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Abstract: This paper presents a method for improved ensemble learning, by treating the optimization of an ensemble of classifiers as a compressed sensing problem. Ensemble learning methods improve the performance of a learned predictor by integrating a weighted combination of multiple predictive models. Ideally, the number of models needed in the ensemble should be minimized, while optimizing the weights associated with each included model. We solve this problem by treating it as an example of the compressed sensing problem, in which a sparse solution must be reconstructed from an under-determined linear system. Compressed sensing techniques are then employed to find an ensemble which is both small and effective. An additional contribution of this paper, is to present a new performance evaluation method (a new pairwise diversity measurement) called the roulette-wheel kappa-error. This method takes into account the different weightings of the classifiers, and also reduces the total number of pairs of classifiers needed in the kappa-error diagram, by selecting pairs through a roulette-wheel selection method according to the weightings of the classifiers. This approach can greatly improve the clarity and informativeness of the kappa-error diagram, especially when the number of classifiers in the ensemble is large. We use 25 different public data sets to evaluate and compare the performance of compressed sensing ensembles using four different sparse reconstruction algorithms, combined with two different classifier learning algorithms and two different training data manipulation techniques. We also give the comparison experiments of our method against another five state-of-the-art pruning methods. These experiments show that our method produces comparable or better accuracy, while being significantly faster than the compared methods. [Copyright &y& Elsevier]

Abstract: Non-rigid 3D shape retrieval has become an active and important research topic in content-based 3D object retrieval. The aim of this paper is to measure and compare the performance of state-of-the-art methods for non-rigid 3D shape retrieval. The paper develops a new benchmark consisting of 600 non-rigid 3D watertight meshes, which are equally classified into 30 categories, to carry out experiments for 11 different algorithms, whose retrieval accuracies are evaluated using six commonly utilized measures. Models and evaluation tools of the new benchmark are publicly available on our web site . [Copyright &y& Elsevier]

The number of methods available for classification of multi-label data has increased rapidly over recent years, yet relatively few links have been made with the related task of classification of sequential data. If labels indices are considered as time indices, the problems can often be seen as equivalent. In this paper we detect and elaborate on connections between multi-label methods and Markovian models, and study the suitability of multi-label methods for prediction in sequential data. From this study we draw upon the most suitable techniques from the area and develop two novel competitive approaches which can be applied to either kind of data. We carry out an empirical evaluation investigating performance on real-world sequential-prediction tasks: electricity demand, and route prediction. As well as showing that several popular multi-label algorithms are in fact easily applicable to sequencing tasks, our novel approaches, which benefit from a unified view of these areas, prove very competitive against established methods. [ABSTRACT FROM AUTHOR]

Classification is an essential task for predicting the class values of new instances. Both k -fold and leave-one-out cross validation are very popular for evaluating the performance of classification algorithms. Many data mining literatures introduce the operations for these two kinds of cross validation and the statistical methods that can be used to analyze the resulting accuracies of algorithms, while those contents are generally not all consistent. Analysts can therefore be confused in performing a cross validation procedure. In this paper, the independence assumptions in cross validation are introduced, and the circumstances that satisfy the assumptions are also addressed. The independence assumptions are then used to derive the sampling distributions of the point estimators for k -fold and leave-one-out cross validation. The cross validation procedure to have such sampling distributions is discussed to provide new insights in evaluating the performance of classification algorithms. [ABSTRACT FROM AUTHOR]

Abstract: Random Forests receive much attention from researchers because of their excellent performance. As Breiman suggested, the performance of Random Forests depends on the strength of the weak learners in the forests and the diversity among them. However, in the literature, many researchers only considered pre-processing of the data or post-processing of the Random Forests models. In this paper, we propose a new method to increase the diversity of each tree in the forests and thereby improve the overall accuracy. During the training process of each individual tree in the forest, different rotation spaces are concatenated into a higher space at the root node. Then the best split is exhaustively searched within this higher space. The location where the best split lies decides which rotation method to be used for all subsequent nodes. The performance of the proposed method here is evaluated on 42 benchmark data sets from various research fields and compared with the standard Random Forests. The results show that the proposed method improves the performance of the Random Forests in most cases. [Copyright &y& Elsevier]

