Simplicial principal component analysis for density functions in Bayes spaces Probability density functions are frequently used to characterize the distributional properties of large-scale database systems. As functional compositions, densities primarily carry relative information. As such, standard methods of functional data analysis (FDA) are not appropriate for their statistical processing. The specific features of density functions are accounted for in Bayes spaces, which result from the generalization to the infinite dimensional setting of the Aitchison geometry for compositional data. The aim is to build up a concise methodology for functional principal component analysis of densities. A simplicial functional principal component analysis (SFPCA) is proposed, based on the geometry of the Bayes space B 2 of functional compositions. SFPCA is performed by exploiting the centred log-ratio transform, an isometric isomorphism between B 2 and L 2 which enables one to resort to standard FDA tools. The advantages of the proposed approach with respect to existing techniques are demonstrated using simulated data and a real-world example of population pyramids in Upper Austria. Nowadays, an increasing number of studies are based on complex data, such as curves, surfaces or images. As a direct consequence, the importance of Functional Data Analysis (FDA, e.g., Ramsay and Silverman, 2002 , and references therein) has recently strongly increased. In recent years, a large body of literature has been developed in this field (e.g., Ramsay and Silverman, 2005; Horváth and Kokoszka, 2012 , and references therein), however, still little attention has been paid to the problem of dealing with functional data that are probability density functions (Delicado, 2007 (Delicado, , 2011 Nerini and Ghattas, 2007; Zhang and Müller, 2011; Menafoglio et al., 2014a,b) . Even though it might seem that density functions are just a special case of functional data -with a constant-integral-constraint equal to one -standard FDA methods appear to be inappropriate for their treatment, as they do not consider the particular constrained nature of the data. This problem is well known in the finite dimensional setting, where specific techniques have been worked out to deal with compositional data (e.g., Aitchison, 1986; Pawlowsky-Glahn and Egozcue, 2001; Egozcue, 2009; Pawlowsky-Glahn and Buccianti, 2011 , and references therein), i.e., multivariate data carrying only relative information, usually represented in proportions or percentages. Those techniques are mainly based on a geometric perspective grounded on the Aitchison geometry in the simplex, which properly incorporates the compositional nature of the data. In this context, probability density functions have recently been interpreted as functional compositional data, i.e., functional data carrying only relative information. To handle this kind of data, the Aitchison geometry has been recently extended to the so called Bayes spaces:. a Hilbert space structure for σ -finite measures, including probability measures, has been worked out in Van den Boogaart et al. (2014) , based on the pioneering work of and the subsequent developments of Van den Boogaart et al. (2010) and Egozcue et al. (2013) . The name Bayes spaces comes from the primary purpose of the approach, which is to assign a simple algebraic interpretation for the basic notions of mathematical statistics (e.g., the Bayes theorem as a paradigm of information acquisition; Van den Boogaart et al., 2010) . The idea of Bayes spaces was first exploited in Delicado (2011) for the statistical analysis of density functions in the context of dimensionality reduction through multidimensional scaling. Very recently, the Hilbert space structure of probability density functions with a compact support has been used by Menafoglio et al. (2014a,b) to elaborate a kriging methodology for probability density functions.. The aim of this work is to take a step forward in the direction of functional principal component analysis in Bayes spaces, moving from the work of Delicado (2011) . In particular, we shall geometrically solve the problem of functional principal component analysis (FPCA) in the Bayes Hilbert space of probability density functions. The sample space of compositional data -i.e., the infinite dimensional simplex -motivates the name simplicial functional principal component analysis (SFPCA). Furthermore, we will propose the use of the centred log-ratio transform (clr, Van den Boogaart et al., 2014; Menafoglio et al., 2014a) for its practical implementation. We remark that, unlike the non-linear transformations which are commonly used for probability density functions (e.g., the logarithmic transformation), the centred log-ratio transformation is an isometric isomorphism between the Bayes space of probability density functions and the space L 2 of square-integrable real measurable functions. From an application viewpoint this is extremely important, as it allows to solve the problem of FPCA with the usual L 2 geometry, while accounting for the specific features of Bayes spaces. The remaining part of the paper is organized as follows. Section 2 introduces the Bayes space of probability density functions as well as the clr-transformation which will be used for their processing. FPCA is recalled in Section 3 for L 2 data. The extension of FPCA to Bayes spaces is proposed in Section 4, and is further explored in Section 5 through a simulation study. In Section 6, we apply the developed methodology to a real case study dealing with age distributions in Upper Austria. Section 7 eventually concludes the work. The choice of an appropriate space to perform the analysis is crucial prior to any statistical processing using FDA methods. This is particularly evident in the presence of constrained data, such as functional compositions. We focused on the problem of dimensionality reduction for probability density functions. In this case, although the numerical problems resulting from the unit-integral constraint of densities could be overcome by applying an appropriate pre-processing (e.g., logtransformation), their inherent properties -as scale invariance and relative scale -are only captured when the theory of Bayes spaces is incorporated. The centred log-ratio transformation isometrically maps the Bayes space B 2 (I) into the space L 2 (I), and provides a way to easily apply the well-known FDA methods in the presence of functional compositions. In this sense, it is possible to meaningfully use the standard tools for the interpretation of FPCA (e.g., the plot of mean ± eigenfunctions), if interpreted in the light of the Aitchison geometry which takes into account the relative information captured by density functions. We note that our proposal stands in continuity with the work of Delicado (2011) , who pointed out that his most promising results were obtained through multidimensional scaling in the Bayes space B 2 (I). However, our methodological developments provide a clear direction for the extension to density functions of several methods which are in use in FDA, besides opening a variety of challenges for the future. One of these is the possibility of considering alternative computational tools, such as the log-ratio transformations with respect to an orthonormal basis in the Bayes space, with the aim of avoiding the zero-integral constraint resulting from the clr-transformation. Even more promising could be the possibility of extending the support I to the general case of the whole real line (or any Borel subset) as proposed in Van den Boogaart et al. (2014) . The choice of a non-uniform reference measure still needs to be thoroughly discussed in terms of applicative consequences, and certainly deserves to be further investigated. ) -Czech Republic. Moreover, Dr. Jitka Machalová (Palacký University in Olomouc) is thanked for the computation of smoothed densities related to the dataset in Section 5.

