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Graph convolutional neural networks (GCNs) have demonstrated powerful representing ability of irregular data, e.g., skeletal data and graph-structured data, providing the effective mechanism to fuse the neighbor nodes. However, inheriting from the deep learning, GCN also lacks interpretability, which hinders its application to scenarios that have high demand for transparency. Although, there have been many efforts on the interpretability of deep learning, they mainly concentrate on i.i.d data that is hard to be deployed to GCNs, which involve not only the node feature, but also the graph structure. There are few works that attempt to explain it with post-hoc manner, which can be biased, resulting in mis-representation of the true explanation. Therefore, in this paper, we propose a framework, namely ExpFiGCN, that reveals explainability of the GCNs from the perspective of graph structure and mathematical analysis. Specifically, ExpFiGCN can find the most intrinsically relevant node to the central node and obtain the informative and discriminative signals while performing denoising. For the graph structure, we find K -nearest nodes; for the mathematical analysis, every channel of a node and its neighborhoods contribute dynamically to the final channel signal, which can capture the inherent difference of different channels and neighbor nodes. Meanwhile, it can enhance the representation ability of nodes and ameliorate the over-smoothing problem. On the other hand, our model can dynamically adjust the importance of neighborhoods to the central vertex. We empirically validate the effectiveness of the proposed framework ExpFiGCN on various benchmark datasets. Experimental results show that our method achieves substantial improvements and outperforms the state-of-the-art performance strikingly. • We propose ExpFiGCN explaining GCNs by structure of graph and mathematical analysis. • Our framework effectively tackles the unequal importance of information. • Our framework ExpFiGCN implementation is simple and efficient. • Our method achieves promising results and outperform SOTA methods significantly. [ABSTRACT FROM AUTHOR]

Abstract: Numerous industrial and research databases include missing values. It is not uncommon to encounter databases that have up to a half of the entries missing, making it very difficult to mine them using data analysis methods that can work only with complete data. A common way of dealing with this problem is to impute (fill-in) the missing values. This paper evaluates how the choice of different imputation methods affects the performance of classifiers that are subsequently used with the imputed data. The experiments here focus on discrete data. This paper studies the effect of missing data imputation using five single imputation methods (a mean method, a Hot deck method, a Naı¨ve-Bayes method, and the latter two methods with a recently proposed imputation framework) and one multiple imputation method (a polytomous regression based method) on classification accuracy for six popular classifiers (RIPPER, C4.5, K-nearest-neighbor, support vector machine with polynomial and RBF kernels, and Naı¨ve-Bayes) on 15 datasets. This experimental study shows that imputation with the tested methods on average improves classification accuracy when compared to classification without imputation. Although the results show that there is no universally best imputation method, Naı¨ve-Bayes imputation is shown to give the best results for the RIPPER classifier for datasets with high amount (i.e., 40% and 50%) of missing data, polytomous regression imputation is shown to be the best for support vector machine classifier with polynomial kernel, and the application of the imputation framework is shown to be superior for the support vector machine with RBF kernel and K-nearest-neighbor. The analysis of the quality of the imputation with respect to varying amounts of missing data (i.e., between 5% and 50%) shows that all imputation methods, except for the mean imputation, improve classification error for data with more than 10% of missing data. Finally, some classifiers such as C4.5 and Naı¨ve-Bayes were found to be missing data resistant, i.e., they can produce accurate classification in the presence of missing data, while other classifiers such as K-nearest-neighbor, SVMs and RIPPER benefit from the imputation. [Copyright &y& Elsevier]

Abstract: An algorithm for polygonal approximation based on dominant point (DP) deletion is presented in this paper. The algorithm selects an initial set of DPs and starts eliminating them one by one depending upon the error associated with each DP. The associated error value is based on global measure. A local optimization of few neighboring points is performed after each deletion. Although the algorithm does not guarantee an optimal solution, the combination of local and global optimization is expected to produce optimal results. The algorithm is extensively tested on various shapes with varying number of DPs and error threshold. In general, optimal results were observed for about 96% of the times. A good comparative study is also presented in this paper [Copyright &y& Elsevier]