Abstract: One class classification is a binary classification task for which only one class of samples is available for learning. In some preliminary works, we have proposed One Class Random Forests (OCRF), a method based on a random forest algorithm and an original outlier generation procedure that makes use of classifier ensemble randomization principles. In this paper, we propose an extensive study of the behavior of OCRF, that includes experiments on various UCI public datasets and comparison to reference one class namely, Gaussian density models, Parzen estimators, Gaussian mixture models and One Class SVMs—with statistical significance. Our aim is to show that the randomization principles embedded in a random forest algorithm make the outlier generation process more efficient, and allow in particular to break the curse of dimensionality. One Class Random Forests are shown to perform well in comparison to other methods, and in particular to maintain stable performance in higher dimension, while the other algorithms may fail. [Copyright &y& Elsevier]

Traditionally, in the field of Pattern Recognition (PR), the moments of the class-conditional densities of the respective classes have been used to perform classification. However, the use of phenomena that utilized the properties of the Order Statistics (OS) were not reported. Recently, in [10,8], we proposed a new paradigm named CMOS, Classification by the Moments of Order Statistics, which specifically used these quantifiers. It is fascinating that CMOS is essentially “anti”-Bayesian in its nature because the classification is performed in a counter-intuitive manner, i.e., by comparing the testing sample to a few samples distant from the mean, as opposed to the Bayesian approach in which the task is based on the central points of the distributions. In our initial works, we proposed the foundational theory of CMOS for the uni-dimensional Uniform and some other distributions. These results were extended for various symmetric and asymmetric uni-dimensional distributions within the exponential family in [8]. In this paper, we generalize these results for multi-dimensional distributions. The multi-dimensional generalization is particularly non-trivial because there is no well-established method for achieving the ordering of multi-dimensional data specified in terms of its uni-dimensional components. The strategy is analogous to a Naïve-Bayes' approach, although it really is of an anti-Naïve-Bayes' paradigm. We provide here the analytical and experimental results for the 2-dimensional Uniform, Doubly Exponential and Gaussian distributions, and also clearly specify the way by which one should extend the results for higher dimensions. The analogous results for the other distributions in the exponential family, which were discussed in [10,8] are alluded to, but omitted to avoid repetition. [ABSTRACT FROM AUTHOR]

Abstract: The One-vs-One strategy is one of the most commonly used decomposition technique to overcome multi-class classification problems; this way, multi-class problems are divided into easier-to-solve binary classification problems considering pairs of classes from the original problem, which are then learned by independent base classifiers. The way of performing the division produces the so-called non-competence. This problem occurs whenever an instance is classified, since it is submitted to all the base classifiers although the outputs of some of them are not meaningful (they were not trained using the instances from the class of the instance to be classified). This issue may lead to erroneous classifications, because in spite of their incompetence, all classifiers' decisions are usually considered in the aggregation phase. In this paper, we propose a dynamic classifier selection strategy for One-vs-One scheme that tries to avoid the non-competent classifiers when their output is probably not of interest. We consider the neighborhood of each instance to decide whether a classifier may be competent or not. In order to verify the validity of the proposed method, we will carry out a thorough experimental study considering different base classifiers and comparing our proposal with the best performer state-of-the-art aggregation within each base classifier from the five Machine Learning paradigms selected. The findings drawn from the empirical analysis are supported by the appropriate statistical analysis. [Copyright &y& Elsevier]