O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O B I O O O O O O O O O O B I I I O O O O B I I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I I O B I O O O O O O O O O O O O O O O O O B I I I O O O O O O O O O O O O O O B I O O O O O O O O O B I I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Nonlinear Operator for Oriented Texture Texture is an important part of the visual world of animals and humans and their visual systems successfully detect, discriminate, and segment texture. Relatively recently progress was made concerning structures in the brain that are presumably responsible for texture processing. Neurophysiologists reported on the discovery of a new type of orientation selective neuron in areas V1 and V2 of the visual cortex of monkeys which they called grating cells. Such cells respond vigorously to a grating of bars of appropriate orientation, position and periodicity. In contrast to other orientation selective cells, grating cells respond very weakly or not at all to single bars which do not make part of a grating. Elsewhere we proposed a nonlinear model of this type of cell and demonstrated the advantages of grating cells with respect to the separation of texture and form information. In this paper, we use grating cell operators to obtain features and compare these operators in texture analysis tasks with commonly used feature extracting operators such as Gabor-energy and co-occurrence matrix operators. For a quantitative comparison of the discrimination properties of the concerned operators a new method is proposed which is based on the Fisher (1923) linear discriminant and the Fisher criterion. The operators are also qualitatively compared with respect to their ability to separate texture from form information and their suitability for texture segmentation. F EATURE-BASED classification and segmentation methods operate on a feature vector field that is the result of the application of a vector operator on an input image. Certain operators will be particularly effective for processing texture.. Several authors have made a comparison of the performance of various operators and features for texture segmentation. Most of these studies are based on the so-called classification result comparison [1] . In this method a segmentation algorithm is applied to a feature vector field and the segmentation performance and suitability of the used features are evaluated by using the number of misclassified pixels. One of the first studies based on this principle was performed by Weszka et al. [2] . They compared texture features based on the Fourier power spectrum, on co-occurrence matrices, and on gray level differences. Du Buf et al. [3] compared seven different types of texture features, including the co-occurrence matrix features as proposed by Haralick [4] , the methods of Unser [5] , Laws Manuscript received March 16, 1998 ; revised February 23, 1999 . The work of P. Kruizinga was supported by a grant from the Massively Parallel Computing Programme of the Dutch Organization for Scientific Research (NWO) and by a grant by Foundation National Computing Facilities of NWO. The associate editor coordinating the review of this manuscript and approving it for publication was Prof. Robert J. Schalkoff.. The authors are with the Institute of Mathematics and Computing Science, University of Groningen, 9700 AV Groningen, The Netherlands (e-mail: peterkr@cs.rug.nl; petkov@cs.rug.nl).. Publisher Item Identifier S 1057-7149(99)07573-9.. [6], and Mitchell [7] , the fractal dimension approach [8] , and a method based on general operator processor (GOP) operations [9] . They used the boundary error in the segmentation result as a comparison measure. In [10] Ohanian and Dubes discussed four types of texture features, by comparing the error rates in the segmentation result. They considered co-occurrence matrix features, Gabor features [11] , [12] , Markov random field features [13] , and fractal features. Other recent studies in which the classification result comparison method was used include [14] - [16] . The segmentation algorithms that were applied in these studies classify individual pixels using their associated feature vectors. In a recent study, Ojala et al. [17] used a different segmentation algorithm that performs the pixel classification on the basis of the distribution of the feature vectors in the surrounding of the concerned pixel. They compared the following four texture features: gray level differences, Laws texture features, center-symmetric covariance features, and local binary patterns. A comparison between four segmentation algorithms was made by Wang et al. [18] using co-occurrence matrix features. A more theoretical study was carried out by Conners and Harlow [1] . They made a comparison of the texture features that were used by Weszka et al. [2] and used the amount of texture-context information that is contained in the intermediate matrices as a quality measure of the texture features.. In this paper, we assess the properties of a new type of texture operator and compare it with existing texture operators. This new operator has been inspired by the function of a recently discovered type of an orientation-selective neuron in areas V1 and V2 of the visual cortex of monkeys, called the grating cell [19] , [20] . About 4% of the cells in V1 and 1.6% of the cells in V2 can be characterized as grating cells and it is estimated that about 4 million grating cells in V1 subserve the central 4 of vision [20] . Similarly to other orientation selective neurons, such as simple, complex, and hyper-complex cells [21] - [23] , grating cells respond vigorously to a grating of bars of appropriate orientation, position, and periodicity. In contrast to other orientation selective cells, grating cells respond very weakly or do not respond at all to single bars, this means, bars which are isolated and do not make part of a grating. This behavior of grating cells cannot be explained by linear filtering followed by half-wave rectification as in the case of simple cells [24] - [28] , neither can it be explained by three-stage models of the type used for complex cells [29] - [33] . Most grating cells start to respond when a grating of a few bars (2-5) is presented. In most cases the response rises linearly with the number of bars in the grating up to a given number (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) after which it quickly saturates and the addition of new bars to the grating causes the response to rise only slightly or not to rise at all and in some cases 1057-7149/99$10.00 © 1999 IEEE even to decline. Similarly, the response rises with the length of the bars up to a given length after which saturation and in some cases inhibition is observed. The responses to moving gratings are unmodulated and do not depend on the direction of movement. The dependence of the response on contrast shows a switching characteristic, in that turn-on and saturation contrast values lie pretty close: the most sensitive grating cells start to respond at a contrast of 1% and level off at 3%. In general, grating cells are more selective than simple cells, having half-response spatial frequency bandwidths in the range of 0.4 to 1.4 octaves, with median 1 octave, and half-response orientation bandwidths of about 20 . For comparison, simple cell spatial frequency bandwidths at half response vary in the range 0.4 to 2.6 octaves with median 1.4 octave; their median orientation bandwidth is about 40 [34] .. The above properties suggest that the primary role of grating cells is to detect periodicity in oriented patterns. In previous work, we proposed a computational model of grating cells, which explains the results of the neurophysiological experiments [35] , [36] . In this paper we focus on the properties of the grating cell operator as a texture analysis operator. It is compared with other, commonly used texture operators. For a quantitative comparison, however, we do not use the classification result comparison method that is used in most previous studies because this method characterizes the joint performance of a feature operator and a subsequent classifier. We rather propose a new method which characterizes the feature operator only. This method is based on a statistical approach to evaluate the capability of a feature operator to discriminate two textures by quantifying the distance between the corresponding clusters of points in the feature space according to Fisher's criterion [37] , [38] .. The paper is organized as follows: in Section II we review the Gabor filter; the output of the Gabor filter is used as input to the grating cell operator. Gabor-energy features that are closely related to Gabor filters are introduced. The computational model of grating cells is given in Section III. In Section IV, the co-occurrence matrix features are described. The texture analysis properties of the grating cell operator, the Gaborenergy operator, and a co-occurrence matrix based operator are examined and compared in Section V in a series of computational experiments. In Section VI we summarize the results of the study and draw conclusions. In order to compare the texture segmentation performance of the grating cell operator with the two other texture operators, we applied the operators to three test images to obtain feature vector fields to which the -means segmentation algorithm was applied. The results are shown in Fig. 14. The leftmost column shows the input images with two, five, and nine different textures, respectively. The perfect segmentations (ground truth) of these images are shown in the second column. The other three columns show the segmentation results based on the three vector operators considered above.. It is clear that the results obtained with the grating cell features are considerably better than the results obtained with the other two types of features. The only misclassified pixels are located near the texture borders. This is due to the fact that two or more different textures fall in the receptive field of the grating cell operator, causing an inaccurate estimate of the feature vector. Because of the large distance between the clusters of feature vectors, such inaccurate estimates do not immediately result in misclassification.. The segmentation based on the Gabor-energy operator features (Fig. 14, second column from the right) is clearly worse than the one based on the grating cell operator. Even the segmentation of two textures is poor. When more different textures are added, segmentation performance decreases rapidly. Pixels are classified incorrectly not only at the texture border but also inside a texture region. The rightmost column of Fig. 14 shows the segmentation results obtained with the co-occurrence matrix operator. The same effect is observed as with the Gabor-energy operator. The segmentation of the image which contains just two texture images is correct, but for more than two textures, the segmentation results get worse very quickly.