Abstract: This paper addresses the issue of automatic selection of the best and the optimum number of representative views for each object in a database that can enable the accurate recognition of that object from any single arbitrary view of the object. The object boundary in each view is represented by its curvature scale space (CSS) image. The CSS representation has been selected for MPEG-7 standardisation as a contour shape descriptor. The paper also presents a novel method for fusion of results from combined shape descriptors. The utilisation of this method for multi-view three-dimensional (3-D) object recognition has been explored. The object boundary of each view is represented effectively using the CSS technique, moment invariants and Fourier descriptors. It has been shown that the results obtained from the fusion method are superior to the results obtained from any single technique. The method has been tested on a collection of free-form 3-D objects. Each object has been modelled using an optimal number of silhouette contours obtained from different viewpoints. This number varies depending on the complexity of the object and the measure of expected accuracy. A comprehensive analysis of the performance of the system has been given. [Copyright &y& Elsevier]

Automatic recognition of mathematical expressions is a challenging pattern recognition problem since there are many ambiguities at different levels. On the one hand, the recognition of the symbols of the mathematical expression. On the other hand, the detection of the two-dimensional structure that relates the symbols and represents the math expression. These problems are closely related since symbol recognition is influenced by the structure of the expression, while the structure strongly depends on the symbols that are recognized. For these reasons, we present an integrated approach that combines several stochastic sources of information and is able to globally determine the most likely expression. This way, symbol segmentation, symbol recognition and structural analysis are simultaneously optimized. In this paper we define the statistical framework of a model based on two-dimensional grammars and its associated parsing algorithm. Since the search space is too large, restrictions are introduced for making the search feasible. We have developed a system that implements this approach and we report results on the large public dataset of the CROHME international competition. This approach significantly outperforms other proposals and was awarded best system using only the training dataset of the competition. [ABSTRACT FROM AUTHOR]

In this paper, we investigate ways to learn efficiently from uncertain data using belief functions. In order to extract more knowledge from imperfect and insufficient information and to improve classification accuracy, we propose a supervised learning method composed of a feature selection procedure and a two-step classification strategy. Using training information, the proposed feature selection procedure automatically determines the most informative feature subset by minimizing an objective function. The proposed two-step classification strategy further improves the decision-making accuracy by using complementary information obtained during the classification process. The performance of the proposed method was evaluated on various synthetic and real datasets. A comparison with other classification methods is also presented. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we will present a mathematical analysis of the transition proportion for the normal threshold (NorT) based on the transition method. The transition proportion is a parameter of NorT which plays an important role in the theoretical development of NorT. We will study the mathematical forms of the quadratic equation from which NorT is computed. Through this analysis, we will describe how the transition proportion affects NorT. Then, we will prove that NorT is robust to inaccurate estimations of the transition proportion. Furthermore, our analysis extends to thresholding methods that rely on Bayes rule, and it also gives the mathematical bases for potential applications of the transition proportion as a feature to estimate stroke width and detect regions of interest. In the majority of our experiments, we used a database composed of small images that were extracted from DIBCO 2009 and H-DIBCO 2010 benchmarks. However, we also report evaluations using the original (H-)DIBCO׳s benchmarks. [Copyright &y& Elsevier]

Abstract: In this paper, we propose a new approach to interactive image segmentation via kernel propagation (KP), called KP Cut. The key to success in interactive image segmentation is to preserve characteristics of the user׳s interactive input and maintain data-coherence effectively. To achieve this, we employ KP which is very effective in propagating the given supervised information into the entire data set. KP first learns a small-size seed-kernel matrix, and then propagates it into a large-size full-kernel matrix. It is based on a learned kernel, and thus can fit the given data better than a predefined kernel. Based on KP, we first generate a small-size seed-kernel matrix from the user׳s interactive input. Then, the seed-kernel matrix is propagated into the full-kernel matrix of the entire image. During the propagation, foreground objects are effectively segmented from background. Experimental results demonstrate that KP Cut effectively extracts foreground objects from background, and outperforms the state-of-the-art methods for interactive image segmentation. [Copyright &y& Elsevier]

