Statistical modeling for simultaneous data clustering, features selection, and outliers rejection

Model-based approaches and in particular finite mixture models are widely used for data clustering, which is a crucial step in several applications of practical importance. Indeed, many pattern recognition, computer vision, and image processing applications can be approached as feature space clustering problems. However, the use of these approaches for complex high-dimensional data presents several challenges such as the presence of many irrelevant features, which may affect the speed, and compromise the accuracy of the used learning algorithm. Another problem is the presence of outliers which potentially influence the resulting model parameters. Generally; clustering, features selection, and outliers detection problems have been approached separately. In this thesis, we propose a unified statistical framework to address the three problems simultaneously. The proposed statistical model partitions a given data set without a priori information about the number of clusters, the saliency of the features, or the number of outliers. We illustrate the performance of our approach using different applications involving synthetic data, real data, and objects shape clustering

Support Vector Machine Implementations for Classification & Clustering

BACKGROUND: We describe Support Vector Machine (SVM) applications to classification and clustering of channel current data. SVMs are variational-calculus based methods that are constrained to have structural risk minimization (SRM), i.e., they provide noise tolerant solutions for pattern recognition. The SVM approach encapsulates a significant amount of model-fitting information in the choice of its kernel. In work thus far, novel, information-theoretic, kernels have been successfully employed for notably better performance over standard kernels. Currently there are two approaches for implementing multiclass SVMs. One is called external multi-class that arranges several binary classifiers as a decision tree such that they perform a single-class decision making function, with each leaf corresponding to a unique class. The second approach, namely internal-multiclass, involves solving a single optimization problem corresponding to the entire data set (with multiple hyperplanes). RESULTS: Each SVM approach encapsulates a significant amount of model-fitting information in its choice of kernel. In work thus far, novel, information-theoretic, kernels were successfully employed for notably better performance over standard kernels. Two SVM approaches to multiclass discrimination are described: (1) internal multiclass (with a single optimization), and (2) external multiclass (using an optimized decision tree). We describe benefits of the internal-SVM approach, along with further refinements to the internal-multiclass SVM algorithms that offer significant improvement in training time without sacrificing accuracy. In situations where the data isn't clearly separable, making for poor discrimination, signal clustering is used to provide robust and useful information – to this end, novel, SVM-based clustering methods are also described. As with the classification, there are Internal and External SVM Clustering algorithms, both of which are briefly described

A Robust Approach for Multivariate Binary Vectors Clustering and Feature Selection

International audienceGiven a set of binary vectors drawn from a ¯nite multiple Bernoulli mixture model, an important problem is to determine which vectors are outliers and which features are relevant. The goal of this paper is to propose a model for binary vectors clustering that accommo- dates outliers and allows simultaneously the incorporation of a feature selection methodology into the clustering process. We derive an EM al- gorithm to ¯t the proposed model. Through simulation studies and a set of experiments involving handwritten digit recognition and visual scenes categorization, we demonstrate the usefulness and e®ectiveness of our method

Positive Data Clustering based on Generalized Inverted Dirichlet Mixture Model

Recent advances in processing and networking capabilities of computers have caused an accumulation of immense amounts of multimodal multimedia data (image, text, video). These data are generally presented as high-dimensional vectors of features. The availability of these highdimensional data sets has provided the input to a large variety of statistical learning applications including clustering, classification, feature selection, outlier detection and density estimation. In this context, a finite mixture offers a formal approach to clustering and a powerful tool to tackle the problem of data modeling. A mixture model assumes that the data is generated by a set of parametric probability distributions. The main learning process of a mixture model consists of the following two parts: parameter estimation and model selection (estimation the number of components). In addition, other issues may be considered during the learning process of mixture models such as the: a) feature selection and b) outlier detection. The main objective of this thesis is to work with different kinds of estimation criteria and to incorporate those challenges into a single framework. The first contribution of this thesis is to propose a statistical framework which can tackle the problem of parameter estimation, model selection, feature selection, and outlier rejection in a unified model. We propose to use feature saliency and introduce an expectation-maximization (EM) algorithm for the estimation of the Generalized Inverted Dirichlet (GID) mixture model. By using the Minimum Message Length (MML), we can identify how much each feature contributes to our model as well as determine the number of components. The presence of outliers is an added challenge and is handled by incorporating an auxiliary outlier component, to which we associate a uniform density. Experimental results on synthetic data, as well as real world applications involving visual scenes and object classification, indicates that the proposed approach was promising, even though low-dimensional representation of the data was applied. In addition, it showed the importance of embedding an outlier component to the proposed model. EM learning suffers from significant drawbacks. In order to overcome those drawbacks, a learning approach using a Bayesian framework is proposed as our second contribution. This learning is based on the estimation of the parameters posteriors and by considering the prior knowledge about these parameters. Calculation of the posterior distribution of each parameter in the model is done by using Markov chain Monte Carlo (MCMC) simulation methods - namely, the Gibbs sampling and the Metropolis- Hastings methods. The Bayesian Information Criterion (BIC) was used for model selection. The proposed model was validated on object classification and forgery detection applications. For the first two contributions, we developed a finite GID mixture. However, in the third contribution, we propose an infinite GID mixture model. The proposed model simutaneously tackles the clustering and feature selection problems. The proposed learning model is based on Gibbs sampling. The effectiveness of the proposed method is shown using image categorization application. Our last contribution in this thesis is another fully Bayesian approach for a finite GID mixture learning model using the Reversible Jump Markov Chain Monte Carlo (RJMCMC) technique. The proposed algorithm allows for the simultaneously handling of the model selection and parameter estimation for high dimensional data. The merits of this approach are investigated using synthetic data, and data generated from a challenging namely object detection