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Entropy-Functional-Based Online Adaptive Decision Fusion Framework With Application to Wildfire Detection in Video Abstract-In this paper, an entropy-functional-based online adaptive decision fusion (EADF) framework is developed for image analysis and computer vision applications. In this framework, it is assumed that the compound algorithm consists of several subalgorithms, each of which yields its own decision as a real number centered around zero, representing the confidence level of that particular subalgorithm. Decision values are linearly combined with weights that are updated online according to an active fusion method based on performing entropic projections onto convex sets describing subalgorithms. It is assumed that there is an oracle, who is usually a human operator, providing feedback to the decision fusion method. A video-based wildfire detection system was developed to evaluate the performance of the decision fusion algorithm. In this case, image data arrive sequentially, and the oracle is the security guard of the forest lookout tower, verifying the decision of the combined algorithm. The simulation results are presented.Index Terms-Active learning, decision fusion, entropy maximization, online learning, projections onto convex sets, wildfire detection using video. An EADF is proposed for image analysis and computer vision applications with drifting concepts. In this framework, it is assumed that the main algorithm for a specific application is composed of several subalgorithms, each of which yields its own decision as a real number centered around zero, representing its confidence level. Decision values are linearly combined with weights, which are updated online by performing nonorthogonal e-projections onto convex sets describing subalgorithms. This general framework is applied to a real computer vision problem of wildfire detection. The proposed adaptive decision fusion strategy takes into account the feedback from guards of forest watch towers. Experimental results show that the learning duration is decreased with the proposed online adaptive fusion scheme. It is also observed that error rate of the proposed method is the lowest in our data set, compared with the ULP and the NLMS-based schemes.. The proposed framework for decision fusion is suitable for problems with concept drift. At each stage of the algorithm, the method tracks the changes in the nature of the problem by performing an nonorthogonal e-projection onto a hyperplane describing the decision of the oracle.

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One iteration CHC algorithm for learning Bayesian networks: an effective and efficient algorithm for high dimensional problems Abstract It is well known that learning Bayesian networks from data is an NP-hard problem. For this reason, usually metaheuristics or approximate algorithms have been used to provide a good solution. In particular, the family of hill climbing algorithms has a key role in this scenario because of its good trade-off between computational demand and the quality of the learned models. In addition, these algorithms have several good theoretical properties. In spite of these characteristics of quality and efficiency, when it comes to dealing with high-dimensional datasets, they can be improved upon, and this is the goal of this paper. Recent papers have tackled this problem, usually by dividing the learning task into two or more iterations or phases. The first phase aims to constrain the search space, and, once the space is pruned, the second one consists of a (local) search in this constrained search space. Normally, the first iteration is the one with the highest computational complexity. One such algorithm is constrained hill climbing (CHC), which in its initial iteration not only progressively constrains the search space, but also learns good quality Bayesian networks. A second iteration, or even more, is used in order to improve these networks and also to ensure the good theoretical properties exhibited by the classical hill climbing algorithm. In this latter algorithm we can see that the first iteration is extremely fast when compared to simi- lar algorithms, but the performance decays over the rest of the iterations with respect to the saved CPU time. In this paper, we present an improvement on this CHC algorithm, in which, to put it, briefly, we avoid the last iteration while still obtaining the same theoretical properties. Furthermore, we experimentally test the proposed algorithms over a set of different domains, some of them quite large (more than 1,000 variables), in order to study their behavior in practice. The goal of data mining can be understood as compressing the available data into a more compact representation called a model. Later, this model can be used to tackle different descriptive (e.g. identifying dependences relations, clusters, etc.) or predictive (e.g. classification, computing posterior beliefs) tasks. Bayesian Networks [24, 27, 31] have become one of the favorite knowledge representation formalisms for model-based data mining because of their double descriptive/predictive capability and their innate uncertainty management.. Bayesian Networks (BNs) are graphical models that are able to efficiently represent and manipulate n-dimensional probability distributions [31] . The knowledge base that a BN encodes can be viewed as a double representation model divided into a qualitative (a directed acyclic graph or DAG) and a quantitative part (a set of locally specified probability distributions). Thus, descriptive tasks are carried out by performing relevance analysis over the graph, while predictive tasks are based on a clever use of the (in)dependences codified in the DAG to allow efficient probabilistic inference. As BNs are such attractive models, and due to the increasing availability of data, it is not strange to find such a large number of works in the literature that tackle the BN structure learning problem. Somewhat generalizing, there are two main approaches for learning BNs:. -Score+search methods A function f is used to score a network/DAG with respect to the training data, and a search method is used to look for the network with the best score. Different scoring metrics [11, 25, 30] and search methods, mainly of a heuristic (e.g. [3, 4, 9, 14, 16, 25, 30] ) and metaheuristic (e.g. [2, 8, 12, 28] ) nature have been proposed due to the NP-hardness of the BN structure learning problem [7] . -Constraint-based methods The idea underlying these methods is to satisfy as many independences present in the data as possible [30, 35] . Statistical hypotheses testing is used to determine the validity of conditional independence sentences. There also exist hybrid algorithms that combine these two approaches, e.g. [1] or even hybrid scoring metrics [11] .. Dealing with larger data sets, and therefore designing scalable algorithms, is nowadays one of the major challenges of machine learning [21] . In BN structure learning in the space of DAGs, local search-based approach (e.g. [9, 13, 14, 16, 17, 25, 30, 36] ) stands out when dealing with large datasets (very large number of variables), because of its good trade-off between the resources required (e.g. CPU time) and the accuracy of the model obtained.. Our main motivation in this paper is to scale up local search algorithms for learning BNs, such as hill climbing, while maintaining the theoretical properties that this method offers. As the cardinality of this search space is superexponential [33] , a good idea, especially in domains with a large number of variables, is to limit in the areas of the search space to be visited in some way. This idea is not new and has been exploited previously in the literature, as we will briefly review in Sect. 2.2.. Our proposal in this paper is to develop a one-stage singleiteration constrained hill climbing algorithm, with the goal of significantly reducing its running time and so applying it to databases with a larger number of variables. Our experiments confirm that the resulting hill climbing algorithm, called the FastCHC algorithm, is faster than previous approaches from the state-of-the-art algorithms, while maintaining the quality of the discovered network close to that of those learnt by this family of algorithms.. This paper is structured as follows: We begin in Sect. 2 by presenting the notation and definitions concerning BNs necessary to build our proposal. In Sect. 3, we describe in detail some local search methods for learning BNs and previous algorithms in the CHC family. Section 4 is devoted to explaining in our proposal. In Sect. 5 we describe the experiments carried out to validate our claim about the quality of our new algorithm. Finally, in Sect. 6 we present our conclusions. In this paper, we have proposed an improved version of the algorithms in the CHC family, which in turn are improved versions of the standard hill climbing approach for learning Bayesian networks. This new algorithm avoids the necessity of iterating the search algorithm by updating the constrained search space after applying the local action/operation selected at each step. This behaviour prevents the possibility that the marginally independent variables will be considered as conditionally independent when in the actual (underlying) probability distribution there are not.. Obviously, as the FastCHC algorithm requires only one iteration, it is much more efficient than previous CHC algorithms. This is clear in our experimental evaluation, in which the superiority of FastCHC over MMHC is also made evident.. Therefore, FastCHC