Abstract: Several meta-learning techniques for multi-label classification (MLC), such as chaining and stacking, have already been proposed in the literature, mostly aimed at improving predictive accuracy through the exploitation of label dependencies. In this paper, we propose another technique of that kind, called dependent binary relevance (DBR) learning. DBR combines properties of both, chaining and stacking. We provide a careful analysis of the relationship between these and other techniques, specifically focusing on the underlying dependency structure and the type of training data used for model construction. Moreover, we offer an extensive empirical evaluation, in which we compare different techniques on MLC benchmark data. Our experiments provide evidence for the good performance of DBR in terms of several evaluation measures that are commonly used in MLC. [Copyright &y& Elsevier]

Abstract: This paper proposes an efficient algorithm for inexact graph matching based on spectral embedding with missing value. We commence by building an association graph model based on initial matching algorithm. Then, by dot product representation of graph with missing value, a new embedding method (co-embedding), where the correspondences between unmatched nodes are treated as missing data in an association graph, is presented. At last, a new graph matching algorithm which alternates between the co-embedding and point pattern matching is proposed. Convictive experimental results on both synthetic and real-world data demonstrate the effectiveness of the proposed graph matching algorithm. [Copyright &y& Elsevier]

Abstract: In multilabel classification tasks the aim is to find hypotheses able to predict, for each instance, a set of classes or labels rather than a single one. Some state-of-the-art multilabel learners use a thresholding strategy, which consists in computing a score for each label and then predicting the set of labels whose score is higher than a given threshold. When this score is the estimated posterior probability, the selected threshold is typically 0.5. In this paper we introduce a family of thresholding strategies which take into account the posterior probability of all possible labels to determine a different threshold for each instance. Thus, we exploit some kind of interdependence among labels to compute this threshold, which is optimal regarding a given expected loss function. We found experimentally that these strategies outperform other thresholding options for multilabel classification. They provide an efficient method to implement a learner which considers the interdependence among labels in the sense that the overall performance of the prediction of a set of labels prevails over that of each single label. [Copyright &y& Elsevier]

Abstract: The analysis of spatial relations among objects in an image is an important vision problem that involves both shape analysis and structural pattern recognition. In this paper, we propose a new approach to characterize the spatial relation along, an important feature of spatial configurations in space that has been overlooked in the literature up to now. We propose a mathematical definition of the degree to which an object A is along an object B, based on the region between A and B and a degree of elongatedness of this region. In order to better fit the perceptual meaning of the relation, distance information is included as well. In order to cover a more wide range of potential applications, both the crisp and fuzzy cases are considered. In the crisp case, the objects are represented in terms of 2D regions or 1D contours, and the definition of the alongness between them is derived from a visibility notion and from the region between the objects. However, the computational complexity of this approach leads us to the proposition of a new model to calculate the between region using the convex hull of the contours. On the fuzzy side, the region-based approach is extended. Experimental results obtained using synthetic shapes and brain structures in medical imaging corroborate the proposed model and the derived measures of alongness, thus showing that they agree with the common sense. [Copyright &y& Elsevier]

Abstract: This paper presents a novel mathematical method for incoming target detection in a cluttered background motivated by the robust properties of the human visual system (HVS). The robust detection of small targets is very important in IRST (Infrared Search and Track) applications for self-defense or attacks. HVS shows the best efficiency and robustness for the task of object detection in cluttered backgrounds. The robust properties of HVS include the contrast mechanism of figure-ground, multi-resolution representation of an object, size adaptation of object boundary, and pop-out phenomena in a complex environment. Based on these facts, a plausible computational model integrating these facts is proposed using Laplacian scale-space theory and an optimization method. Simultaneous target signal enhancement and background clutter suppression are achieved by tuning and maximizing the signal-to-clutter ratio (TM-SCR) in Laplacian scale-space. At the first stage, Tune–Max of the signal to background contrast produces candidate targets with estimated target scale. At the second stage, Tune–Max of the signal-to-clutter ratio (SCR) produces maximal SCR that is used to sort the detection results. Especially, the row-directional-local background removal filter (RD-LBRF) is preprocessed in the horizontal region to enhance the TM-SCR method. The evaluation results of incoming target sequence validate the detection capability of the proposed method from dim, small targets to strong, large targets in comparison with the Top-hat method at the same rate of false alarms. The experimental results of various cluttered background images show that the proposed TM-SCR produces less false alarms (4.3 times reduction) compared to that of the Top-hat at the same detection rate. Finally, TM-SCR after RD-LBRF can maximize the detection rate in horizontal regions. [Copyright &y& Elsevier]

