynomial-based neural network. Although the above approaches show good testing performances, they use high number of nodes and thus, can hardly be applied to high dimensional nonlinear problems. In comparison, Chebyshev polynomial radial basis function and neuralfuzzy networks were developed to perform efficient shoreline extraction from coastal imagery [START_REF] Rigos | A Chebyshev polynomial radial basis function neural network for automated shoreline extraction from coastal imagery[END_REF] and predict coastal erosion [START_REF] Tsekouras | A neural-fuzzy network based on Hermite polynomials to predict the coastal erosion[END_REF].

In this paper, we propose a feed-forward neural network that employs Legendre polynomials as activation functions to model the shoreline beach rotation of a perched beach (Ammoudara, Crete Fig. 1). Linear combinations of the input variables are generated and appropriately scaled by constraining the corresponding weighting parameters. The scaled functions maintain the linearity of the input variables (which is an important issue when regression analysis is to be applied) and the output is expanded into truncated Legendre series. Since the network's connection weights are constrained, the training process becomes a constrained nonlinear optimization problem solved by the barrier method.

The paper is organized as follows. Section 2 describes the experimental setup and the data acquisition process. Section 3 provides a detailed analysis of the proposed network and the training process used. Section 4 illustrates the simulation experiments, and the paper concludes in Section 5.

Experimental Setup and Raw Data Extraction

The study area is the eastern sector of Ammoudara beach, a 6.1 km long microtidal, urban perched beach, located at the west of the port of Heraklion, Crete, Greece (Fig. 1). The beach, is fronted by a submerged beachrock reef, oriented almost parallel to the shoreline, the width of which and its distance from the shoreline vary between 15-50 m and 40-70 m, respectively. Before detailing the experimental setup and the data acquisition process, it is convenient to discuss some concepts involved in the analysis as well as the physical meaning of the input-output variables used in this paper. The vertical white dashed line corresponds to one out of 52 cross-shore sections used in our experiments. Each cross-shore section is associated with a bathymetry profile, which is shown in Fig. 2(a). It is widely accepted that specific morphological characteristics of a reef can affect beach rotation; the reef acts in a similar manner to a submerged breakwater, absorbing the incoming wave energy [START_REF] Velegrakis | Shoreline variability of an urban beach fronted by a beachrock reef from video imagery[END_REF][START_REF] Lowe | Morphological constraints to wave-driven circulation in coastal reef-lagoon systems: A numerical study[END_REF][START_REF] Alexandrakis | The Effect of beach rock formation on the morphological evolution of a beach. The case study of an Eastern Mediterranean beach: Ammoudara, Greece[END_REF]. The reef morphological characteristics used as inputs are enumerated as follows (Fig. 2): the reef depth (in meters) from the sea surface is denoted as d (Fig. 2(a)), the reef inshore and offshore slopes as 1 ω and 2 ω (Fig. 2(b)) and the reef width (in meters) at 1.2 meters water depth as w (Fig. 2(b)). In the latter case, the depth of 1.2 meters was decided after a specialized data processing that showed that this reef width at this water depth had the most substantial effects. Apart from the above parameters that quantify the bathymetry characteristics, we use two more parameters that describe the wave conditions namely, the significant wave height denoted as S H (in meters), and the peak wave period symbolized P T (in seconds). Note that the last two are important as they impose a direct control on beach morphodynamics [START_REF] Thomas | A Centurial Record of Beach Rotation[END_REF][START_REF] Ranasinghe | The Southern Oscillation Index, Wave Climate and Beach Rotation[END_REF][START_REF] Gallop | The influence of coastal reefs on spatial variability in seasonal sand fluxes[END_REF]. All above parameters form the input variables of our analysis. The output variable quantifying beach rotation is the distance (in meters) from the reef top point (crown) to the shoreline denoted as y in Fig. 2(a). Indeed, the variability of this parameter (cross-shore distance) along the shoreline defines beach rotation [START_REF] Thomas | A Centurial Record of Beach Rotation[END_REF][START_REF] Thomas | Mesoscale Morphological Change, Beach Rotation and Storm Climate Influences along a Macrotidal Embayed Beach[END_REF][START_REF] Ranasinghe | The Southern Oscillation Index, Wave Climate and Beach Rotation[END_REF][START_REF] Klein | Seasonal-term Beach Rotation Processes in Distinct Headland Bay Systems[END_REF][START_REF] Gallop | The influence of coastal reefs on spatial variability in seasonal sand fluxes[END_REF]. In summary, the input variables are:

1 x d = , 2 1 tan x ω = , 3 2 tan x ω = , 4 x w = , 5

S

x H = , and 6

P

x T = , and the output variable is y (input variables 6 p = and one output).

The experimental methodology consists of high detailed nearshore bathymetric data, and a long-term time series (10-month period from January 2014 to November 2014) of shoreline position and wave conditions. More specifically, bathymetric data were obtained through a single beam digital Hi-Target HD 370 echo-sounder and a Differential GPS (Topcon Hipper RTK-DGPS) deployed from a very shallow draft inflatable boat. Using interpolation, from these bathymetric data 52 cross-shore sections were derived (a sample is given in Figs 1 and2). Information on the shoreline position for the 10-month period was obtained from coastal video imagery provided by a system consisting of 3 PointGrey FLEA-2 video cameras, installed on the study area, monitoring a beach stretch of 1400 m long (the fields of vision of these 3 cameras are shown in Fig 1(b)). A detailed description of the system and the automated procedure developed to extract the shoreline from the video images is provided in Velegrakis et al. [START_REF] Velegrakis | Shoreline variability of an urban beach fronted by a beachrock reef from video imagery[END_REF]. The above experiments provided the raw data for the input variables 1 4 x x -, and for the output variable y . Data concerning the variables 5 S

x H = , and 6

P

x T = were obtained by an offshore wave buoy (POSEIDON E1-M3A buoy) located about 35 km to the north of the beach (35.66 0 N and 24.99 0 E) at 1440 m water depth (see Fig. 1(a)), installed/operated by the Greek National Centre for Marine Research (GNCMR).

In total, the experimental setup generated

4148 N = input-output data of the form { } 1 ; N k k k y = x with [ ] 1 2 3 4 5 6 T k k k k k k k x x x x x x = x
. These data are going to be elaborated by the proposed neural network in order to model/predict beach rotation.