constitutes a good candidate for learning BNs in high dimensional problems, in which scalable algorithms are required. Furthermore, because the speed up achieved with respect to competing algorithms we think that there is room to improve the quality of the discovered network, by slightly sacrificing the speed of the search. That is, for the future we plan to search more in order to search better. Thus, the idea is to use FastCHC as the basic building block for using some local search-based meta-heuristics like taboo search or simulated annealing, which have proven to able to scape from local optima.. Let D be a dataset containing m iid samples from some distribution p. LetĜ be the DAG obtained by running the learning algorithm and taking a DAG G 0 as the initial solution. Let us consider a consistent and locally consistent metric f to evaluate DAGs during the search, and finally we consider the number of cases m grows large. In the following tables, we present a summary of the results we obtained after running the 6 algorithms over the 16 domains (see Table 1 ). The summarand also the Structural Hamming Distance (SHD) with respect to the golden model (the one used to sample training and test sets). SHD is measured as in [36] , based on comparing the essential graphs.. The structural Hamming distance is computed for a pair of partially directed acyclic graphs (PDAGs). Thus, the output models obtained by each algorithm are converted into a PDAG. Then, for every pair of graphs, SHD is computed as the number of edges missing in the first graph with respect to the second, plus the number of extra edges in the first graph with respect to the second, and plus the number of edges present in both graphs but with different directions. This last set of edges includes the reversed edges and also the edges that are undirected in one of them and directed in the other. y consists of the average rank of each algorithm in each dataset, from 1 to 6, 1 being the best result. The complete list of results The best results are highlighted in bold a Those results not significantly worse than the best one can be seen in Appendix B. The MMHC algorithm could not handle many of the big datasets, especially those with 5,000 instances. The reason is that the algorithm needs more memory than that available in the computer, or the process does not finish before the set limit of 1 week. 5 In these cases, we consider that the algorithm gives a worse result than the others in order to penalize the fact that it cannot produce a result under the given conditions. For each one of the indicators, we performed a Friedman test [15] in order to discover whether we can assume that all algorithms deliver the same performance, and in the case that we cannot assume so we use the Holm's post hoc test [26] to see which algorithms can be taken as not statistically worse than the best one. In all the tests, the significance level is set to 0.05.. In Table 2 , we can see the results for the averaged likelihood of the obtained network for the five dataset sampled for validation. The Friedman test rejects the null hypothesis in all cases. Regardless of the size of the dataset, the best algorithm is always hill climbing, with CHC* not being significantly worse. MMHC is the worst in all cases. It is important to notice that FastCHC improves its rank as the dataset increases, from 4.63 to 3.60, being the only algorithm that has this improvement consistently as the size of dataset increases. Table 3 shows the second quality factor, SHD. Here the Friedman test rejects the null hypothesis in all cases as well. As in the previous case, hill climbing is the best algorithm, but now not only CHC* produces comparable results. FastCHC is also comparable to hill climbing in all sizes and iCHC and MMHC in the smaller ones.. Looking at these two result tables together we can draw the conclusion that the HC algorithm probably obtains such good results in likelihood because it overfits the network model to the data by adding many additional arcs that in turn deteriorate its performance in terms of SHD. The best results are highlighted in bold a Those results not significantly worse than the best one The best results are highlighted in bold a Those results not significantly worse than the best one Finally, we study the efficiency indicator, namely the number of statistics (scores) computed, as this number is proportional to CPU time. In Table 4 , we can see that the most efficient algorithm is FastCHC. The hill climbing algorithm is the least efficient in general. In this case, the Friedman test suggests that the null hypothesis has to be rejected, and the post hoc test indicates that only 2iCHC is not significantly worse than FastCHC.. In summary, the above tables seem to indicate that the FastCHC algorithm is the best in terms of scalability and efficiency, while HC is the best algorithm in terms of the quality of the model. However, even though the output obtained by HC is sometimes better than that obtained by FastCHC, the cost associated with this improvement may not be worth it. To support this statement, in Table 5 we show the combined result of the resulting model's likelihood and the effort required to obtain it. This is the trade-off between quality and efficiency, the ratio between the difference in likelihood for each learned model and the empty network and the number of computations each algorithm needs to obtain such a gain. It can be formulated as. , where M i, j is the model obtained by the algorithm i on the dataset j, Empt y j is the empty model estimated for the dataset j, and #computations i, j is the number of statistics computed by the algorithm i on the dataset j. This factor indicates how much benefit per computation is produced by each algorithm.. To end with the analysis of the results and as a sort of graphical summary, we represent in Fig. 2a comparison of the results obtained by the six algorithms over three dimensions: (log)likelihood, structural Hamming distance (SHD) and number of computed statistics. To allow for a fast and visual comparison, we average the result over all the datasets for each algorithm, and take the inverse when necessary, in such a way, that in all the cases, the greater the value, the worse the behaviour of the algorithm. As we can observe from Fig. 2 (and also from full results shown in Appendix B), the differences in two of the three axes (loglikelihood and SHD) are small, while the big difference appears in the third axe (number of statistics), what graphically reinforces the analysis exposed above. The idea of learning BNs in large domains by constraining the search space is not new and has been exploited previously. For example, in [5] they restrict the number of possible parents for a variable to be the k most correlated with it, and then, the K2 algorithm [10] is used to learn the BN structure. By using no restriction on the order of the nodes, we can use the Max-Min Hill Climbing (MMHC) algorithm [36] , which is also a two-step algorithm that in its first stage tries to identify the parents and children of each variable and in the second one uses a local search algorithm to look for the network, but with the search restricted to the set of previously found adjacencies (parents and children). In [29] , the first step is carried out as in MMHC but in the second phase substructures are learned using the information gathered in first phase. In [16] , an iterated hill climbing algorithm is proposed that at each (outer) iteration restricts the number of candidate parents for each variable to the k most promising ones, k having the same value for every variable.. There also exists global search methods in which the search space is also restricted, for example in [37] they first construct an undirected graph or skeleton by using zero-and first-order dependence tests, and then a genetic algorithm is employed which is restricted to searching for DAGs belonging to this skeleton. The approach taken in [39] is slightly different in that it also uses a first stage based on low order conditional independence tests.. As we can observe, the common feature in all the aforementioned algorithms is that all of them use two clearly separated stages: (1) search space restriction; and (2) running of a search algorithm over the restricted search space. In [17] , the authors propose a different way of learning BNs, namely by carrying out these two stages simultaneously. Thus, a hill climbing algorithm is launched directly without previously restricting the search space, and then it takes advantage of the computations carried out at each search step to guess which edges should not be considered from then on. In this way the search space is pruned progressively as the search advances. However, in order to maintain the nice theoretical property that under the faithfulness condition the CHC algorithm always returns a minimal I-map, at least one extra iteration should be executed. These last iterations are usually short in local steps but are time-consuming in global terms due to the extra load of computing new statistics from data. This means that the time saving with respect to previous twostage proposals diminishes, even though the first iteration is really very fast.. Our proposal in this paper is to avoid these extra iterations in order to improve the CHC algorithm significantly reducing its running time and so applying it to databases with a larger number of variables. To do this, we propose to check the restrictions applied previously for each variable parent set in order to guarantee the minimal I-map condition in only one iteration.

