A Simple Iterative Algorithm for Parsimonious Binary Kernel Fisher Discrimination

By applying recent results in optimization theory variously known as optimization transfer or majorize/minimize algorithms, an algorithm for binary, kernel, Fisher discriminant analysis is introduced that makes use of a non-smooth penalty on the coefficients to provide a parsimonious solution. The problem is converted into a smooth optimization that can be solved iteratively with no greater overhead than iteratively re-weighted least-squares. The result is simple, easily programmed and is shown to perform, in terms of both accuracy and parsimony, as well as or better than a number of leading machine learning algorithms on two well-studied and substantial benchmarks

KCRC-LCD: Discriminative Kernel Collaborative Representation with Locality Constrained Dictionary for Visual Categorization

We consider the image classification problem via kernel collaborative representation classification with locality constrained dictionary (KCRC-LCD). Specifically, we propose a kernel collaborative representation classification (KCRC) approach in which kernel method is used to improve the discrimination ability of collaborative representation classification (CRC). We then measure the similarities between the query and atoms in the global dictionary in order to construct a locality constrained dictionary (LCD) for KCRC. In addition, we discuss several similarity measure approaches in LCD and further present a simple yet effective unified similarity measure whose superiority is validated in experiments. There are several appealing aspects associated with LCD. First, LCD can be nicely incorporated under the framework of KCRC. The LCD similarity measure can be kernelized under KCRC, which theoretically links CRC and LCD under the kernel method. Second, KCRC-LCD becomes more scalable to both the training set size and the feature dimension. Example shows that KCRC is able to perfectly classify data with certain distribution, while conventional CRC fails completely. Comprehensive experiments on many public datasets also show that KCRC-LCD is a robust discriminative classifier with both excellent performance and good scalability, being comparable or outperforming many other state-of-the-art approaches

Parsimonious Kernel Fisher Discrimination

By applying recent results in optimization transfer, a new algorithm for kernel Fisher Discriminant Analysis is provided that makes use of a non-smooth penalty on the coefficients to provide a parsimonious solution. The algorithm is simple, easily programmed and is shown to perform as well as or better than a number of leading machine learning algorithms on a substantial benchmark. It is then applied to a set of extreme small-sample-size problems in virtual screening where it is found to be less accurate than a currently leading approach but is still comparable in a number of cases

A new regularized least squares support vector regression for gene selection

<p>Abstract</p> <p>Background</p> <p>Selection of influential genes with microarray data often faces the difficulties of a large number of genes and a relatively small group of subjects. In addition to the curse of dimensionality, many gene selection methods weight the contribution from each individual subject equally. This equal-contribution assumption cannot account for the possible dependence among subjects who associate similarly to the disease, and may restrict the selection of influential genes.</p> <p>Results</p> <p>A novel approach to gene selection is proposed based on kernel similarities and kernel weights. We do not assume uniformity for subject contribution. Weights are calculated via regularized least squares support vector regression (RLS-SVR) of class levels on kernel similarities and are used to weight subject contribution. The cumulative sum of weighted expression levels are next ranked to select responsible genes. These procedures also work for multiclass classification. We demonstrate this algorithm on acute leukemia, colon cancer, small, round blue cell tumors of childhood, breast cancer, and lung cancer studies, using kernel Fisher discriminant analysis and support vector machines as classifiers. Other procedures are compared as well.</p> <p>Conclusion</p> <p>This approach is easy to implement and fast in computation for both binary and multiclass problems. The gene set provided by the RLS-SVR weight-based approach contains a less number of genes, and achieves a higher accuracy than other procedures.</p

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

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

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

Fast subcellular localization by cascaded fusion of signal-based and homology-based methods

<p>Abstract</p> <p>Background</p> <p>The functions of proteins are closely related to their subcellular locations. In the post-genomics era, the amount of gene and protein data grows exponentially, which necessitates the prediction of subcellular localization by computational means.</p> <p>Results</p> <p>This paper proposes mitigating the computation burden of alignment-based approaches to subcellular localization prediction by a cascaded fusion of cleavage site prediction and profile alignment. Specifically, the informative segments of protein sequences are identified by a cleavage site predictor using the information in their N-terminal shorting signals. Then, the sequences are truncated at the cleavage site positions, and the shortened sequences are passed to PSI-BLAST for computing their profiles. Subcellular localization are subsequently predicted by a profile-to-profile alignment support-vector-machine (SVM) classifier. To further reduce the training and recognition time of the classifier, the SVM classifier is replaced by a new kernel method based on the perturbational discriminant analysis (PDA).</p> <p>Conclusions</p> <p>Experimental results on a new dataset based on Swiss-Prot Release 57.5 show that the method can make use of the best property of signal- and homology-based approaches and can attain an accuracy comparable to that achieved by using full-length sequences. Analysis of profile-alignment score matrices suggest that both profile creation time and profile alignment time can be reduced without significant reduction in subcellular localization accuracy. It was found that PDA enjoys a short training time as compared to the conventional SVM. We advocate that the method will be important for biologists to conduct large-scale protein annotation or for bioinformaticians to perform preliminary investigations on new algorithms that involve pairwise alignments.</p