The Proposed Legendre Polynomial Feedforward Network

In this section, we introduce a feed-forward neural network (FFNN), the nodes of which utilize Legendre polynomials as activation functions. The Legendre polynomials possess powerful function approximation capabilities, and they are defined by the subsequent formula [START_REF] Bell | Special functions for scientists and engineers[END_REF],

2 1 ( ) ( 1) 2 ! n n n n n d P x x n dx   = -   (1)
where 0,1,... n = is the polynomial order. The Legendre polynomials are orthogonal for [ ]

1, 1 x ∈ -
satisfying the following inner product condition [START_REF] Patra | Nonlinear channel equalization for wireless communication systems using Legendre neural networks[END_REF][START_REF] Bell | Special functions for scientists and engineers[END_REF],

1 1 2 ( ) ( ) 2 , 1 0, m n P x P x m n m dx n n -   = ≠  = +   ∫ (2)
In addition, they can be generated by the next recurrent relations [START_REF] Bell | Special functions for scientists and engineers[END_REF], ( ) ( ) ( ) ( )

1 2 0 1 1 ( ) 2 1 ( ) 1; ( ) ; 2 1 n n n P x P x x P f x n xP x n r n o P x n - - = - --     = = ≥ (3)
Let us assume that the available input-output dataset is denoted as,

( ) { } 1 2
, : [ , ,..., ] , 1, 2,...,

T k k k k k kp S y x x x k N = = = x x ( 4
)
where p is the dimension of the input space, and N is the number of the training data (note that in the application discussed in this paper: 6 p = and 4148 N =

). The proposed neural network is illustrated in Fig. 3. There are four layers involved. Given that the desired order of the Legendre polynomials is n , the Layer 1 comprises n nodes, each of which generates a linear combination of the input variables, ( )

1 p j j j h a x = = ∑ x   (5)
where 1 n ≤ ≤  , 1 j p ≤ ≤ , and j a  are the weight parameters.

The Layer 2 applies a scaling procedure, which maps the values of ( ) ( )

1 h n ≤ ≤ x   in the interval [ ] 1, 1 - .
Fig. 3 The Legendre polynomial feedforward neural network.

As mentioned above, the reason for this scaling procedure is that the Legendre polynomials are orthogonal in the interval [ ] 1, 1 and therefore, they are able to operate only in this interval. To accomplish this task, we introduce a specialized methodology that maintains the linearity with respect to the original inputs. We denote the domain of values associated with j -th input variable as , a and the upper bound U a are pre- selected in terms of a trial-and-error approach as to obtain the best possible results, and are kept fixed throughout the whole learning process.

L U j j j D x x   =   , meaning that L U j j j x x x ≤ ≤ .
The question is to find a transformation to map the functions ( )

h x  in the interval [ ] 1, 1 -
. Based on the interval arithmetic [START_REF] Moore | Interval Analysis[END_REF] the multiplication of the intervals ,

L U j j j D x x   =   and [ ] , L U
A a a = gives the interval ,

j j L U     with, { } min , , , L U L U j L j L j U j U j L a x a x a x a x = (6) { } max , , , L U L U j L j L j U j U j U a x a x a x a x = (7)
Therefore, ( )

1 j j j j L a x U j p ≤ ≤ ≤ ≤  (8)
For all input variables we add the above inequalities, and using eq. ( 5), ( )

1 1 1 p p p j j j j L U j j j L a x U Q h Q = = = ≤ ≤ ⇒ ≤ ≤ ∑ ∑ ∑ x   (9)
where

1 p L j j Q L = = ∑ and 1 p U j j Q U = = ∑ . Thus, ( ) [ ] , L U h Q Q ∈ ∀ x   .
The question of finding a transformation to map the functions ( ) ( )

1 h n ≤ ≤ x  
in the interval

Scaling ( )

n h x 2 ( ) h x 1 ( ) h x 1 ( ) h x  2 ( ) h x  ( ) n h x  . . . . Layer 3 1 β 2 β Layer 4 [ ]
( ) ( ) 2 U L U L U L Q Q h h Q Q Q Q + = - - - x x    (10)
where ( ) [ ]

1, 1 h ∈ - x   . By setting ( ) 2 U L R Q Q = - , ( ) ( ) U L U L Q Q Q Q Ω = + -
and taking into account the eq. ( 5), the eq. ( 10) yields, ( )

1 1 p p j j j j j j h R a x R a x = = = -Ω = -Ω ∑ ∑ x     (11)
The above equation directly indicates that the scaled functions ( ) ( )

1 h n ≤ ≤ x   
are linear combinations of the input variables, something very important for the regression analysis that follows.

The Layer 3 includes n nodes with activation functions the Legendre polynomials of the linear combinations reported in eq. ( 11), (

p j j j P P h P R a x =   = = -Ω       ∑ x x       ) ( ) ( )
Note that, based on (3), the zero order polynomial ( ) 0 P x is always equal to one and has no effect on the input variables. Therefore, it is used as the network's bias.

Finally, the Layer 4 produces the network's estimated output by intertwining the outputs of the Layer 3, in order to expand the linear combinations of eq. ( 11) into the subsequent truncated Legendre series,

0 1 1 ˆp n j j j y P R a x β β = =   = + -Ω       ∑ ∑     (13)
The network's learning process carries out the estimation of weights j a  and β  through the minimization of the network's square error:

2 1 N SE k k k J y y = = - ∑ , which
based on the form of eq. ( 13), constitutes a regression analysis. However, to maintain

( ) [ ] 1, 1 h ∈ - x   , the following relation must hold, , j L j U a A a a a j ∈ ⇒ ≤ ≤ ∀    ( 14
)
Thus, while the estimation of ( )

1 n β ≤ ≤   is unconstrained, the estimation of ( ) 1 ; 1 j a n j p ≤ ≤ ≤ ≤   is constrained.
By splitting the double inequality in ( 14), the constrained optimization problem is now given as follows:

Minimize 2 2 0 1 1 1 1 ˆp N N n SE k k k j j k k j J y y y P R a x β β = = = =     = -= - + -Ω           ∑ ∑ ∑ ∑     (15) Subject to ( ) ( ) 0 1, 2,..., ; 1, 2,..., j j L a a a n j p φ = -+ ≤ = =    (16)
( )

( ) 0 1, 2,..., ; 1, 2,..., j j U a a a n j p ψ = -≤ = =    ( 17
)
It can be easily verified that the feasible area of the problem is convex, because it forms the intersection of plane surfaces (i.e. convex sets). To perform the optimization we could use the well-known penalty method, which approaches to the feasible area from outside [START_REF] Luenberger | Linear and nonlinear programming[END_REF]. However, we are required not to leave the feasible area; otherwise the Legendre polynomials would be forced to operate outside of the orthogonality region. Thus, we choose to use the barrier method [START_REF] Luenberger | Linear and nonlinear programming[END_REF], which searches for a solution only in the feasible area without leaving it. According to the barrier method, the above constrained problem can be exactly resolved by the unconstrained minimization of the following function, ( ) ( )

2 0 1 1 1 1 1 1 1 1 p p N n n k j j k j j j j F y P R a x a a β β γ φ ψ = = = = =         = - + -Ω - +               ∑ ∑ ∑ ∑∑        (18) where ( ) ( ) 1 1 1 1 p
n j j j a a φ ψ = =     +     ∑∑   
is the barrier function and γ is the barrier constant, which is required to take a sufficiently large positive value.