O O O O O O B I O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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Noisy Speech Recognition Based on Integration/Selection of Multiple Noise Suppression Methods Using Noise GMMs SUMMARY To achieve high recognition performance for a wide variety of noise and for a wide range of signal-to-noise ratio , this paper presents methods for integration of four noise reduction algorithms: spectral subtraction with smoothing of time direction , temporal domain SVDbased speech enhancement, GMM-based speech estimation and KLT-based comb-filtering. In this paper, we proposed two types of combination methods of noise suppression algorithms: selection of front-end processor and combination of results from multiple recognition processes . Recognition results on the CENSREC-1 task showed the effectiveness of our proposed methods. key words: noisy speech recognition, noise suppression method selection , CENSREC-1 In recent years, the performance of automatic speech recognition has been improved drastically by applying statistical approaches. However, most speech recognizers still have the serious problem that their recognition performance degrades in noisy environments. It is necessary to realize robust speech recognition under noisy environments for the improvement of recognition accuracy of systems . A vanety of noise suppression methods have been proposed as a front-end of speech recognition. The effect of these methods greatly depends on the noise condition.. There are strong and weak points by the kind and SNR of the noise. In general, it is thought that there are no methods which can effectively suppress various noises over a wide range of SNRs. Therefore, it may be effective to select an appropriate method to each noise condition . This selection seems to be achieved by the noise environment detection.. Some kinds of detection/identification of acoustical events or environments using Gaussian Mixture Models (GMM) have been investigated. In this paper, we propose a method to select an appropriate noise suppression method using GMM for each speech input. The use of GMMs in noisy environments has also been investigated. Lee et al. applied a GMM-based verification of noise and voice signals in a dialog system. Nishimura et al. [2] used GMM to recognize the kind of noise to reflect the behavior of a dialog system. Considering such simple and powerful noise environment classification ability, we first propose a method to select a noise suppression method suitable for a certainn noise condition based on GMM likelihood [3] . The frontend processor first selects a suppression method , applies the method to input speech, and sends the feature to the backend recognizer.. Our above-described solution uses only one recognition procedure, but we can combine several models in parallel to achieve better performance.. Fiscus proposed a first voting-based multiple recognizer output combination, ROVER [4] . ROVER and its variations [5] - [7] have achieved good word error reduction. Parallel decoding is also implemented on parallel computation systems to keep computational efficiency as single decoding systems [8] .. From the viewpoint of noise robust speech recognition, a method for dealing with diversity of noise SNR using Multi-SNR models [10] has been proposed . Matsuda et al. [9] realized the parallel decoding system considering noise environments, in which multiple acoustic models for various noise environments and multiple speech features are used in parallel and decoded on a parallel computational system.. A hypothesis combination method which combines hypotheses generated by multiple recognition systems using feature streams obtained from multiple noise suppression methods [11] has been proposed. But while some of these methods may be very good at suppressing a certain noise , others may not. Furthermore, they involve huge computational cost. In this paper, we incorporate the GMM likelihood to improve the performance considering the individual performance of the methods on the target noise [12] . We also reduce the computational cost while keeping the advantage of a hypothesis combination method.. We used CENSREC-1 (which is also called AURORA-2J [20] ) for evaluation of our method. The CENSREC-1 is a Japanese version of AURORA-2 [13], a common evaluation framework for the noisy connected English digit speech recognition task. We proposed the automatic selection of noise suppression method using GMM corresponding to each noise suppression method. We also proposed an iterative training of HMMs and GMMs for multi-conditional training.. We first proposed to apply the method selection to the frontend processing. We evaluated the proposed method using CENSREC-1 Japanese noisy connected digit speech recognition task and obtained better recognition performance than all the individual methods including the sequential combinations in both clean and multi-training. Then, we proposed the integration method in which noise suppression methods were dynamically selected using GMM in back-end. We

B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O B I I B I I I O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Argument graph as a tool for promoting collaborative online reading This study explored how the construction of an argument graph promotes students' collaborative online reading compared to note-taking. Upper secondary school students (n = 76) worked in pairs. The pairs were asked to search for and read source material on the Web for a joint essay and either construct an argument graph or take notes during online reading. The data consist of transcription protocols of student pairs' discussions and joint essays. The study indicated that argument graphs may be useful tools when teachers want students to pay attention to the argumentative content of online sources and to consider relations between arguments. Additionally, with argument graphs, teachers can support students' post-reading activities, such as source-based argumentative writing. This study indicated that the argument graph helped the students, in particular, to consider relations between arguments and to make these relations explicit. This demonstrates that with the help of an argument graph students are able to explicate their synthesizing processes more effectively. Furthermore, with argument graphs teachers can support students' post-reading activities, such as source-based argumentative writing. Compared to note-taking the argument graph aided the students to include more argumentative content and arguments in their essays. Thus, constructing an argument graph during online reading may support students in identifying arguments in texts, elaborating them jointly, and including arguments systematically in their joint essay. Additional advantages may be achieved with more thorough and explicit instructions and by using the argument graph tool several times during lessons. As many other digital computer tools, the argument graph tool is technically easy to use. Therefore, support for students on the appropriate use of the argument graph should, instead of technical matters, rather focus on higher-order thinking skills, such as understanding the argumentative structure and relations between the arguments in a text. Table 2 . Content categories of the essays. This study indicated that construction of an argument graph may promote students'. collaborative online reading and source-based writing in three ways. First, the pairs in the argument graph group spent less time on locating information during online reading than the pairs in the note-taking group. This means that the students who used the argument graph had more time to concentrate on reading to synthesize information, which best supports developing an understanding of an issue, than the students who took notes. Since in previous studies (e.g. Henry, 2006) locating information has been shown to be a gate-keeping skill for some online readers, further research is needed to explore in what ways an argument graph can support information search.. Second, the argument graph group considered noticeably more relations between concepts or arguments than the note-taking group during the online reading. This indicates that constructing an argument graph provides students with opportunities to make relations between arguments more explicit. Occasionally, the graph caused the student pairs to negotiate whether a new argument box was related to previously added arguments and whether the new argument supported or opposed the previous arguments. It should be noted that the connections that the students created between the argument boxes on their graph without commenting on them aloud are not included in the present analysis. Thus, in addition to verbalized connections the students were able to share connections through visual means provided by the argument graph tool.. Third, the argument graph group included more argumentative content and more arguments (both for the issue and in overall amount) in their essays than the note-taking group. In line with these results, Jansen, Erkens, and Kirschner (2010) found some positive effects of the use of a Graphical Debate tool on students' source-based writing. The essays of the students who used the tool contained more grounds than the essays of the students who used the Textual Debate tool. They also found that the conceptual quality of the essays of the Graphical Debate group was higher. However, no difference was found in the average quality of the grounds between the groups.. Compared to the note-taking, constructing an argument graph offers students with opportunities to construct a shared representation. Almost a third of the student pairs in the note-taking group took separate notes of their own whereas the students in the graph group shared one representation on the screen. Compared to paper-pencil notes the construction of a representation on the screen is easier to follow by both students. As the argument graph tool automatically keeps the relations between argument boxes when boxes are added or replaced, it is also easier to keep up-to-date compared to paper-pencil notes.. In addition to the advantages found here, it has previously been found that argument graphs help students to consider arguments for and against in a balanced way (Van Drie et al., 2005) . However, the present study did not support this result, as the pairs in the argument graph group presented more arguments for than against the issue in question (11.2 vs. 7.1) whereas note-taking group presented arguments in a more balanced way in the essays (6.4 vs. Online reading practices Table 3 shows that both the argument graph and note-taking groups spent most of their working time on reading to synthesize information and on locating information. The argument graph group spent almost 70.5% and the note-taking group 65.5% on reading to synthesize. The corresponding proportions of time spent on locating were 16.4% and 23.0%.. It is noteworthy that the student pairs who constructed argument graphs during online reading spent, on average, less time on locating information than the student pairs who took notes (U = 248; p < 0.05). The average number of locating episodes among the student pairs in the argument graph group was 6.95 whereas in the note-taking group it was 9.47 (U = 262.5; p < 0.05). The amount of off-task discussion was low in both groups, indicating that the students concentrated on the task.