Abstract: Receiver Operating Characteristic (ROC) analysis is one of the most popular tools for the visual assessment and understanding of classifier performance. In this paper we present a new representation of regression models in the so-called regression ROC (RROC) space. The basic idea is to represent over-estimation against under-estimation. The curves are just drawn by adjusting a shift, a constant that is added (or subtracted) to the predictions, and plays a similar role as a threshold in classification. From here, we develop the notions of optimal operating condition, convexity, dominance, and explore several evaluation metrics that can be shown graphically, such as the area over the RROC curve (AOC). In particular, we show a novel and significant result: the AOC is equivalent to the error variance. We illustrate the application of RROC curves to resource estimation, namely the estimation of software project effort. [Copyright &y& Elsevier]

Abstract: Classification with imbalanced data-sets has become one of the most challenging problems in Data Mining. Being one class much more represented than the other produces undesirable effects in both the learning and classification processes, mainly regarding the minority class. Such a problem needs accurate tools to be undertaken; lately, ensembles of classifiers have emerged as a possible solution. Among ensemble proposals, the combination of Bagging and Boosting with preprocessing techniques has proved its ability to enhance the classification of the minority class. In this paper, we develop a new ensemble construction algorithm (EUSBoost) based on RUSBoost, one of the simplest and most accurate ensemble, which combines random undersampling with Boosting algorithm. Our methodology aims to improve the existing proposals enhancing the performance of the base classifiers by the usage of the evolutionary undersampling approach. Besides, we promote diversity favoring the usage of different subsets of majority class instances to train each base classifier. Centered on two-class highly imbalanced problems, we will prove, supported by the proper statistical analysis, that EUSBoost is able to outperform the state-of-the-art methods based on ensembles. We will also analyze its advantages using kappa-error diagrams, which we adapt to the imbalanced scenario. [Copyright &y& Elsevier]

Abstract: This paper, investigating the goal of human-level synthetic intelligence, presents a novel approach to learning an associative memory model using Generalized Hough Transform (GHT) [1]. A human action detection and classification system is also constructed to verify the effectiveness of the proposed GHT-based associative memory model. Existing human action classification systems use machine learning architectures and low-level features to characterize a specific human action. However, existing machine learning architectures often lack restructuring capability, which is an important process of forming the conceptual structures in human-level synthetic intelligence. The gap between low-level features and high-level human intelligence also degrades the performance of existing human action recognition algorithms when the spatial–temporal boundaries of action objects are ambiguous. To eliminate the side effect of temporal ambiguity, the proposed system uses a preprocessing procedure to extract key-frames from a video sequence and provide a compact representation for this video. The image and motion features of patches extracted from each key-frame are collected and used to train an appearance–motion codebook. The training procedure, based on the learnt codebook and GHT, constructs a hypergraph for associative memory learning. For each key-frame of a test video clip, the Hough voting framework is also used to detect salient segments, which are further partitioned into multiple patches, by grouping blocks of similar appearance and motions. The features of the detected patches are used to query the associative memory and retrieve missing patches from key-frames to recall the whole action object. These patches are then used to locate the target action object and classify the action type simultaneously using a probabilistic Hough voting scheme. Results show that the proposed method gives good performance on several publicly available datasets in terms of detection accuracy and recognition rate. [Copyright &y& Elsevier]

Abstract: Feature combination is a popular method for improving object classification performances. In this paper we present a simple and effective weighting scheme for feature combination based on the dominant-set notion of a cluster. Specifically, we use dominant sets clustering to evaluate how accurate a kernel matrix is expected to be for a SVM classifier. This expected kernel accuracy reflects the discriminative power of the kernel matrix and thus used in weighting the kernel matrix in feature combination. Our method is simple, intuitive, memory and computation efficient, and performs comparably to the popular and sophisticated optimization based methods. We conduct experiments with several datasets of diverse object types and validate the effectiveness of the proposed method. In fact, in five out of the six datasets used in our experiments, we obtained the best results until now in our knowledge. [Copyright &y& Elsevier]