To perform the unconstrained minimization of F we use the steepest-descent method based on Armijo's rule [START_REF] Armijo | Minimization of functions having Lipschitz continuous first partial derivatives[END_REF]. To do so we define the vector, ( )

1
+ + +     = =     z ( 19
)
For the

1 t + iteration the learning rule is, ( 1) ( ) ( ) ( ( )) t t t F t η + = - ∇ z z z (20) where ( ) t t η λ = with ( ) 0,1 λ ∈
. The parameter t is the smallest positive integer such that, (

) F t t F t F t t F t η ε η - ∇ - < - ∇ z z z z ) ( ) 2 ( ) ( ) ( ( )) ( ) ( ) ( ( )
. Finally, the partial derivatives in eq. ( 20) and (21) can easily be derived.

Simulation Study

Based on the analysis described in Section 2, the data set includes 4148 N = input-output data pairs (corresponding to 52 beach cross-sections) of the form

{ } 1 ; N k k k y = x with [ ] 1 2 6
...

T k k k k x x x = x
and k y ∈ ℜ . The data set was divided into a training set consisting of the 60% of the original data, and a testing set consisting of the remainder 40%. Table 1 depicts the parameter setting for the Legendre polynomial neural network.

For comparison, two more neural networks were designed. The first one was a radial basis function (RBF) network. The parameters of the basis functions were estimated in terms of the conditional fuzzy clustering, which was developed in [START_REF] Pedrycz | Conditional fuzzy clustering in the design of radial basis function neural networks[END_REF], while the connection weights were calculated by the least-squares method. The second one was a feedforward neural network (FFNN), the activation functions of which read as follows, ( ) tanh 2

x f x = (22)
To train the FFNN we applied the steepest-descent based on the Armijo's rule (see previous Section) in order to minimize the network's square error. All networks were implemented using the Matlab software.

The performance index to conduct the simulations was the root mean square error,

2 1 1 N k k k RMSE y y N = = - ∑ (23)
For the three networks we considered various numbers of nodes, while for each number of nodes we run 20 different initializations. The results reported in Table 2 are visualized also in Fig. 4. There are some interesting remarks: (a) the difference between the Legendre polynomial and the remainder of the networks tested appears to be significant particularly in the testing data; (b) the RBF outperforms the FFNN in both cases; (c) although the best result for the proposed network was obtained for 4 n = , the general tendency is to obtain smaller RMSEs as the number of polynomial nodes increases.

It is very interesting to see how the above results are translated into meaningful observations as far as the beach rotation is concerned. Fig. 5 concerns a specific Although the overall prediction performance of the proposed Legendre polynomial neural network may not appear to be very satisfactory on the basis of the RMSE (9.5 meters), the following should be noted. First, Ammoudara shoreline position is characterized by high spatiotemporal variability, with the difference between the most inshore and most offshore recorded shoreline position during the 10-month monitoring period being between 3 and 8 meters [START_REF] Velegrakis | Shoreline variability of an urban beach fronted by a beachrock reef from video imagery[END_REF]; the proposed network's predictions are of the same order of magnitude and thus may be considered as satisfactory in this high non-linear coastal system, particularly as in many crossshore sections, the network's predictions were much closer to the observed shoreline position (see Fig. 5). Secondly, adjacent sections of the shoreline showed large differences in terms of beach erosion/accretion patterns, suggesting significant control by small differences in reef morphology and the direction of wave approach. Hydrodynamic modeling has shown that small differences in the angle of wave approach result in quite different inshore hydrodynamic regimes (waves and waveinduced currents), even in the case of offshore waves with the same significant wave heights ( S H ) and periods ( P T ) [8]. As the offshore wave data set did not include details on wave direction, the offshore waves used were grouped collectively as northerly waves (those waves affecting the beach); thus, the observed discrepancies could be mainly due to the absence of an additional wave parameter (angle of wave incidence) in the network input variables. As a future research, it would be interesting to test how the above results would be in the case that wave direction was included as an input variable.

Summary and Conclusions

In this paper we present a systematic methodology that includes a sophisticated experimental setup and a novel feedforward neural network to model beach rotation in a reef fronted (perched) beach (Ammoudara, Crete). A set of significant morphological and wave variables were identified that can directly affect beach rotation, which together with records of shoreline position from a coastal video imagery system were used to generate the network's input-output training data. The proposed network consists of four layers. The main task of the first and the second layers has been to obtain linear combinations of the input variables and then, to appropriately scale them before entering the third layer that comprises the Legendre polynomial activation functions. This scaling process was deemed necessary due to limitations imposed by the orthogonality of the Legendre polynomial. As a result, the weights of the linear combinations must be confined in a predetermined domain of values. Therefore, the training process of the network becomes a constrained nonlinear optimization problem, resolved by the barrier method. The comparative simulation experiments carried out showed that the proposed network can effectively model beach rotation, particularly if detailed wave direction data are available to be included as an additional input variable.

Fig. 1

 1 Fig. 1 (a) Ammoudara beach, Heraklion, Crete; the position of the offshore POSEIDON E1-M3A wave buoy is illustrated as a black dot in the inset. (b) Optical system location (diamond point), and field of vision of the 3 deployed cameras (confined within the red lines); the shoreline section examined by video imagery (i.e. detected shoreline) is shown by the dashed black line along the shoreline, with the white vertical dashed-line corresponding to one crossshore section (out of the 52 sections studied); the offshore dark grey zone parallel to the shoreline delineates the beachrock reef. (Satellite image source: Bing Maps, Microsoft)

Fig. 2

 2 Fig. 2 (a) Cross-shore bathymetric profile (see Fig. 1(b)), showing the beachrock reef and the elevation parameters. (b) Zoom on the reef showing its structural parameters.

  Note that the lower and upper bounds L j x and U j x are fixed and depend on the system data, only. Relationally, we can define an interval  and j . The values for lower bound L

Fig. 4

 4 Fig. 4 Mean values of the RMSE as a function of the number of nodes for: (a) the training data, and (b) the testing data.

Fig. 5 A

 5 Fig.5A sample of the cross-shore shoreline postion predicted by the three networks.

  shows the predictions obtained by the three methods. Based on this figure, the proposed network clearly achieves the best beach rotation prediction.

Table 1 .

 1 Parameter setting for the proposed network

	Parameter	Value	Parameter	Value
	a	L	-10	λ	0.05
	U a	10	ε	0.10
	γ	10 8

Table 2 .