Abstract: This paper presents an iterated region merging-based graph cuts algorithm which is a novel extension of the standard graph cuts algorithm. Graph cuts addresses segmentation in an optimization framework and finds a globally optimal solution to a wide class of energy functions. However, the extraction of objects in a complex background often requires a lot of user interaction. The proposed algorithm starts from the user labeled sub-graph and works iteratively to label the surrounding un-segmented regions. In each iteration, only the local neighboring regions to the labeled regions are involved in the optimization so that much interference from the far unknown regions can be significantly reduced. Meanwhile, the data models of the object and background are updated iteratively based on high confident labeled regions. The sub-graph requires less user guidance for segmentation and thus better results can be obtained under the same amount of user interaction. Experiments on benchmark datasets validated that our method yields much better segmentation results than the standard graph cuts and the Grabcut methods in either qualitative or quantitative evaluation. [Copyright &y& Elsevier]

Abstract: Finding clusters in data is a challenging problem. Given a dataset, we usually do not know the number of natural clusters hidden in the dataset. The problem is exacerbated when there is little or no additional information except the data itself. This paper proposes a general stochastic clustering method that is a simplification of nature-inspired ant-based clustering approach. It begins with a basic solution and then performs stochastic search to incrementally improve the solution until the underlying clusters emerge, resulting in automatic cluster discovery in datasets. This method differs from several recent methods in that it does not require users to input the number of clusters and it makes no explicit assumption about the underlying distribution of a dataset. Our experimental results show that the proposed method performs better than several existing methods in terms of clustering accuracy and efficiency in majority of the datasets used in this study. Our theoretical analysis shows that the proposed method has linear time and space complexities, and our empirical study shows that it can accurately and efficiently discover clusters in large datasets in which many existing methods fail to run. [Copyright &y& Elsevier]

Abstract: Linear subspace methods are extensively used in many areas such as pattern recognition and machine learning. Among them, block subspace methods are efficient in terms of the computational complexity. In this paper, we perform a thorough analysis on block subspace methods and give a theoretical framework for understanding block subspace methods. It reveals the relationship between block subspace methods and classical subspace methods. We theoretically show that blockwise PCA has larger reconstruction errors than classical PCA and classical LDA has stronger discriminant power than blockwise LDA in the case of the same number of reduced features. In addition, based on the Fisher criterion, we also give a strategy for selecting an approximate block size for classification problems. The comprehensive experiments on face images and gene expression data are used to evaluate our results and a comparative analysis for various methods is made. Experimental results demonstrate that overly combining subspaces of block subspace methods without considering the subspace distance may yield undesirable performance on undersampled problems. [Copyright &y& Elsevier]

Abstract: In this paper, two significant weaknesses of locally linear embedding (LLE) applied to computer vision are addressed: “intrinsic dimension” and “eigenvector meanings”. “Topological embedding” and “multi-resolution nonlinearity capture” are introduced based on mathematical analysis of topological manifolds and LLE. The manifold topological analysis (MTA) method is described and is based on “topological embedding”. MTA is a more robust method to determine the “intrinsic dimension” of a manifold with typical topology, which is important for tracking and perception understanding. The manifold multi-resolution analysis (MMA) method is based on “multi-resolution nonlinearity capture”. MMA defines LLE eigenvectors as features for pattern recognition and dimension reduction. Both MTA and MMA are proved mathematically, and several examples are provided. Applications in 3D object recognition and 3D object viewpoint space partitioning are also described. [Copyright &y& Elsevier]