Abstract: In this paper, we consider the problem of joint segmentation and classification of sequences in the framework of conditional random field (CRF) models. To effect this goal, we introduce a novel dual-functionality CRF model: on the first level, the proposed model conducts sequence segmentation, whereas, on the second level, the whole observed sequences are classified into one of the available learned classes. These two procedures are conducted in a joint, synergetic fashion, thus optimally exploiting the information contained in the used model training sequences. Model training is conducted by means of an efficient likelihood maximization algorithm, and inference is based on the familiar Viterbi algorithm. We evaluate the efficacy of our approach considering a real-world application, and we compare its performance to popular alternatives. [Copyright &y& Elsevier]

Abstract: Recently, the Student''s t-factor mixture analyzer (tFMA) has been proposed. Compared with the mixture of Student''s t-factor analyzers (MtFA), the tFMA has better performance when processing high-dimensional data. Moreover, the factors estimated by the tFMA can be visualized in a low-dimensional latent space, which is not shared by the MtFA. However, as the tFMA belongs to finite mixtures and the related parameter estimation method is based on the maximum likelihood criterion, it could not automatically determine the appropriate model complexity according to the observed data, leading to overfitting. In this paper, we propose an infinite Student''s t-factor mixture analyzer (itFMA) to handle this issue. The itFMA is based on the nonparametric Bayesian statistics which assumes infinite number of mixing components in advance, and automatically determines the proper number of components after observing the high-dimensional data. Moreover, we derive an efficient variational inference algorithm for the itFMA. The proposed itFMA and the related variational inference algorithm are used to cluster and classify high-dimensional data. Experimental results of some applications show that the itFMA has good generalization capacity, offering a more robust and powerful performance than other competing approaches. [Copyright &y& Elsevier]

Abstract: Remote sensing has become an unavoidable tool for better managing our environment, generally by realizing maps of land cover using classification techniques. Traditional classification techniques assign only one class (e.g., water, soil, grass) to each pixel of remote sensing images. However, the area covered by one pixel contains more than one surface component and results in the mixture of these surface components. In such situations, classical classification is not acceptable for many major applications, such as environmental monitoring, agriculture, mineral exploration and mining, etc. Most methods proposed for treating this problem have been developed for hyperspectral images. On the contrary, there are very few automatic techniques suited to multispectral images. In this paper, we propose new unsupervised spatial methods (called 2D-Corr-NLS and 2D-Corr-NMF) in order to unmix each pixel of a multispectral image for better recognizing the surface components constituting the observed scene. These methods are related to the blind source separation (BSS) problem, and are based on sparse component analysis (SCA), clustering and non-negativity constraints. Our approach consists in first identifying the mixing matrix involved in this BSS problem, by using the first stage of a spatial correlation-based SCA method with very limited source sparsity constraints, combined with clustering. Non-negative least squares (NLS) or non-negative matrix factorization (NMF) methods are then used to extract spatial sources. An important advantage of our proposed methods is their applicability to the possibly globally underdetermined, but locally (over)determined BSS model in multispectral remote sensing images. Experiments based on realistic synthetic mixtures and real multispectral images collected by the Landsat ETM+ and the Formosat-2 sensors are performed to evaluate the performance of the proposed approach. We also show that our methods significantly outperform the sequential maximum angle convex cone (SMACC) method. [Copyright &y& Elsevier]

Abstract: For classification problems, in practice, real-world data may suffer from two types of noise, attribute noise and class noise. It is the key for improving recognition performance to remove as much of their adverse effects as possible. In this paper, a formalism algorithm is proposed for classification problems with class noise, which is more challenging than those with attribute noise. The proposed formalism algorithm is based on evidential reasoning theory which is a powerful tool to deal with uncertain information in multiple attribute decision analysis and many other areas. Thus, it may be more effective alternative to handle noisy label information. And then a specific algorithm—Evidential Reasoning based Classification algorithm (ERC) is derived to recognize human faces under class noise conditions. The proposed ERC algorithm is extensively evaluated on five publicly available face databases with class noise and yields good performance. [Copyright &y& Elsevier]