 2 Comparative results in terms of the RMSE mean values and the corresponding standard deviations obtained by the three networks for various numbers

			of nodes in the hidden layer
			n=3	n=4	n=5
	Proposed	Training Data	9.838 ± 0.196	9.569± 0.208	9.594 ± 0.152
	Network	Testing Data	10.053 ± 0.183	9.438 ± 0.186	9.525 ± 0.249
	RBF	Training Data Testing Data	10.637 ± 0.113 10.627 ± 0.168	10.319 ± 0.081 10.346 ± 0.142	10.298 ± 0.092 10.299 ± 0.135
	FFNN	Training Data Testing Data	11.106 ± 0.838 11.107 ± 0.926	11.056 ± 0.799 10.856 ± 0.748	10.711 ± 0.740 10.938 ± 0.846

Acknowledgments

This research has been co-financed in 85% by the EEA GRANTS, 2009-2014, and 15% by the Public Investments Programme (PIP) of the Hellenic Republic. Project title: Recording of and Technical Responses to Coastal Erosion of Touristic Aegean island beaches (ERA BEACH).


Nicolas Tsapatsoulis
email: nicolas.tsapatsoulis@cut.ac.cy

Web Image Indexing using WICE and a learning-free Language Model

Keywords: image retrieval, web image indexing, web page parsing, language models

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

Introduction

Since the beginning of the World Wide Web (WWW) and the development of cheap digital recording and storage devices the amount of available on-line digital images, continuously increases. The increasing popularity of online social networks, like Instagram, that are based on visual information push further this tendency. As a result, effective and efficient web image indexing and retrieval schemes are of high importance and a lot of research has been devoted towards this end.

In general, image retrieval research efforts are falling into two broad categories: content-based and text-based. Content-based methods retrieve images by analyzing and comparing the content of a given image example as a starting point. Text-based methods are similar to document retrieval and retrieve images using keywords. The latter is the approach of preference both for ordinary users and search engine engineers. Besides the fact that the majority of users are familiar with text-based queries, content-based image retrieval lacks semantic meaning. Furthermore, image examples that have to be given as a query are rarely available. From the search engine perspective, text-based image retrieval methods get advantage of the well established techniques for document indexing and are integrated into a unified document retrieval framework. However, for text-based image retrieval to be feasible, images must be somehow related with specific keywords or textual description. In contemporary search engines this kind of textual description is, usually, obtained from the web page, or the document, containing the corresponding images and includes HTML alternative text, the file names of the images, captions, metadata tags and surrounding text [START_REF] Souza Coelho | Image retrieval using multiple evidence ranking[END_REF][START_REF] Datta | Image retrieval: Ideas, influences, and trends of the new age[END_REF]. Text metadata are not always available, and in most cases are not accurate (i.e., they do not fully describe the visual content of the image). In addition, disambiguation of different visual aspects of the same term is very difficult using text metadata without taking into consideration the context. Surrounding text, is the text that surrounds a Web image inside an HTML document. This text is, indeed, a very important source of semantic information for the image. However, automatic localization of surrounding text is by no means easy mainly due to the modern web-page layout formatting techniques which are based on external files (stylesheets). As a result, visual segmentation (parsing) of the rendered web-page is required in order to identify the surrounding text of an image. The need to automatically extract the semantically related, to an image, textual blocks and assign them to this image led to what we call Web Image Context Extraction (WICE). In that terms, WICE is the process of automatically assigning the textual blocks of a web document to the images of the same document they refer to [START_REF] Tryfou | Web image context extraction based on semantic representation of web page visual segments[END_REF].

In content-based image retrieval features such as color, shape or texture are used for indexing and searching web images. The user provides a target image and the system retrieves the best ranked images based on their similarity from the user's query. Although it has been a long time since the scientists, working on this area, defined the semantic gap [START_REF] Del Bimbo | Visual information retrieval[END_REF], i.e., the inability of a system to interpret images based on automatically extracted low-level features, a solution still does not exist. WICE methods may be used as a means of bridging this gap. For instance, in [START_REF] Wang | Annosearch: Image auto-annotation by search[END_REF] the authors propose an auto-annotation system which combines a content-based search stage to image annotation along with a text-based stage in order to leverage the image dataset in learning from similar annotations.

Despite the fact that image context identification and text-based image indexing is very important per se, the huge amount of images which do no appear in web-pages or they do not have a clearly related context, either as surrounding text or as specific keywords, puts another challenge. Recently, the idea of visual concept modeling [START_REF] Theodosiou | Image retrieval using keywords: The machine learning perspective[END_REF][START_REF] Xu | Automatic image annotation using modified keywords transfer mechanism base on image-keyword graph[END_REF] was proposed as possible solution to this problem. In these approaches keywords are modeled through via low-level features and nonannotated images are passed through these models in order to identify possible matches with the visual representation of the models and assigned the corresponding keywords. The approach is promising but the keyword models require proper training, usually approached as a learning by example procedure, and, thus, they depend heavily on the selected corpus and keyword identification. So far the training set was created using manually annotated data and, for quality assurance on the keyword selection, crowdsourcing methods were adopted [START_REF] Theodosiou | Modelling crowdsourcing originated keywords within the athletics domain[END_REF][START_REF] Theodosiou | Crowdsourcing annotation: Modelling keywords using low level features[END_REF]. Recently, Giannoulakis and Tsapatsoulis [START_REF] Giannoulakis | Instagram hashtags as image annotation metadata[END_REF] investigated the case of Instagram as a source for annotated images concluding that an overall 26% of hashtags accompanying photos in Instagram are related with photos' visual content. Thus, filtering approaches are still required for a proper training set to be created.

In this paper we investigate the automatic extraction of keywords, from a web-image's context, that can be used either for image indexing or for the automatic creation for training datasets for the visual modeling of keywords mentioned above. Our method deviates from existing approaches in a very important aspect: It does not require any sort of training since it is based on a priori fixed English language model to identify the importance of a keyword in a text fragment. The latter is identified through a computationally efficient visual-based html parsing algorithm. The fact that image context is in most cases concise leads traditional approaches, like probabilistic, tf-idf based and clustering based ones, to failure. Thus, image context needs to extended, but, in this case the correlation of the selected text with a specific image in the web page decreases and all images in the web-page tend to share the same indexes (which are also similar to the indexes of the web-page itself).

WICE methods

In text-based web image retrieval, image file names, anchor texts, surrounding paragraphs or even the whole text of the hosting web page are traditionally used. The user provides keywords or key phrases and text retrieval techniques are used for the retrieval of the best ranked image. Early examples of these methods include [START_REF] Alexandre | Web image indexing: Combining image analysis with text processing[END_REF][START_REF] Smith | An image and video search engine for the world-wide web[END_REF][START_REF] Ortega-Binderberger | Webmars: A Multimedia Search Engine For The World Wide Web[END_REF]. However, it turned out very soon that the relevant, to each image, text fragment of the hosting web page must be extracted for better accuracy of retrieval. This is the well-known WICE problem [START_REF] Tryfou | Web image context extraction based on semantic representation of web page visual segments[END_REF], already mentioned in introduction. The high diversity of designing patterns in web pages, the noisy environment (advertisements, graphics, navigational objects etc), end the existence of too much textual and visual information in single documents are prohibiting factors a WICE system must overcome.