B I O O O O O O B I O O O O O O O O B I O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O B I O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O B I O B I O O O O O O O O B I O O O O O O O O B I O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O B I O O O O O O O O O O O O O O O B I O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O B I O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Improving convergence of evolutionary multi-objective optimization with local search: a concurrent-hybrid algorithm Abstract A local search method is often introduced in an evolutionary optimization algorithm, to enhance its speed and accuracy of convergence to optimal solutions. In multiobjective optimization problems, the implementation of local search is a non-trivial task, as determining a goal for local search in presence of multiple conflicting objectives becomes a difficult task. In this paper, we borrow a multiple criteria decision making concept of employing a reference point based approach of minimizing an achievement scalarizing function and integrate it as a search operator with a concurrent approach in an evolutionary multi-objective algorithm. Simulation results of the new concurrent-hybrid algorithm on several two to four-objective problems compared to a serial approach, clearly show the importance of local search in aiding a computationally faster and accurate convergence to the Pareto optimal front. Evolutionary algorithms have been widely used to solve multi-objective optimization problems since more than a decade. Evolutionary multi-objective optimization (EMO) deals with a population of points and yields a set of solutions which are non-dominated and near to the Pareto optimal front. Some of the main advantages of using EMO algorithms include: obtaining a set of non-dominated solutions in a single run, overcoming multiple local Pareto optimal fronts easily and flexibility in handling: discrete, nonlinear, multimodal and large-scale problems. These algorithms have been commonly used in many practical problems including engineering design (Deb 2001; Coello and Lamont 2004) , financial applications (Tapia and Coello 2007) and scheduling applications (Ishibuchi and Murata 1998; Jaszkiewicz 2002; Shaw et al. 1999) .. Commonly used EMO algorithms such as non-dominated sorting genetic algorithm (NSGA-II) (Deb et al. 2002a) , strength Pareto evolutionary algorithm (SPEA) (Zitzler and Thiele 1998a) , etc. particularly focus on the distribution quality. Despite their success and wide-spread applications, these algorithms are often criticized for their lack of theoretical convergence proof to the Pareto optimal front. A past study (Laumanns et al. 2002) has demonstrated and argued that, EMO algorithms such as NSGA-II, SPEA, etc. with a finite size archive for storing non-dominated solutions, can allow an evolving population to fluctuate near the Pareto optimal front (convergence to the Pareto optimal front followed by a departure of some solutions out of the front). This phenomenon can result from a constant emphasis on the diversity maintenance pursued in EMO on a finite size population. In other words, to make the diversity among non-dominated solutions better, a Pareto optimal solution may be replaced by a non-Pareto optimal solution, as the algorithm has no way to determine the Pareto optimality of solutions without the use of any optimality conditions.. Multiple criteria decision making (MCDM) techniques (Sawaragi et al. 1985; Chankong and Haimes 1983; Miettinen 1999) are also commonly used to deal with multiobjective optimization problems. These techniques constitute a collection of approaches (Miettinen 1999) and have theoretical convergence proofs. In MCDM a multi-objective problem is often scalarized into a single-objective problem, accounting for the preference information of a human decision maker (DM) (Miettinen 1999) . Subsequently, the scalarized problem is solved by using an appropriate mathematical programming technique to find a single Pareto optimal solution. The MCDM field has many methods to solve multiobjective optimization problems. Among them, the reference point method is commonly used (Miettinen 1999) . Reference points which are formed by the aspiration values of the DM, can be utilized to derive an achievement scalarization function (Wierzbicki 1980 ). An achievement scalarization function has optimal solutions on the Pareto optimal front only (Miettinen 1999; Wierzbicki 1980) . In simple words, with this function a reference point is projected on to the Pareto optimal front.. The criticism of EMO algorithms can be bridged somewhat by incorporating MCDM approaches into EMO algorithms as a local search. The EMO algorithm as a global optimizer deploys a global search to find promising regions of importance, while a MCDM approach as a local optimizer starts from a particular solution in an EMO algorithm population and converges quickly to a locally optimal solution. The roles of global and local optimizers can be used to negotiate different multi-modal function landscapes and reach the Pareto optimal front fast and accurately. Such a hybridization shall give rise to a global search algorithm with guaranteed convergence provided the chosen local search approach guarantees converging to a local optimum. Convergence in this paper is an indicator of the proximity of non-dominated solutions generated by using an EMO algorithm to the Pareto optimal front.. Incorporating local search in an EMO approach is not easy, as the local search usually involves a single objective to be minimized. Multi-objective optimization problems involve multiple conflicting objectives and choosing one among them is unfair, as all are equally important at least during the optimization process. The principal goal of our research is to have an algorithm with two prominent features, i.e., convergence and speed to reach the Pareto optimal front and use an appropriate scalarizing function in local search. The Karush-Kuhn-Tucker (KKT) (Kuhn and Tucker 1951) termination conditions of mathematical programming techniques to be utilized in local search can be used to guarantee convergence for our concurrent-hybrid EMO algorithm. On these lines, we have suggested an approach to combine an achievement scalarizing function (to be optimized in the local search phase) with the NSGA-II. In our concurrenthybrid algorithm, any appropriate mathematical programming technique can be used in the local search phase and we fix the mathematical programming technique only during the numerical tests. In this paper, we extend our previous approach into a structured algorithm, perform extensive numerical tests including a parametric study of our concurrent-hybrid EMO algorithm and explain the interactions between an EMO algorithm and a local search to make the overall algorithm efficient. Henceforth, we refer our concurrent-hybrid EMO algorithm as the concurrent-hybrid NSGA-II algorithm.. The rest of this paper is organized as follows. In Sect. 2, we introduce some concepts and specifically describe achievement scalarizing functions. Then in Sect. 3, we summarize a broad survey of available literature on hybridization ideas suggested for EMO algorithms. Our concurrent-hybrid NSGA-II algorithm is presented in Sect. 4 with an overview on frequency of local search and termination criteria. Then Sect. 5 describes the test and parameter settings, parametric study and results obtained from the comparison studies between the concurrent-hybrid NSGA-II and serial-hybrid NSGA-II algorithms on a number of test and practical problems. This section also briefly discusses possible approaches for ensuring diversity in a concurrent-hybrid algorithm. In Sect. 6, we discuss the dynamics of our concurrent-hybrid NSGA-II algorithm. Finally, conclusions are drawn in Sect. 7. In this paper, we have argued that an efficient implementation (balance between exploration and exploitation) of a local search procedure in an EMO algorithm is not straightforward. To take advantage of fast and accurate convergence to the Pareto optimal solutions, EMO algorithms must use a continuous, directed and provable local search procedure (a mathematical programming technique with convergence proofs). In this study, we have proposed a concurrent-hybrid NSGA-II algorithm, where we have suggested an augmented achievement scalarizing function to be optimized with a local search method. The local search procedure has been implemented as an additional operator in a concurrent approach and applied to EMO populations with a varying probability. There are two prominent advantages for an achievement scalarizing function: an optimal solution of an achievement scalarizing function is always a Pareto optimal solution and any properly Pareto optimal solution can be obtained by changing the reference point. This has definitely helped EMO algorithms to improve performance. We have successfully solved several standard test problems, involving two to four objectives and two practical problems in a computationally faster way, with good diversity and accuracy.. This study has addressed a fundamental aspect of hybridizing an EMO algorithm and a local search. As the explanations and simulation results indicate, the extent of local search must be balanced with respect to global search in an EMO algorithm. This balance of exploiting current non-dominated solutions by a local search and the limited frequency of local search for allowing a proper exploration of the search space by an evolutionary algorithm is vital for a successful working of the hybrid algorithm. Here, we have used a carefully designed probability distribution function for local search to achieve this exploitation-exploration balance. However, other techniques and variants of probability functions can also be used. It remains important to investigate which mechanism would provide more flexibility and stability in the performance of the hybrid algorithm.. Achieving convergence and diversity of solutions to the Pareto optimal front are our quest. Although in this study we have relied on the NSGA-II crowding distance operator for diversity preservation, the faster and accurate convergence achieved with the proposed local search is now ready to be coupled with a more efficient and explicit diversity ensuring operator. However, the present study has clearly shown the advantage and potential of hybridizing a local search in a fast and accurate computation of Pareto optimal solutions.