Abstract: The Pap smear test is a manual screening procedure that is used to detect precancerous changes in cervical cells based on color and shape properties of their nuclei and cytoplasms. Automating this procedure is still an open problem due to the complexities of cell structures. In this paper, we propose an unsupervised approach for the segmentation and classification of cervical cells. The segmentation process involves automatic thresholding to separate the cell regions from the background, a multi-scale hierarchical segmentation algorithm to partition these regions based on homogeneity and circularity, and a binary classifier to finalize the separation of nuclei from cytoplasm within the cell regions. Classification is posed as a grouping problem by ranking the cells based on their feature characteristics modeling abnormality degrees. The proposed procedure constructs a tree using hierarchical clustering, and then arranges the cells in a linear order by using an optimal leaf ordering algorithm that maximizes the similarity of adjacent leaves without any requirement for training examples or parameter adjustment. Performance evaluation using two data sets show the effectiveness of the proposed approach in images having inconsistent staining, poor contrast, and overlapping cells. [Copyright &y& Elsevier]

Abstract: Choosing appropriate classification algorithms for a given data set is very important and useful in practice but also is full of challenges. In this paper, a method of recommending classification algorithms is proposed. Firstly the feature vectors of data sets are extracted using a novel method and the performance of classification algorithms on the data sets is evaluated. Then the feature vector of a new data set is extracted, and its k nearest data sets are identified. Afterwards, the classification algorithms of the nearest data sets are recommended to the new data set. The proposed data set feature extraction method uses structural and statistical information to characterize data sets, which is quite different from the existing methods. To evaluate the performance of the proposed classification algorithm recommendation method and the data set feature extraction method, extensive experiments with the 17 different types of classification algorithms, the three different types of data set characterization methods and all possible numbers of the nearest data sets are conducted upon the 84 publicly available UCI data sets. The results indicate that the proposed method is effective and can be used in practice. [Copyright &y& Elsevier]

Abstract: In many real-world applications, pattern recognition systems are designed a priori using limited and imbalanced data acquired from complex changing environments. Since new reference data often becomes available during operations, performance could be maintained or improved by adapting these systems through supervised incremental learning. To avoid knowledge corruption and sustain a high level of accuracy over time, an adaptive multiclassifier system (AMCS) may integrate information from diverse classifiers that are guided by a population-based evolutionary optimization algorithm. In this paper, an incremental learning strategy based on dynamic particle swarm optimization (DPSO) is proposed to evolve heterogeneous ensembles of classifiers (where each classifier corresponds to a particle) in response to new reference samples. This new strategy is applied to video-based face recognition, using an AMCS that consists of a pool of fuzzy ARTMAP (FAM) neural networks for classification of facial regions, and a niching version of DPSO that optimizes all FAM parameters such that the classification rate is maximized. Given that diversity within a dynamic particle swarm is correlated with diversity within a corresponding pool of base classifiers, DPSO properties are exploited to generate and evolve diversified pools of FAM classifiers, and to efficiently select ensembles among the pools based on accuracy and particle swarm diversity. Performance of the proposed strategy is assessed in terms of classification rate and resource requirements under different incremental learning scenarios, where new reference data is extracted from real-world video streams. Simulation results indicate the DPSO strategy provides an efficient way to evolve ensembles of FAM networks in an AMCS. Maintaining particle diversity in the optimization space yields a level of accuracy that is comparable to AMCS using reference ensemble-based and batch learning techniques, but requires significantly lower computational complexity than assessing diversity among classifiers in the feature or decision spaces. [Copyright &y& Elsevier]

Abstract: In this paper, the similarity of moment vectors between the test and the reference image blocks together with the result from the block classification are used in the formulation of an image quality metric (IQM). First, the reference and the test images are divided into non-overlapping 8×8 blocks and transformed into moment domain using Discrete Tchebichef Transform. The moment features are then used in two operations: the local quality index calculation and the image content (block) classification. The local quality index is obtained from the similarity measure of moment vectors between the reference and the test image blocks. Next, the content of each reference image block is classified into three types: “plain”, “edge” and “texture”, based on its moment energy level and moment energy distribution. The local quality indices obtained from all the image blocks are then averaged based on the block types to obtain three mean quality scores for each test image. The performance of these three mean quality scores and their combinations are studied using the LIVE database. The results show that the performance of the metric is significantly improved by combining the mean quality scores from the edge and texture image region. The best combination (the proposed metric) is then compared with five other IQMs using the LIVE database and four other independent databases. The results show that the proposed metric performs comparatively well for all the databases. [Copyright &y& Elsevier]