Several WICE methods have been proposed in the literature. A first category of approaches as [START_REF] Fauzi | Webpage segmentation for extracting images and their surrounding contextual information[END_REF] and [START_REF] Alcic | A clustering-based approach to web image context extraction[END_REF], make use of the DOM tree structure of the hosting web page. In general these methods are not adaptive and they are designed for specific design patterns.

Web page visual segmentation is a second category of approaches to the WICE problem. This kind of approaches was initially proposed in [START_REF] He | Clustering and searching www images using link and page layout analysis[END_REF], where the authors use Vision based Page Segmentation (VIPS) [START_REF] Cai | Vips: a vision based page segmentation algorithm[END_REF] in order to extract blocks, which contain both image and text, and construct an image graph using link structures. Web page segmentation is indeed a more adequate solution to the problem of text extraction since it is adaptable to different web page styles and depends on the visual cues that form each web page. Most of the proposed algorithms falling within this approach they are computationally heavy [START_REF] Tryfou | Using visual cues for the extraction of web image semantic information[END_REF] and they are not designed specifically for the problem of image indexing [START_REF] Tryfou | Extraction of web image information: Semantic or visual cues?[END_REF]; therefore, they often deliver poor results [START_REF] Alcic | Measuring performance of web image context extraction[END_REF]. In addition the creators of VIPS stopped its maintenance as early as in 2011.

In the proposed approach, the WICE problem is tackled through HTML code parsing of the rendered web page. This approach is computationally light and easily applicable and in modern web pages that include several CSS files, for styling purposes, as well as dynamic elements (such as PHP code), is quite effective. It executes html parsing by combining the ideas and the tool presented in [START_REF] Pappas | Extracting informative textual parts from web pages containing user-generated content[END_REF] with the open source code of Mozilla web browser1 .

Web image indexing from concise text fragments

The text fragments identified by WICE methods are usually very concise; as a result traditional keyword extraction (tf-idf like methods) does not apply. Web image retrieval based on clickthrough data is more relevant and effective. Clickthrough data are usually collected from search logs and include text queries and data from relevance feedback [START_REF] Park | A large-scale study of user image search behavior on the web[END_REF]. These methods [START_REF] Tsikrika | Image retrieval using multiple evidence ranking[END_REF][START_REF] Fang | Towards msrbing challenge: Ensemble of diverse mod-els for image retrieval[END_REF][START_REF] Hua | Clickage: Towards bridging semantic and intent gaps via mining click logs of search engines[END_REF][START_REF] Sarafis | Weighted svm from clickthrough data for image retrieval[END_REF] are quite effective but they are based on machine learning; thus, they suffer from the scalability problem and they are inappropriate for large scale web image retrieval.

The proposed method uses a learning-free language model for web image indexing using text fragments located by a new WICE method explained next.

The proposed method

The overall architecture of the proposed method is shown in Fig. 1

The WICE algorithm

The aim of the WICE algorithm is to identify the context (text fragment) of an image given its URL. First the position of the image and its (rendered) dimensions are computed with the aid of the Mozilla open source code. Small images and graphic types (i.e., gif) corresponding to logos and banners are discarded in this stage. Next the nearby sentences (text belonging to the same level as the image in the DOM tree and being within a radius equal to 0.3 of web page's rendered height from image's center) of the image are selected along with the caption, alternative text (if exists) and the hyperlink text. All these text data are merged together to form the text fragment (referred to as image context in the following) related to the given image.

An English language model for image retrieval

The relative frequency f w of appearance of a word 'w' in natural (human) languages follows the well known Zipf law [START_REF] Manning | Foundations of Statistical Natural Language Processing[END_REF]; that is the product of f w with the ranking R w of word 'w' is approximately constant:

f w • R w = c (1)
Given that the number of words in web pages is very large and continuously increasing, due to new documents, misspelling, slang, etc., the probability of

P (w) = c R w (2)
In text-based retrieval a common keyword identification method involves the well-known tf-idf score. Words, or more general, tokens [START_REF] Manning | Foundations of Statistical Natural Language Processing[END_REF] with high tf-idf score in a given document or text fragment are considered important (keywords) for its description and can be used as indices. However, while the tf (term frequency) value depends only in the specific document the idf (inverse document frequency) value is computed based on a relative large number of relevant documents. Thus, in order to compute tf-idf we need a training corpus.

In this paper, we argue that web images appear in every type of document in the web, and, as a result it is not necessary to collect a specific domain corpus to compute idf and find the keywords of a text fragment. Therefore, we approximate the idf value with 1 P (w) and we arrive in a learning free indexing method for text fragments related with web images. Equation 2 gives a rough approximation of P (w). After a little experimentation (see Table 1 for some examples) we found that a more accurate language model can be obtained by:

P (w) = c R w + k Rw (3)
where c = 0.12 and k = 1.1.

In any case, in order for a language model given above to be useful the ranking R w3 of every word should be available. In this work we get advantage of the 'Wordcount' project4 for this purpose.

Keyword extraction is facilitated by the language model and involves a series of steps: (a) text fragment segmentation into sentences, (b) stopwords removal, (c) part of speech (POS) tagging, (e) noun and proper noun selection as candidate indices, (f) ranking of selected terms based on the adopted language model, and (g) final selection of the indexing terms (keywords) based on the S = tf P (w) score (terms whose score exceeds an empirically derived threshold T are kept as keywords).

Experimental evaluation

In order to evaluate the proposed method 978 web images taken from 243 web pages were used. Three annotators (students of the Cyprus University of Technology) were asked, independently, to: (a) for each image identify and copy its context (text fragment), and (b) select the keywords from context that best describe the image. The contexts and keywords from the three annotators were merged and used as the gold standard for the evaluation of the proposed method. Indicative examples of images, their context and the keywords chosen by the annotators and found by the algorithm are online available 5 . Table 2 summarizes the results of context extraction. By TP we denote the 'True Positive' rate, that is, the tokens that were in the gold standard and found by the algorithm. Similarly FP denotes 'False Positive' rate, i.e., tokens found by the algorithm but not in the gold standard and FN denotes 'False Negative' rate, that is, tokens in the gold standard that were not found. Recall (R), Precision (P ) and F-score (F ) values are computed as usual by: R = T P T P + F N (4) P = T P T P + F P (5)

F = 2 • P • R P + R (6)
We can see in Table 2 that the algorithm tends to include in image context more tokens than those identified by the annotators. This is mainly caused by our decision to include in image context not only the nearby sentences but the tokens in image caption and image's hyperlink. The latter was typically never selected by the annotators although from several studies we know that the information in hyperlinks is of utmost importance in information retrieval. Overall, the results are satisfactory given the simplicity of the proposed method. For comparison see the results reported by Alcic & Conrad [START_REF] Alcic | A clustering-based approach to web image context extraction[END_REF]. Table 3 shows the results of keyword identification. We observe that the recall rate is close to 50% which is very promising compared to similar methods (see for instance [START_REF] Sarafis | Weighted svm from clickthrough data for image retrieval[END_REF]). Human annotators tend to use more 'emotional' words to describe images even in cases where the visual content does not correspond clearly to these terms. On the hand the proposed algorithm promotes nouns as keywords (a choice made during the design of the algorithm) and especially named entities (as a result of the use of the proposed language model). Similarly to the context extraction case the algorithm identifies, in general, more keywords than the annotators causing the recall to become higher than precision. Nevertheless, in information retrieval the tendency is to pursuit higher recall than precision (irrelevant results are better than no results).