Abstract: Euclidean norm calculations arise frequently in scientific and engineering applications. Several approximations for this norm with differing complexity and accuracy have been proposed in the literature. Earlier approaches were based on minimizing the maximum error. Recently, Seol and Cheun proposed an approximation based on minimizing the average error. In this paper, we first examine these approximations in detail, show that they fit into a single mathematical formulation, and compare their average and maximum errors. We then show that the maximum errors given by Seol and Cheun are significantly optimistic. [ABSTRACT FROM AUTHOR]

Abstract: Support vector data description (SVDD) is a data description method that can give the target data set a spherically shaped description and be used to outlier detection or classification. In real life the target data set often contains more than one class of objects and each class of objects need to be described and distinguished simultaneously. In this case, traditional SVDD can only give a description for the target data set, regardless of the differences between different target classes in the target data set, or give a description for each class of objects in the target data set. In this paper, an improved support vector data description method named two-class support vector data description (TC-SVDD) is presented. The proposed method can give each class of objects in the target data set a hypersphere-shaped description simultaneously if the target data set contains two classes of objects. The characteristics of the improved support vector data descriptions are discussed. The results of the proposed approach on artificial and actual data show that the proposed method works quite well on the 3-class classification problem with one object class being undersampled severely. [ABSTRACT FROM AUTHOR]

Abstract: Functions of moments of 2D images that are invariant under some changes are important in image analysis and pattern recognition. One of the most basic changes to a 2D image is geometric change. Two images of the same plane taken from different viewpoints are related by a projective transformation. Unfortunately, it is well known that geometric moment invariants for projective transformations do not exist in general. Yet if we generalize the standard definition of the geometric moments and utilize some additional information from the images, certain type of projective invariants of 2D images can be derived. This paper first defines co-moment as a moment-like function of image that contains two reference points. Then a set of functions of co-moments that is invariant under general projective transformations is derived. The invariants are simple and in explicit form. Experimental results validated the mathematical derivations. [Copyright &y& Elsevier]

Abstract: In this paper we present a generalization on the notion of image connectivity similar to that modeled by second-generation connections. The connected operators based on this new type of connection make use of image partitions aided by mask images to extract path-wise connected regions that were previously treated as sets of singletons. This leads to a redistribution of image power which affects texture descriptors. These operators find applications in problems involving contraction-based connectivities, and we show how they can be used to counter the over-segmentation problem of connected filters. Despite restrictions which prevent extensions to gray-scale, we present a method for gray-scale spectral analysis of biomedical images characterized by filamentous details. Using connected pattern spectra as feature vectors to train a classifier we show that the new operators outperform the existing contraction-based ones and that the classification performance competes with, and in some cases outperforms methods based on the standard 4- or 8-connectivity. Finally, combining the two methods we enrich the texture description and increase the overall classification rate. [Copyright &y& Elsevier]

Abstract: In this paper, we propose a general learning framework based on local and global regularization. In the local regularization part, our algorithm constructs a regularized classifier for each data point using its neighborhood, while the global regularization part adopts a Laplacian regularizer to smooth the data labels predicted by those local classifiers. We show that such a learning framework can easily be incorporated into either unsupervised learning, semi-supervised learning, and supervised learning paradigm. Moreover, many existing learning algorithms can be derived from our framework. Finally we present some experimental results to show the effectiveness of our method. [Copyright &y& Elsevier]

Abstract: In many applied sciences the problem of revealing the underlying (crisp or fuzzy) structure (partitions or covers) in a collection of objects to be represented in non-temporal situations, measures, observations, phenomena, etc., is an essential task. Motivated by the independent use of some different partitions criteria and the theoretical and empirical analysis of some of its properties, in this paper, we introduce an incremental nested partition method which combines these partitions criteria for finding the inner structure of static and dynamic datasets. For this, we proved that there are relationships of nesting between partitions obtained, respectively, from these partition criteria, and besides that the sensitivity when a new object arrives to the dataset is rigorously studied. Our algorithm exploits all of these mathematical properties for obtaining the hierarchy of clusterings. Moreover, we realize a theoretical and experimental comparative study of our method with classical hierarchical clustering methods such as single-link and complete-link and other more recently introduced methods. The experimental results over databases of UCI repository and the AFP and TDT2 news collections show the usefulness and capability of our method to reveal different levels of information hidden in datasets. [Copyright &y& Elsevier]