Abstract: In this paper, we present an adaptive method for the binarization of historical manuscripts and degraded document images. The proposed approach is based on maximum likelihood (ML) classification and uses a priori information and the spatial relationship on the image domain. In contrast with many conventional methods that use a decision based on thresholding, the proposed method performs a soft decision based on a probabilistic model. The main idea is that, from an initialization map (under-binarization) containing only the darkest part of the text, the method is able to recover the main text in the document image, including low-intensity and weak strokes. To do so, fast and robust local estimation of text and background features is obtained using grid-based modeling and inpainting techniques; then, the ML classification is performed to classify pixels into black and white classes. The advantage of the proposed method is that it preserves weak connections and provides smooth and continuous strokes, thanks to its correlation-based nature. Performance is evaluated both subjectively and objectively against standard databases. The proposed method outperforms the state-of-the-art methods presented in the DIBCO’09 binarization contest, although those other methods provide performance close to it. [Copyright &y& Elsevier]

Abstract: This paper extends the previous work in smooth support vector machine (SSVM) from binary to k-class classification based on a single-machine approach and call it multi-class smooth SVM (MSSVM). This study implements MSSVM for a ternary classification problem and labels it as TSSVM. For the case , this study proposes a one-vs.-one-vs.-rest (OOR) scheme that decomposes the problem into k(k−1)/2 ternary classification subproblems based on the assumption of ternary voting games. Thus, the k-class classification problem can be solved via a series of TSSVMs. The numerical experiments in this study compare the classification accuracy for TSSVM/OOR, one-vs.-one, one-vs.-rest schemes on nine UCI datasets. Results show that TSSVM/OOR outperforms the one-vs.-one and one-vs.-rest for all datasets. This study includes further error analyses to emphasize that the prediction confidence of OOR is significantly higher than the one-vs.-one scheme. Due to the nature of OOR design, it can detect the hidden (unknown) class directly. This study includes a “leave-one-class-out” experiment on the pendigits dataset to demonstrate the detection ability of the proposed OOR method for hidden classes. Results show that OOR performs significantly better than one-vs.-one and one-vs.-rest in the hidden-class detection rate. [Copyright &y& Elsevier]

Abstract: Recently, increasing attention has been directed to the study of the emotional content of speech signals, and hence, many systems have been proposed to identify the emotional content of a spoken utterance. This paper is a survey of speech emotion classification addressing three important aspects of the design of a speech emotion recognition system. The first one is the choice of suitable features for speech representation. The second issue is the design of an appropriate classification scheme and the third issue is the proper preparation of an emotional speech database for evaluating system performance. Conclusions about the performance and limitations of current speech emotion recognition systems are discussed in the last section of this survey. This section also suggests possible ways of improving speech emotion recognition systems. [ABSTRACT FROM AUTHOR]

Abstract: Locality preserving projection (LPP) is a manifold learning method widely used in pattern recognition and computer vision. The face recognition application of LPP is known to suffer from a number of problems including the small sample size (SSS) problem, the fact that it might produce statistically identical transform results for neighboring samples, and that its classification performance seems to be heavily influenced by its parameters. In this paper, we propose three novel solution schemes for LPP. Experimental results also show that the proposed LPP solution scheme is able to classify much more accurately than conventional LPP and to obtain a classification performance that is only little influenced by the definition of neighbor samples. [Copyright &y& Elsevier]