Conclusion and further work

In this paper we have presented a method for web page image indexing which is based on language models. The method can be applied to identify keywords for any web image without training on a particular corpus. It is based on raw html parsing of web pages to identify the nearest (to the image) text block and then a metric which combines the frequency of terms in the block with their frequency ranking, in the corresponding language, is used. Preliminary results, on an especially designed and annotated web image database, are promising and show the effectiveness of the proposed method. However, there are also some limitations that need to be surpassed for the method to be widely applied while some improvements are planned for (near) future work. The effectiveness of the proposed system on 'carousel' type web images needs to be tested. Furthermore, the algorithm is currently applied only on English web pages since we get advantage of the ranking of English words to create our language model. However, once such a study for any other natural language exists the extension of the proposed method is straightforward.

An improvement of the proposed method is to consider the structure of the surrounding text to further weight the terms. Thus, terms that appear in headers, subheaders, weblinks, etc., will be given higher importance than the terms in the plain text. Finally, the method will be used in the context of visual concept modeling [START_REF] Theodosiou | Modelling crowdsourcing originated keywords within the athletics domain[END_REF] for automatic creation of image-keywords pairs that are required for training purposes. In this context, the other basic limitation of this work, that is, the inability of applying it to non-web images, will be overcome. For more information on this, please see [START_REF] Theodosiou | Image retrieval using keywords: The machine learning perspective[END_REF][START_REF] Xu | Automatic image annotation using modified keywords transfer mechanism base on image-keyword graph[END_REF].

  Finally, probabilistic, tf-idf and clustering based approaches require training. As a result the problem is recycled: In order to automatically index non-explicitly annotated images you need training examples but in order to automatically create the training examples you need train the indexing extraction algorithms! 2 Related Work

  along with an illustrative example. It consists of three main steps: (a) html parsing, obtained with the aid of the lxml parser 2 , (b) the WICE algorithm, and (c) an English language model accompanied by an keyword extraction algorithm.

Fig. 1 .

 1 Fig. 1. The architecture of the proposed method through an example

Table 1 .

 1 Examples of the performance of language model. P (w) is the actual probability of word w

	Word (w) Rw	P (w)	c Rw	c Rw +k Rw
	of	2	0.0280	0.0600	0.0374
	to	3	0.0260	0.0400	0.0277
	with	14	0.0060	0.0086	0.0067
	at	15	0.0056	0.0080	0.0063
	his	24	0.0038	0.0050	0.0035
	but	25	0.0038	0.0048	0.0034
	appearance P (w) of a word 'w' in a web page can be approximated by considering
	P (w)=f w as follows:

Table 2 .

 2 Evaluation results for context extraction. GS denotes gold standard

		# tokens in GS	# tokens found	TP	FP	FN	R	P	F-measure
	context localization	61683	65918	52267 13651 9416 0.847 0.793 0.819

Table 3 .

 3 Evaluation results for keyword identification

		# keywords in GS	# keywords found	TP	FP	FN	R	P	F-measure
	keyword identification	5966	7237	2836 3130 4401 0.475 0.392 0.430

http://www.mozilla.org/en-US/

http://lxml.de/parsing.html

http://www.wordcount.org/main.php

http://www.wordcount.org/about.html

http://cis.cut.ac.cy/ nicolas.tsapatsoulis/ckasapi/showImages.php


Paul Ștefan Popescu

Mihai Mocanu
email: mmocanu@software.ucv.ro

Costel Ionașcu
email: icostelm@yahoo.com

Marian Cristian Mihăescu

Marian Cristian Mihăescu
email: mihaescu@software.ucv.ro

Design of an Advanced Smart Forum for Tesys e-Learning Platform

Keywords: e-Learning, machine learning, forum

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

Introduction

Online educational environments are a constantly growing field of education. This field is important because it creates the opportunity to learn even when there is no physical presence like in regular educational environments. The physical presence in the classroom is important in terms of interaction because students are able to talk easily, change opinions and help each others. From the teachers perspective they can easily response to questions, and create some sort of ranking in terms of knowledge. There will always be some learners that have better knowledge in some educational areas; these learners can help share their knowledge to others.

In online educational environments interaction of any kind is different [START_REF] Tu | The Relationship of Social Presence and Interaction in Online Classes[END_REF] than in regular environments, the engagement in educational activities is also different [START_REF] Richardson | The Role of Students' Cognitive Engagement in Online Learning[END_REF] and this may lead to lower student's results [START_REF] Choo | New Benchmarks in Higher Education: Student Engagement in Online Learning[END_REF]. Going further from this lack of inter-action e-learning platforms integrates more and more smart capabilities; from better data logging that allows data analysts to accomplish more advanced data mining and machine learning tasks to advanced smart tools that offers many facilities (i.e. subjects of interest recommendations, predicting students failure or academic performance, better data logging).

In this paper we present a forum that encapsulates smart capabilities aimed to improve the student's interaction and to create a friendlier virtual environment included in e-learning platforms. The system's design aims to ensure enough flexibility to easily adjust and install in any e-Learning platform but first we will refer Tesys e-Learning platform that runs at the University of Craiova and offers us data. Tesys is a custom e-learning platform built at the University of Craiova which fulfils the professors and students needs in terms of online educational environments necessary for distance learning. The platform is under continuous development and based on the knowledge gained from we can make further development like this Smart Forum.

The forum is designed to be strongly integrated in the e-learning platform, being available in every discipline, and well isolated in terms of implementation. We don't design it as a plug-in that uses some sort of bridge to relate between forum and elearning platform. This sort of integration ensures more specific and subject related topics of discussion.

Related Work

In the area of educational data mining there has been a lot of work. This paper lies on the border of machine learning and information retrieval offering a design of a system that encapsulates feature extraction techniques that are the prerequisites for employing data mining and machine learning algorithms. Some other forums were used to employ data mining techniques and to gain more knowledge from discussions. The purpose of [START_REF] Dringus | Using data mining as a strategy for assessing asynchronous discussion forums[END_REF] is to present some data mining techniques that offer a strategy for data representation. For their approach the instructor's view of the output of a thread forum is somehow limited as the can review a transcript of the written dialogue produced by participants. Because of big amount of data that consists of forum contributions the paper seeks to intersect the information an instructor wish to extract from the forum with some useful information that the system may extract from the instructor's query. This will help the instructor to improve his ability to evaluate the progress of a threaded discussion.