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O B I I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


A QoS-aware dynamic bandwidth allocation scheme for multi-hop WiFi-based long distance networks In this paper, we propose a QoS-aware dynamic bandwidth allocation scheme to mitigate congestion problem in gateway-based multi-hop WiFi-based long distance networks and thereby enhance QoS guarantees for real-time traffic. It presents a dynamic slot scheduling scheme which efficiently distributes the unused TDMA time slots among the needy nodes. The distribution process is carried out in a hierarchical manner through the use of parent-child relationship of a tree topology. By doing so, end-to-end performance of real-time traffic is enhanced manifold. Furthermore, the proposed protocol provides assured packet forwarding for already admitted flows by allowing transmission of nodes according to the capacity of ancestral links. Simulation results show that the proposed protocol achieves a significant performance improvement in terms of throughput and delay of real-time traffic. In recent times, WiFi-based Long Distance (WiLD) networks have become very popular in bridging the rural urban digital divide. WiLD links are used to extend Internet connectivity to the remote areas and under-served regions by using only a few number of hops from gateway node [1] . The use of WiFi for covering a rural region is triggered by the wide availability of commodity IEEE 802.11 hardware at low cost and its license-free operation in the ISM band.. Voice-and video-based real-time services have become an indispensable part of today's Internet. The prospective real-time applications over WiLD networks such as videoconferencing in rural telemedicine, e-learning, and voice over IP are required to operate while meeting the user expectations. For example, voice quality of most multimedia services involving voice and video transmission deteriorate dramatically if delay increases beyond a certain limit. Similarly, bandwidth-bound applications involving video streaming expect a minimum level of [3] [4] [5] . In a typical TDMA scheme, scheduling of transmissions aim at increasing the overall network performance. In dynamic traffic situations, provisioning of dedicated bandwidth through TDMA scheduling merely solves the QoS issue. A major challenge in QoS provisioning is to schedule access to the medium based on dynamic traffic demands.. In multi-hop WiLD networks, all the links cannot be allowed to transmit at their maximum capacities even if they can do so. Otherwise, congestion is expected to occur around the root node. Therefore, transmission of the nodes towards the bottom of the tree topology should be restricted in order to avoid congestion near the root node. In such situation, end-to-end QoS provisioning becomes more challenging. MAC protocols proposed for WiLD networks in [3, 4, 6] do not address this issue, rather they focus on maximizing slot reuse among various neighboring links and thereby improving overall network performance. Although the purpose of multi-hop WiLD and sensor networks are different, they resemble in many aspects particularly in their architectures. Taking cognizance of the congestion possibility, research in sensor networks have developed some interesting MAC protocols such as presented in [7] [8] [9] [10] to avoid congestion and hence achieve high end-to-end data rate. To overcome the congestion problem, most of the protocols propose a hybrid MAC combining CSMA and TDMA protocols. Normally, CSMA-and TDMA-based protocols are suitable in low and high traffic load situations, respectively. To assign relative transmission opportunity, several metrics such as distance from the sink to the node, queue length of children node, and node's slot usage history are used. None of the above-mentioned protocols specifically address the QoS issues of real-time traffic. QDBA [11] reserves one part of the TDMA frame for real-time voice traffic and the other part is kept for the dynamic part of real-time video traffic. Dynamic rescheduling of unused TDMA slots to the needy nodes across different levels is therefore important for end-to-end QoS provisioning.. In this paper, we have proposed a dynamic QoS-aware bandwidth allocation scheme, called DQBA, to provision QoS for real-time applications in multi-hop WiLD networks. The proposed scheme classifies network traffic into two categories: real-time and best-effort. It takes the bandwidth demands of the nodes in parent-child structure and dynamically schedules channel access based on the received demands. The proposed protocol avoids congestion in the network which is otherwise inherent in multi-hop WiLD networks due to funneling effect [9] . The contributions of this paper can be listed as follows: a) a dynamic bandwidth allocation scheme based on traffic demands is proposed which ensures efficient slot reuse, b) it facilities assured traffic forwarding over multiple hops through the process of static time slot allocation, c) it provides higher priority to real-time traffic over best effort, and d) a minimum of 20% time slots are kept reserved for each node to avoid node starvation problem. The mechanisms of dynamically reusing time slots in the proposed protocol greatly improves the network performance and provide some luxury to QoS-bound traffic. The simulation results show substantial improvement in throughput and delay for real-time traffic.. The rest of the paper is organized into five sections. Section 2 takes a look on the related works and discusses the different existing TDMA-based MAC protocols proposed for WiLD as well as for sensor networks with reference to their QoS support. The assumptions, design, and algorithms of the proposed protocol have been discussed in Section 3. Simulation results of the proposed dynamic bandwidth allocation scheme and its performance comparison with TreeMAC is presented in Section 4. Finally, Section 5 concludes the paper. In this paper, we have presented a dynamic QoSaware bandwidth allocation scheme for multi-hop WiLD networks which addresses the congestion problem and hence facilitates QoS support for real-time traffic. The proposed dynamic slot scheduling mechanism efficiently distributes the unused bandwidth among the needy nodes. Twenty percent of the total available slots of each node are not allowed for distribution so as to avoid node starvation problem. Giving higher preference to the realtime traffic, the proposed protocol ensures end-to-end throughput and delay guarantees for the real-time traffic. In skewed load situations, the non-utilized time slots of the nodes are carried over multiple hops easily which provides a feel of using a dedicated link. In the best case, almost two times real-time connections can be supported by the proposed protocol than that of TreeMAC. The simulation results show that the proposed protocol achieves a substantial improvement in throughput and delay of realtime traffic. In this work, we have considered throughput and delay as QoS performance metrics. Uses of other parameters like jitter and packet loss are left as a part of future work. In the literature of WiLD networks, MAC protocols like 2P [3] , WiLDNet [4] , JazzyMAC [6] , JaldiMAC [12] , and Lit MAC [13, 14] have literally changed the face of WiLD networks. Most of these protocols focus on overall network performance enhancement. Unfortunately, QoS issues in multi-hop WiLD networks are hardly addressed. TDMA-based MAC protocols proposed in [3, 4] mainly focus on throughput optimization by generating optimal TDMA schedule considering efficient slot reuse. JazzyMAC [6] assigns variable length transmission slots according to the traffic demands of nodes. This protocol is specifically designed to allow neighbors to proceed with parallel independent transmissions without waiting for the marker packet to arrive. It causes increased throughput performance. Unlike the 2P-based MAC protocols, JaldiMAC supports single-hop point-to-multipoint network architecture which relies on loose node synchronization. It allows dynamic traffic patterns with varying symmetry ratios to adapt with the asymmetry of Internet traffic and allocates transmission slot based on demands. However, JaldiMAC cannot be scaled up for multi-hop topology with ease and will have similar problems as JazzyMAC.. Sensor network topology is predominantly