Abstract: Hidden Markov models (HMMs) have been shown to provide a high level performance for detecting anomalies in sequences of system calls to the operating system kernel. Using Boolean conjunction and disjunction functions to combine the responses of multiple HMMs in the ROC space may significantly improve performance over a “single best” HMM. However, these techniques assume that the classifiers are conditional independent, and their of ROC curves are convex. These assumptions are violated in most real-world applications, especially when classifiers are designed using limited and imbalanced training data. In this paper, the iterative Boolean combination (IBC) technique is proposed for efficient fusion of the responses from multiple classifiers in the ROC space. It applies all Boolean functions to combine the ROC curves corresponding to multiple classifiers, requires no prior assumptions, and its time complexity is linear with the number of classifiers. The results of computer simulations conducted on both synthetic and real-world host-based intrusion detection data indicate that the IBC of responses from multiple HMMs can achieve a significantly higher level of performance than the Boolean conjunction and disjunction combinations, especially when training data are limited and imbalanced. The proposed IBC is general in that it can be employed to combine diverse responses of any crisp or soft one- or two-class classifiers, and for wide range of application domains. [Copyright &y& Elsevier]

Abstract: Hyperspectral imaging, which records a detailed spectrum of light for each pixel, provides an invaluable source of information regarding the physical nature of the different materials, leading to the potential of a more accurate classification. However, high dimensionality of hyperspectral data, usually coupled with limited reference data available, limits the performances of supervised classification techniques. The commonly used pixel-wise classification lacks information about spatial structures of the image. In order to increase classification performances, integration of spatial information into the classification process is needed. In this paper, we propose to extend the watershed segmentation algorithm for hyperspectral images, in order to define information about spatial structures. In particular, several approaches to compute a one-band gradient function from hyperspectral images are proposed and investigated. The accuracy of the watershed algorithms is demonstrated by the further incorporation of the segmentation maps into a classifier. A new spectral–spatial classification scheme for hyperspectral images is proposed, based on the pixel-wise Support Vector Machines classification, followed by majority voting within the watershed regions. Experimental segmentation and classification results are presented on two hyperspectral images. It is shown in experiments that when the number of spectral bands increases, the feature extraction and the use of multidimensional gradients appear to be preferable to the use of vectorial gradients. The integration of the spatial information from the watershed segmentation in the hyperspectral image classifier improves the classification accuracies and provides classification maps with more homogeneous regions, compared to pixel-wise classification and previously proposed spectral–spatial classification techniques. The developed method is especially suitable for classifying images with large spatial structures. [Copyright &y& Elsevier]

Abstract: This paper formulates pixel labelling as a series of two-category classification. Unlike existing techniques, which assign a determinate label to each pixel, we assign a label set to each pixel and shrink the label set step by step. Determinate labelling is achieved within (n is size of label set) steps. In each step, we bisect the label set into two subsets and discard the one with higher cost of assigning it to the pixel. Simultaneous labelling of an image is carried out by minimizing an energy function that can be minimized via graph cut algorithm. Based on the bisection approach, we propose a bitwise algorithm for pixel labelling, which set one bit of each pixel''s label in each step. We apply the proposed algorithm to stereo matching and image restoration. Experimental results demonstrate that both good performance and high efficiency are achieved. [Copyright &y& Elsevier]

Abstract: Error estimation is a problem of high current interest in many areas of application. This paper concerns the classical problem of determining the performance of error estimators in small-sample settings under a Gaussianity parametric assumption. We provide here for the first time the exact sampling distribution of the resubstitution and leave-one-out error estimators for linear discriminant analysis (LDA) in the univariate case, which is valid for any sample size and combination of parameters (including unequal variances and sample sizes for each class). In the multivariate case, we provide a quasi-binomial approximation to the distribution of both the resubstitution and leave-one-out error estimators for LDA, under a common but otherwise arbitrary class covariance matrix, which is assumed to be known in the design of the LDA discriminant. We provide numerical examples, using both synthetic and real data, that indicate that these approximations are accurate, provided that LDA classification error is not too large. [Copyright &y& Elsevier]