Abstract: Efficient and effective image segmentation is an important task in computer vision and object recognition. Since fully automatic image segmentation is usually very hard for natural images, interactive schemes with a few simple user inputs are good solutions. This paper presents a new region merging based interactive image segmentation method. The users only need to roughly indicate the location and region of the object and background by using strokes, which are called markers. A novel maximal-similarity based region merging mechanism is proposed to guide the merging process with the help of markers. A region R is merged with its adjacent region Q if Q has the highest similarity with Q among all Q''s adjacent regions. The proposed method automatically merges the regions that are initially segmented by mean shift segmentation, and then effectively extracts the object contour by labeling all the non-marker regions as either background or object. The region merging process is adaptive to the image content and it does not need to set the similarity threshold in advance. Extensive experiments are performed and the results show that the proposed scheme can reliably extract the object contour from the complex background. [Copyright &y& Elsevier]

Abstract: Recently, a large amount of work has been devoted to the study of spectral clustering—a powerful unsupervised classification method. This paper brings contributions to both its foundations, and its applications to text classification. Departing from the mainstream, concerned with hard membership, we study the extension of spectral clustering to soft membership (probabilistic, EM style) assignments. One of its key features is to avoid the complexity gap of hard membership. We apply this theory to a challenging problem, text clustering for languages having permeable borders, via a novel construction of Markov chains from corpora. Experiments with a readily available code clearly display the potential of the method, which brings a visually appealing soft distinction of languages that may define altogether a whole corpus. [Copyright &y& Elsevier]

Abstract: In this paper, a novel one-dimensional correlation filter based class-dependence feature analysis (1D-CFA) method is presented for robust face recognition. Compared with original CFA that works in the two dimensional (2D) image space, 1D-CFA encodes the image data as vectors. In 1D-CFA, a new correlation filter called optimal extra-class origin output tradeoff filter (OEOTF), which is designed in the low-dimensional principal component analysis (PCA) subspace, is proposed for effective feature extraction. Experimental results on benchmark face databases, such as FERET, AR, and FRGC, show that OEOTF based 1D-CFA consistently outperforms other state-of-the-art face recognition methods. This demonstrates the effectiveness and robustness of the novel method. [Copyright &y& Elsevier]

Abstract: In this paper an efficient feature extraction method named as locally linear discriminant embedding (LLDE) is proposed for face recognition. It is well known that a point can be linearly reconstructed by its neighbors and the reconstruction weights are under the sum-to-one constraint in the classical locally linear embedding (LLE). So the constrained weights obey an important symmetry: for any particular data point, they are invariant to rotations, rescalings and translations. The latter two are introduced to the proposed method to strengthen the classification ability of the original LLE. The data with different class labels are translated by the corresponding vectors and those belonging to the same class are translated by the same vector. In order to cluster the data with the same label closer, they are also rescaled to some extent. So after translation and rescaling, the discriminability of the data will be improved significantly. The proposed method is compared with some related feature extraction methods such as maximum margin criterion (MMC), as well as other supervised manifold learning-based approaches, for example ensemble unified LLE and linear discriminant analysis (En-ULLELDA), locally linear discriminant analysis (LLDA). Experimental results on Yale and CMU PIE face databases convince us that the proposed method provides a better representation of the class information and obtains much higher recognition accuracies. [Copyright &y& Elsevier]

Abstract: One of the main challenges in face recognition is represented by pose and illumination variations that drastically affect the recognition performance, as confirmed by the results of recent face recognition large-scale evaluations. This paper presents a new technique for face recognition, based on the joint use of 3D models and 2D images, specifically conceived to be robust with respect to pose and illumination changes. A 3D model of each user is exploited in the training stage (i.e. enrollment) to generate a large number of 2D images representing virtual views of the face with varying pose and illumination. Such images are then used to learn in a supervised manner a set of subspaces constituting the user''s template. Recognition occurs by matching 2D images with the templates and no 3D information (neither images nor face models) is required. The experiments carried out confirm the efficacy of the proposed technique. [Copyright &y& Elsevier]