There are also some other paper [START_REF] Liu | Semiautomatic Annotation of MOOC Forum Posts, Chapter State-of-the-Art and Future Directions of Smart Learning Part of the series Lecture Notes in Educational Technology[END_REF] that show that students who use discussion forums have a higher chance of finishing a course. This implies MOOCs (Massive Online Open Courses) and they use some machine learning techniques to extrapolate a small set of annotation to the whole forum. These annotations help in two main ways: summarize the state of the forum and the also allow researchers to deeper understand how the forum is implied in the learning process. Some recent research [START_REF] Romero | Predicting students' final performance from participation in on-line discussion forums[END_REF] predicts the students performance based on on-line discussion forums which are considered as communities of people learning from each other. They aim that forums not only inform the students about their peers' doubts or problems but it is a way to inform the professors about the learner's knowledge. In the paper they select some instances and attributes, run different supervised learning algorithms and then they measure the accuracy and comprehensibility of the prediction. Some related work was done for the design and development of several machine learning algorithms [START_REF] Huang | Extreme learning machine: Theory and applications[END_REF]. For the supervised learning tasks we can use decision trees [START_REF] Purdila | Fast Decision Tree Algorithm[END_REF] or regression analysis [START_REF] Chao-Ying | Ingersolla, An Introduction to Logistic Regression Analysis and Reporting[END_REF] and we aim to evaluate the system using several machine learning metrics like area under the ROC curve [START_REF] Bradley | The use of the area under the ROC curve in the evaluation of machine learning algorithms[END_REF].

Goals

Building and integrating Smart Forum aims to achieve three goals: create a virtual space for improving the users' interaction, generate more high quality logged data that can be analyzed and offering useful functionalities for improving the students' performance.

Interaction Improvement

Improving the users' interaction can be achieved by extending the means of interaction by number and quality. Forums are environments that allow message exchange, the particularity refers that the messages are most public or available for registered users and also the messages are grouped on subjects of discussion. For our approach, messages wrote on Smart Forum are available for students and instructors from a specific course. Adding a new mean of communication with specific features creates a environments which impact can be measured in terms of interaction. After the system is integrated and used for at least a semester, we evaluate the interaction and adjust some parameters like notification frequency or messages of interest alert frequency.

Data Logging

Data already logged in e-learning platforms refers users and learning resources. We threat Smart Forum as an important learning resource which can produce a important amount of data that refers both other learning resources and users. We can analyze what chapters of course were more discussed and what concepts from which chapters are referred in the most discussed topics. For user profiling we can add more data based on the actions that are perform on the forum. Logging more data can reveal several new patterns and also improve the actual models.

Improving the student's performance

This is a permanent topic of interest in the Educational Data Mining Area. There are so many solutions out there but there is also enough space for improvement. Collecting more relevant data and adding it to the existing models may lead the data analyst to better result. There are also many correlations that can be made between the forum activity and educational results, forum activity and the activity performed over other learning resources or the overall activity and final grades. One thing that may influence the student's performance is also the interaction between them and what they can learn from each other. By using the described platform one study can reveal if students that interact more and learn more from their colleagues will have better results or at least an ascending learning curve.

System Design

Smart forum creates a virtual space for interaction between all entities that perform activities in e-Learning platforms: students, professors and administrative staff. Every entity has his specific tasks that are related to their topics of interests; students discuss about the subjects related to the disciplines, professors may response to questions and may launch challenges, the administrative staff may respond to administrative questions of common interest.

Fig. 2. Forum integration

Fig. 2 presents the components that are encapsulated in a discipline. On the upper part of the picture we have the main actors that perform their activities on one discipline: students, professors, and secretaries. Every actor has his own interface and access to specific features of the e-Learning platform. Chapters, Homework, questions and references come at the same level with the forum and are related to the discipline covering several learning areas. The chapters are represented by documents that form the course, homework are used to assign learners tasks that take more time while questions are used for tests and exams. The forum is used to discus subjects related to a specific discipline; this makes the data collected from it to be more specific. For example, suppose a data analyst wants to analyze the subjects related to discipline "x", he needs to find the specific subjects related to the discipline "x" by using some analysis techniques which will most likely not offer 100% accuracy or the topics will have tags that were allocated by the topic initiator which will also may not offer 100% accuracy all the time. Distributing the forum over the discipline offers one more topic focus attribute over the existing ones. On the forum there will always be moderators which are represented by professors or/and best students, these moderators will make sure there will not be topics out of the discipline area on a specific forum Fig. 3. Data Analysis Pipeline Fig. 3 presents the main architecture of the data analysis pipeline. There are two main components that contribute to data logging: Smart Forum and Tesys. Although the forum is integrated in the e-learning platform, it provides a specific amount of data that can be converted in a set of features that can be combined with the features extracted from Tesys in order to build better models. There are also some specific data analysis tasks that will be performed only on the data gathered from Tesys or Smart Forum and there will be some specific tasks that will be performed only on the combined model and these tasks will not be used for validation purposes.

Validation of the system in terms o data analysis can be performed by comparing the results obtained using the combined models with the models obtained using only the features from Tesys.

Functionalities and Data Analysis Processes

In this section we present the main functionalities of the proposed system. These capabilities are specific to a forum that is integrated in an e-learning platform and are dependent on the data that is logged from the forum. There are two types of actions that are available in this forum: regular one and smart ones that includes the usage of several data mining and machine learning algorithms.

Proposed features

Several features may be extracted using Smart Forum. These features ensure better user modelling for forum activity analysis and also may improve the overall student's profile.

 NO_POSTS -number of posts written on the forum  NO_TOPICS -the number of topics started on the forum  NO_QUESTIONS -the number of questions asked on forum  NO_USEFUL_ANSWER -the number of answers written on the forum considered to be useful by other users  NO_ACTIVE_DAYS _FORUM -the number of days when the user was active on the forum  AVG_TIME_READ -the average time that passed between a new post/topic appeared and the moment of reading that post/topic  NO_CONCEPTS_COURSE -the number of concepts extracted from a course that were referred by a students in his posts. This feature will give us a view of how focused on the course is a student when he posts.  FRQ_POSTS -the frequency of posting messages on the forum  FRQ_TOPICS -the frequency of posting new topics on the forum Based on these features we can model the users and the activity but only after the experiments we can say which of the features will remain. Feature selection is a complex problem because we need to choose the features that are strongly related for the learner's activity but also we need to choose the ones that offer better results for the chosen algorithms.

Regular Functionalities

Posting new topics. Posting messages and replies to a topic, in this capability we include the possibility to edit or delete a message for a specific amount of time. It is also important here to save the original message in the database for a period so the moderators can solve any complains.

Well defined profiles. User profiles include the number of messages posted on the forum, for the current discipline but also the number of the other posts. The profiles also refer the total number of answered questions and the number of questions that were correctly answered. Still regarding the user profiles we may have the number of questions from the forum that were answered by user and was marked as useful answer by the topic initiator or other users. This capability provides us with a vision over how trustworthy the student is when he answers at questions from the forum.