tree like; mostly with low bandwidth and short distance links. Unlike traditional wireless networks, wireless sensor networks (WSNs) consist of spatially distributed autonomous sensors which do not need to communicate directly with the nearest high-power base station. Rather, the sensor nodes cooperatively pass their data through the network to a central location, called sink node, by communicating with their local peers. The nodes forward traffic hop-by-hop as such the major traffic patterns are manyto-one forming a tree [7] . Thus, the sensor network architecture has a phenomenal similarity with multi-hop WiLD networks although traffic characteristics are quite different.. In tree-based networks, nodes closer to the root need to forward more data packets than others. Traditional MAC protocols tend to provide fair access and hence are not suitable in such network architecture. If traditional MAC protocols are used in many-to-one network topology, congestion towards the root node is inevitable. Recognizing this fact in WSN, a number of protocols such as presented in [7, 8, 11, [15] [16] [17] [18] are developed. A hybrid approach using schedule-based medium access in trafficintensive regions and contention-based MAC in low traffic zones is proposed in [8, 15, 17] . Z-MAC [8] acts like a contention-based protocol under low traffic conditions and a schedule-based protocol under high traffic conditions by using the schedule computed by DRAND (Distributed RAND) [19] . It allocates time slots to every node ensuring that no two nodes among a 2-hop neighborhood are assigned the same time slot. In order to improve utilization in low load situation, Z-MAC allows 'non-owners' of a slot to contend for a slot if it is not being used by its 'owner. ' Similarly, Funneling-MAC [15] tried to mitigate the funneling problem by a sink-oriented scheduling protocol which is also a hybrid of TDMA and CSMA protocols. It uses TDMA scheduling in the intensity region and employs CSMA in the rest of the network to provide flexibility. It is localized in operation because TDMA only operates in the intensity region close to the sink and not across the complete sensor network. These two protocols employ fixed slot TDMA and hence do not provide any priority to the nodes considering their requirements. I-MAC [16] assigns different levels of priority to different nodes according to their role in the network. During scheduling of any slot, the owner of the slot gets the first priority. The non-owner nodes can compete to use a slot only when the owner node does not need it. The chance of getting a slot by a non-owner node also depends on its priority level. Queue-MAC [10] is another hybrid protocol which has addressed the issue of burst network traffic by allocating time slots of dynamic size. In this protocol, packets coming from the children nodes carry their load information through a special field called queue indicator. The frame comprises a CSMA and a TDMA component. Initially, a node starts its transmission using CSMA protocol. With an increase in load, the active TDMA period is accordingly extended by adding more time slots to increase the bandwidth. Queue-MAC considers only single-hop topology because of which it needs multi-hop extension to fit in WiLD networks.. TreeMAC [7] attempted to solve the congestion problem by using only TDMA-based MAC for the entire WSN.. In this protocol, time slots are allocated to the nodes following a two-dimensional approach. A time cycle is divided into frames and each frame into slots. A parent node determines children node's frame assignment based on their relative bandwidth demand, and each node calculates its own slot assignment according to its hop distance to the sink. Each children node notifies its parent of its bandwidth demand by piggybacking this information in a routing beacon message. Making use of queue length of all the sensor nodes, iQueue-MAC [17] assigns TDMA slots of variable size for packet transmission. iQueue-MAC uses CSMA and TDMA protocols in light and high load situations respectively. It integrates a variable namely TDMA period to provide adaptive data transmission based on children node's queue length. Utilization-based scheduling [18] used Spatial-TDMA (STDMA)-based dynamic channel access mechanism to increase throughput in wireless mesh networks. In accordance with the node's slot usage history and packet-queue occupancy, each node is assigned a dynamic weight value which approximates the node's demand for transmission slots in the next frame. The number of times TDMA slots assigned to each node in a single frame is proportional to its weight. To allocate bandwidth dynamically for real-time traffic, a QoS-aware dynamic bandwidth allocation (QDBA) scheme for WiMAX-based networks is proposed in [11] . QDBA scheme divided a TDMA frame into two parts, one is steady part for real-time voice traffic and the other is the dynamic part for real-time video traffic. The base station allocates bandwidth to the subscriber stations based on the QoS requirements of the connections.. The MAC protocols discussed above have mostly addressed the congestion issue by employing a TDMAbased MAC at high traffic load. TDMA slot assignment is further improved by incorporating adaptive or variable TDMA which allocates time slots based on demands. The traffic demand is decided from the role of a node in the network and explicit information such as queue length, slot usage history, etc. However, none of the above protocols consider provisioning QoS for the real-time traffic with dynamic bandwidth allocation in a precise manner. This motivates us in designing a dynamic bandwidth allocation scheme which will ensure end-to-end QoS for real-time traffic. Performance of the proposed bandwidth allocation scheme has been evaluated through extensive simulations in NS-2 [20] and compared with TreeMAC [7] . TreeMAC is a very similar protocol proposed for wireless sensor networks in which parent node allocates dynamic bandwidth to children nodes according to their traffic demands. The proposed protocol treats QoS-bound and besteffort traffic demands differently whereas TreeMAC does not.. The following metrics have been considered for performance evaluation of our proposed protocol:. (i) Throughput: Throughput refers to the average number of successfully delivered bytes at the destination per second. It is an important metric to provide minimum level of service in a network. (ii) Delay: It is the time difference between the time a packet was delivered at the destination and it was sent by the source node. Delay is a very essential parameter for delay-sensitive real-time traffic.. Various experiments have been conducted to analyze the impact of the proposed protocol on throughput and delay of both real-time and best-effort traffic. The simulation is carried out for a duration of 300 s. Table 1 presents the different parameters considered along with their values for the simulation purpose. Videoconferencing traffic is simulated by using VBR application. VBR and CBR applications have been used to introduce real-time (we call it as Q-demand) and best-effort (we call it as A-demand) traffic, respectively. A network topology as shown in Figure 4 is considered for the simulation purpose. Node R is the root node whereas nodes 1, 2, and 3 are intermediate, and nodes A, B, and C are leaf nodes. From this topology, different cases with 1-hop, 2-hop, and 3-hop network topology are created. We represent the real-time and best-effort traffic from a node Y as RT(Y) and BE(Y), respectively. Throughput and delay performance of the proposed scheme is analyzed in two different situations: i) when all the children nodes of a cluster have equal bandwidth demand. This scenario is simulated by offering similar Q-demands and A-demands from both the sub-trees of the root. The demands generated are gradually increased by adding more numbers of CBR connections and ii) when Q-demand is available only in a few children nodes. The other nodes may or may not have A-demand. This scenario is created by offering both Q-demands and A-demands from the left sub-tree and only A-demands from the right sub-tree. In a similar setup, all the above experiments have been carried out using TreeMAC protocol. Finally, the throughput and delay performance of DQBA is compared with TreeMAC.

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