Abstract: Since the multiple kernel representation opened in tracking the possibility of representing several features of the target in the same model, tracking multiple features using kernel-based methods has received a great attention. In spite of these efforts, the formulation has been reduced to tracking planar targets or targets rotating inside a plane parallel to the image plane. The aim of this paper is to extend the multi-kernel tracking to cope with situations different to those. To this end, we consider the triangular mesh described by the centers of the kernels and we develop the estimation of a set of affine transforms, one at each mesh triangle, subject to the constraints that each affine transform of a triangle must be compatible with the affine transforms coming from contiguous triangles. The method is applied to sequences including face and car tracking. Results show an outperformance respect to previous kernel tracking methods, which generally work with a too restricted set of movements. [Copyright &y& Elsevier]

Abstract: Static handwritten scripts originate as images on documents and do not, by definition, contain any dynamic information. To improve the accuracy of static handwriting recognition systems, many techniques aim to estimate dynamic information from the static scripts. Mostly, the pen trajectories of the scripts are estimated. However, the efficacy of the resulting pen trajectories are rarely evaluated quantitatively. This paper proposes a protocol for the objective evaluation of automatically determined pen trajectories. A hidden Markov model is derived from a ground-truth trajectory. An estimated trajectory is then matched to the derived model. Statistics describing substitution, insertion and deletion errors are then computed from this match. The proposed algorithm is especially useful for performance comparisons between different pen trajectory estimation algorithms. [Copyright &y& Elsevier]

Abstract: A pattern classification problem usually involves using high-dimensional features that make the classifier very complex and difficult to train. With no feature reduction, both training accuracy and generalization capability will suffer. This paper proposes a novel hybrid filter–wrapper-type feature subset selection methodology using a localized generalization error model. The localized generalization error model for a radial basis function neural network bounds from above the generalization error for unseen samples located within a neighborhood of the training samples. Iteratively, the feature making the smallest contribution to the generalization error bound is removed. Moreover, the novel feature selection method is independent of the sample size and is computationally fast. The experimental results show that the proposed method consistently removes large percentages of features with statistically insignificant loss of testing accuracy for unseen samples. In the experiments for two of the datasets, the classifiers built using feature subsets with 90% of features removed by our proposed approach yield average testing accuracies higher than those trained using the full set of features. Finally, we corroborate the efficacy of the model by using it to predict corporate bankruptcies in the US. [Copyright &y& Elsevier]

Abstract: This paper explores the problem of multi-view feature matching from an unordered set of widely separated views. A set of local invariant features is extracted independently from each view. First we propose a new view-ordering algorithm that organizes all the unordered views into clusters of related (i.e. the same scene) views by efficiently computing the view-similarity values of all view pairs by reasonably selecting part of extracted features to match. Second a robust two-view matching algorithm is developed to find initial matches, then detect the outliers and finally incrementally find more reliable feature matches under the epipolar constraint between two views from dense to sparse based on an assumption that changes of both motion and feature characteristics of one match are consistent with those of neighbors. Third we establish the reliable multi-view matches across related views by reconstructing missing matches in a neighboring triple of views and efficiently determining the states of matches between view pairs. Finally, the reliable multi-view matches thus obtained are used to automatically track all the views by using a self-calibration method. The proposed methods were tested on several sets of real images. Experimental results show that it is efficient and can track a large set of multi-view feature matches across multiple widely separated views. [Copyright &y& Elsevier]

Abstract: Linear discriminant analysis (LDA) has been widely used for dimension reduction of data sets with multiple classes. The LDA has been recently extended to various generalized LDA methods that are applicable regardless of the relative sizes between the data dimension and the number of data items. In this paper, we propose several multiclass classifiers based on generalized LDA (GLDA) algorithms, taking advantage of the dimension reducing transformation matrix without requiring additional training or parameter optimization. A marginal linear discriminant classifier (MLDC), a Bayesian linear discriminant classifier (BLDC), and a one-dimensional BLDC are introduced for multiclass classification. Our experimental results illustrate that these classifiers produce higher ten-fold cross validation accuracy than kNN and centroid-based classifiers in the reduced dimensional space obtained from GLDA. [Copyright &y& Elsevier]

