Multiple Data-Dependent Kernel Fisher Discriminant Analysis for Face Recognition

Kernel Fisher discriminant analysis (KFDA) method has demonstrated its success in extracting facial features for face recognition. Compared to linear techniques, it can better describe the complex and nonlinear variations of face images. However, a single kernel is not always suitable for the applications of face recognition which contain data from multiple, heterogeneous sources, such as face images under huge variations of pose, illumination, and facial expression. To improve the performance of KFDA in face recognition, a novel algorithm named multiple data-dependent kernel Fisher discriminant analysis (MDKFDA) is proposed in this paper. The constructed multiple data-dependent kernel (MDK) is a combination of several base kernels with a data-dependent kernel constraint on their weights. By solving the optimization equation based on Fisher criterion and maximizing the margin criterion, the parameter optimization of data-dependent kernel and multiple base kernels is achieved. Experimental results on the three face databases validate the effectiveness of the proposed algorithm

A practical view of large-scale classification: feature selection and real-time classification

Tesis doctoral inédita, Universidad Autónoma de Madrid, Escuela Politécnica Superior, mayo de 201

Two-Stage Fuzzy Multiple Kernel Learning Based on Hilbert-Schmidt Independence Criterion

© 1993-2012 IEEE. Multiple kernel learning (MKL) is a principled approach to kernel combination and selection for a variety of learning tasks, such as classification, clustering, and dimensionality reduction. In this paper, we develop a novel fuzzy multiple kernel learning model based on the Hilbert-Schmidt independence criterion (HSIC) for classification, which we call HSIC-FMKL. In this model, we first propose an HSIC Lasso-based MKL formulation, which not only has a clear statistical interpretation that minimum redundant kernels with maximum dependence on output labels are found and combined, but also enables the global optimal solution to be computed efficiently by solving a Lasso optimization problem. Since the traditional support vector machine (SVM) is sensitive to outliers or noises in the dataset, fuzzy SVM (FSVM) is used to select the prediction hypothesis once the optimal kernel has been obtained. The main advantage of FSVM is that we can associate a fuzzy membership with each data point such that these data points can have different effects on the training of the learning machine. We propose a new fuzzy membership function using a heuristic strategy based on the HSIC. The proposed HSIC-FMKL is a two-stage kernel learning approach and the HSIC is applied in both stages. We perform extensive experiments on real-world datasets from the UCI benchmark repository and the application domain of computational biology which validate the superiority of the proposed model in terms of prediction accuracy

Design of Machine Learning Algorithms with Applications to Breast Cancer Detection

Machine learning is concerned with the design and development of algorithms and techniques that allow computers to 'learn' from experience with respect to some class of tasks and performance measure. One application of machine learning is to improve the accuracy and efficiency of computer-aided diagnosis systems to assist physician, radiologists, cardiologists, neuroscientists, and health-care technologists. This thesis focuses on machine learning and the applications to breast cancer detection. Emphasis is laid on preprocessing of features, pattern classification, and model selection. Before the classification task, feature selection and feature transformation may be performed to reduce the dimensionality of the features and to improve the classification performance. Genetic algorithm (GA) can be employed for feature selection based on different measures of data separability or the estimated risk of a chosen classifier. A separate nonlinear transformation can be performed by applying kernel principal component analysis and kernel partial least squares. Different classifiers are proposed in this work: The SOM-RBF network combines self-organizing maps (SOMs) and radial basis function (RBF) networks, with the RBF centers set as the weight vectors of neurons from the competitive layer of a trained SaM. The pairwise Rayleigh quotient (PRQ) classifier seeks one discriminating boundary by maximizing an unconstrained optimization objective, named as the PRQ criterion, formed with a set of pairwise const~aints instead of individual training samples. The strict 2-surface proximal (S2SP) classifier seeks two proximal planes that are not necessary parallel to fit the distribution of the samples in the original feature space or a kernel-defined feature space, by ma-ximizing two strict optimization objectives with a 'square of sum' optimization factor. Two variations of the support vector data description (SVDD) with negative samples (NSVDD) are proposed by involving different forms of slack vectors, which learn a closed spherically shaped boundary, named as the supervised compact hypersphere (SCH), around a set of samples in the target class. \Ve extend the NSVDDs to solve the multi-class classification problems based on distances between the samples and the centers of the learned SCHs in a kernel-defined feature space, using a combination of linear discriminant analysis and the nearest-neighbor rule. The problem of model selection is studied to pick the best values of the hyperparameters for a parametric classifier. To choose the optimal kernel or regularization parameters of a classifier, we investigate different criteria, such as the validation error estimate and the leave-out-out bound, as well as different optimization methods, such as grid search, gradient descent, and GA. By viewing the tuning problem of the multiple parameters of an 2-norm support vector machine (SVM) as an identification problem of a nonlinear dynamic system, we design a tuning system by employing the extended Kalman filter based on cross validation. Independent kernel optimization based on different measures of data separability are a~so investigated for different kernel-based classifiers. Numerous computer experiments using the benchmark datasets verify the theoretical results, make comparisons among the techniques in measures of classification accuracy or area under the receiver operating characteristics curve. Computational requirements, such as the computing time and the number of hyper-parameters, are also discussed. All of the presented methods are applied to breast cancer detection from fine-needle aspiration and in mammograms, as well as screening of knee-joint vibroarthrographic signals and automatic monitoring of roller bearings with vibration signals. Experimental results demonstrate the excellence of these methods with improved classification performance. For breast cancer detection, instead of only providing a binary diagnostic decision of 'malignant' or 'benign', we propose methods to assign a measure of confidence of malignancy to an individual mass, by calculating probabilities of being benign and malignant with a single classifier or a set of classifiers