Smart Functionalities

The smart functionalities make the difference between a regular discussion forum and Smart Forum. These functionalities are enhanced by some data mining and machine learning algorithms. Extracting several features from this Smart Forum creates the possibility to implement the features that makes the forum to get the "smart" attribute. Below we present the main functionalities that can be implemented and a short description.

Subjects of interest.

Based on the educational results the forum may offer some subjects of interest for students. This capability will be accomplished by performing an analysis over the student's answered questions and text analysis over the posts. If we have a match between the concepts that can be extracted from the wrong answered questions and the concepts extracted from some specific posts or topics from the forum we can recommend those posts to the students. Going further for this capability we can also see what concepts are considered interesting by the student and we can recommend him/her some topics that weren't read by him/her.

Approach. This capability can be accomplished also by having a match between concepts extracted from the forum and the concepts extracted from the topics that were read or answered by the student and the questions that were correctly answered.

There are two directions to gain the subjects that may be interesting for a student: offering the ones that are addressed a lot or the ones that reveals lower results. In order to get the ones that are the most addressed we need to perform text analysis (i.e. concept extraction) on both the questions answered and on the messages posted on forum.

Fig. 4. Overview of the matching mechanism

In Fig. 4 is presented an overview o the system. First we need to use clustering algorithms (i.e. SKM clustering algorithm [START_REF] Kanungo | An efficient k-means clustering algorithm: analysis and implementation[END_REF]) for getting the learning that are most addressed by the students and the area from the forum that is most addressed then the concepts can be extracted using stemming algorithms from both collections. Having a bigger percent of concepts that match means a better matching and then we can recommend them to be read. In order to improve students' performances we need to get the learning resources (questions and home works) on which the learner got lower results, then using stemming getting the common concepts from them. Based on posts analysis we can get the most related messages and offer them to the learner to be read. Computing trends. Computing trends for students will also be a smart capability In Fig. 5 we present an example of trend that can be computed for a student over a full semester. On the OX axe we have the weeks from 1 to 12 and on OY axe we have the student's activity. At a deeper analysis we can see that the student starts from a activity of 4.5 and have a small progress to the week 6, then there is a decline of two weeks and then he has an ascending trend until the last week of the semester. The green line with no dots on it is the trend computed based on the student's activity. As we can see in this case is an ascending trend based on the student's activity. This activity can be approximated using several attributes that defines it. Fig. 6. Trend divided in periods Fig. 6 presents the trend discretized for three periods, on the OX axe we have the weeks and on OY on every of the third graphs we have the level of activity. In Fig. 6 the grey line with dots represents the acitivity, the green line withought dots ascending trends, the blue line represents a stable trend and the red line represents an descendent trend computed for the student.

For the section a) of the Fig. 6 the first period is represented by the first three weeks and have an ascending trend. We choose week number four to start the second period because there the trend is changing and we have stable trend untill we reach week number 8 where is another trend switch. The last period consists of the last four weeks and is an ascending trend Another aproach of computing trends is presented in b) were we estimate the first 6 week at an ascending trend, then we have a descending trend between week six and 8 and then we have an ascending trend for the last weeks. This approach is easier to find if we parse the activity line during the period and brings up an allert for the user in week six as he might fail.

Approach. Computing trends based on students actions offers an overview of the student's evolution. This functionality can be accomplished using linear regression or decision trees at specific checkpoints based on the extracted features. Usually we can produce two dimensional trends that take time and another attribute on both axes but that will be one chart for every attribute that can model a student and it is hard to estimate the trend. Our approach collects data from the forum and computes the features from section 5.1; based on them we have two alternatives to address this issue.

Regression approach: The regression approach aims to compute an estimated grade based on the features and add it on a chart having the time stamp and the grade on the axes.

Y i =B 0 +B 1 X 1 +…+B n X n +E (1)
In equation ( 1) we present the computing of "Y i " which is the grade computed for week "i". The formula is standard for a linear regression and has three main components: "B i " which are the coefficients assigned to a variable "X i ", "E" which is the intercept and the variables "X" which represents one of the attributes that models a instance. For every week we need to compute an "Y" and place it on the plot; further analysis of the plot will lead us to the trend analysis.

Machine Learning approach: This approach aims to estimate the grade via classification algorithms and more exactly decision trees. We will have 10 classes (one for every grade) and on the chart's axes we will have the estimated grades and the time stamp.

The main difference between these two approaches is the grade which will have certain values for the classification approach and some continuous values for regression. Comparing the results from these two approaches will lead us to make the best choice.

Alerts. Offering alerts during the semester regarding the student's failure is another capability that needs to be taken into consideration. First there are some tests that need to be performed in order to see if the student's activity on the forum will predict its success/failure or even his final grade.

Approach. The approach for computing alerts when students are at risk there is a need for some pattern matching techniques. We plan to cover this approach with classification algorithms that can be employed using two or three classes. Based on the previous gathered data we can predict if a student is "at_risk" or "not_at_risk" but we also nned to perform some tests having three classes like "at_risk", "not_at_risk" and "avg_risk" where the last class can be used for students as a first warning level and then alert "at_risk" if the situation gets really bad.

Conclusions and Future Work

In this paper we presented the design and the integration approach for a forum that implements several smart functionalities that are based on underlying machine learning obtained models. Adding smart functionalities that address the goals described in the paper can improve the student's experience of the learners that perform their activities in on-line educational environments. From the many possibilities of implementing the prototype of smart forum we have chosen core algorithms that fit presented problems in terms of available input and needed task. Currently, the challenge is to choose proper machine learning algorithms and integrate with the data provided by Tesys e-Learning platform such that tasks within the smart forum may get practical and interpretable output.

The prototype version of the smart forum trains linear regression model in a predictive context for the output variable represented by the final grade. The segmented analysis provides finer grained trends for fixed of variable length timeframes and this approach is a more realistic one for the learning period of a student. Further analysis of trends in observed data is necessary as a mean to get an insight in the learning activity patterns of the students.

The second smart capability modelled as a classification problem and the linear regression model is used as a decision boundary between students "at_risk" or "not_at_risk". Further validation of derived models is needed such that confidence values in obtained predictions and classification are obtained.

As future work, improving the logging mechanism from Tesys and smart form will provide better and comprehensive real world datasets and thus the ability to extract features for better describing the observations from the training dataset.

Another improvement regards implementing more functionality in smart forum for processing the activity traces with the task of creating better student models.

Fig. 1 .

 1 Fig. 1. Tesys disciplines distribution

Fig. 5 .

 5 Fig. 5. Trend Example

available in Smart Forum. This capability is referring by drawing some charts that will reveal how the number of posts, number of questions answered that were marked as useful, number of questions asked or number of topics read are varying over the time. This can be useful for predicting but also for measuring the student's engagement over the platform and, more specific, over the smart forum.