Abstract: This paper presents an algorithm to model volumetric data and other one for non-rigid registration of such models using spheres formulated in the geometric algebra framework. The proposed algorithm for modeling, as opposite to the Union of Spheres method, reduces the number of entities (spheres) used to model 3D data. Our proposal is based in marching cubes idea using, however, spheres, while the Union of Spheres uses Delaunay tetrahedrization. The non-rigid registration is accomplished in a deterministic annealing scheme. At the preprocessing stage we segment the objects of interest by a segmentation method based on texture information. This method is embedded in a region growing scheme. As our final application, we present a scheme for surgical object tracking using again geometric algebra techniques. [Copyright &y& Elsevier]

Abstract: Support vector clustering involves three steps—solving an optimization problem, identification of clusters and tuning of hyper-parameters. In this paper, we introduce a pre-processing step that eliminates data points from the training data that are not crucial for clustering. Pre-processing is efficiently implemented using the R*-tree data structure. Experiments on real-world and synthetic datasets show that pre-processing drastically decreases the run-time of the clustering algorithm. Also, in many cases reduction in the number of support vectors is achieved. Further, we suggest an improvement for the step of identification of clusters. [Copyright &y& Elsevier]

Abstract: This paper focuses on directional texture analysis. We propose a new approach for orientation estimation. This approach hinges on two classes of convolution masks, i.e. the gradient and the valleyness operators. We provide a framework for their optimization regarding bias reduction and noise robustness. As the gradient and the valleyness operators are complementary, we propose a combination named GV-JOE. This combination consists in using the gradient on inflexion pixels, the valleyness on crests and valleys, and a linear mixture of both elsewhere. We implement an adaptive selection of the size of our operators, in order to take into account the variations of the texture scale in the image. We apply our approach both on synthetic and natural textures. These experiments show that, when used separately, both classes of operators are more accurate than classical derivative approaches. In noisy cases, the GV-JOE implementation improves the robustness of our operators without affecting their accuracy. Moreover, compared to well-known orientation estimators, it gives the best estimates in the most difficult cases i.e. for high-frequency textures and low SNR. [Copyright &y& Elsevier]

This paper introduces a new and simple criterion for rigid registration based on Gaussian fields. The criterion is always differentiable and convex in a large neighborhood of the alignment parameters; allowing for the use of well-proven optimization techniques. Using this method we can extend the size of the region of convergence so that no close initialization is needed, thus overcoming local convergence problems of Iterative Closest Point algorithms. Furthermore, the Gaussian energy function can be evaluated with linear complexity using the fast Gauss transform, which permits efficient implementation of the registration algorithm. Experimental analysis on real-world data sets shows the usefulness and points the limits of the approach. [Copyright &y& Elsevier]

This paper presents a table structure understanding algorithm designed using optimization methods. The algorithm is probability based, where the probabilities are estimated from geometric measurements made on the various entities in a large training set. The methodology includes a global parameter optimization scheme, a novel automatic table ground truth generation system and a table structure understanding performance evaluation protocol. With a document data set having 518 table and 10,934 cell entities, it performed at the 96.76% accuracy rate on the cell level and 98.32% accuracy rate on the table level. [Copyright &y& Elsevier]

This paper reports the novel application of digital curvature as a feature for morphological characterization and classification of landmark shapes. By inheriting several unique features of the continuous curvature, the digital curvature provides invariance to translations, rotations, local shape deformations, and is easily made tolerant to scaling. In addition, the bending energy, a global shape feature, can be directly estimated from the curvature values. The application of these features to analyse patterns of cranial morphological geographic differentiation in the rodent species Thrichomys apereoides has led to encouraging results, indicating a close correspondence between the geographical and morphological distributions. [Copyright &y& Elsevier]

In this paper, a novel model is proposed for the orientation field of fingerprints, which can be expressed as the argument of a rational complex function. It is suitable for all types of fingerprints. Experimental results show that it performs much better than the previous works. [Copyright &y& Elsevier]