Sparse machine learning methods with applications in multivariate signal processing

This thesis details theoretical and empirical work that draws from two main subject areas: Machine Learning (ML) and Digital Signal Processing (DSP). A unified general framework is given for the application of sparse machine learning methods to multivariate signal processing. In particular, methods that enforce sparsity will be employed for reasons of computational efficiency, regularisation, and compressibility. The methods presented can be seen as modular building blocks that can be applied to a variety of applications. Application specific prior knowledge can be used in various ways, resulting in a flexible and powerful set of tools. The motivation for the methods is to be able to learn and generalise from a set of multivariate signals. In addition to testing on benchmark datasets, a series of empirical evaluations on real world datasets were carried out. These included: the classification of musical genre from polyphonic audio files; a study of how the sampling rate in a digital radar can be reduced through the use of Compressed Sensing (CS); analysis of human perception of different modulations of musical key from Electroencephalography (EEG) recordings; classification of genre of musical pieces to which a listener is attending from Magnetoencephalography (MEG) brain recordings. These applications demonstrate the efficacy of the framework and highlight interesting directions of future research

Kernel-Based Methods for Hypothesis Testing: A Unified View

International audienceKernel-based methods provide a rich and elegant framework for developing nonparametric detection procedures for signal processing. Several recently proposed procedures can be simply described using basic concepts of reproducing kernel Hilbert space embeddings of probability distributions, namely mean elements and covariance operators. We propose a unified view of these tools, and draw relationships with information divergences between distributions

Discriminant feature extraction by generalized difference subspace

This paper reveals the discriminant ability of the orthogonal projection of data onto a generalized difference subspace (GDS) both theoretically and experimentally. In our previous work, we have demonstrated that GDS projection works as the quasi-orthogonalization of class subspaces. Interestingly, GDS projection also works as a discriminant feature extraction through a similar mechanism to the Fisher discriminant analysis (FDA). A direct proof of the connection between GDS projection and FDA is difficult due to the significant difference in their formulations. To avoid the difficulty, we first introduce geometrical Fisher discriminant analysis (gFDA) based on a simplified Fisher criterion. gFDA can work stably even under few samples, bypassing the small sample size (SSS) problem of FDA. Next, we prove that gFDA is equivalent to GDS projection with a small correction term. This equivalence ensures GDS projection to inherit the discriminant ability from FDA via gFDA. Furthermore, we discuss two useful extensions of these methods, 1) nonlinear extension by kernel trick, 2) the combination of convolutional neural network (CNN) features. The equivalence and the effectiveness of the extensions have been verified through extensive experiments on the extended Yale B+, CMU face database, ALOI, ETH80, MNIST and CIFAR10, focusing on the SSS problem