Bi-Objective Nonnegative Matrix Factorization: Linear Versus Kernel-Based Models

Nonnegative matrix factorization (NMF) is a powerful class of feature extraction techniques that has been successfully applied in many fields, namely in signal and image processing. Current NMF techniques have been limited to a single-objective problem in either its linear or nonlinear kernel-based formulation. In this paper, we propose to revisit the NMF as a multi-objective problem, in particular a bi-objective one, where the objective functions defined in both input and feature spaces are taken into account. By taking the advantage of the sum-weighted method from the literature of multi-objective optimization, the proposed bi-objective NMF determines a set of nondominated, Pareto optimal, solutions instead of a single optimal decomposition. Moreover, the corresponding Pareto front is studied and approximated. Experimental results on unmixing real hyperspectral images confirm the efficiency of the proposed bi-objective NMF compared with the state-of-the-art methods

Automatic Localization of Epileptic Spikes in EEGs of Children with Infantile Spasms

Infantile Spasms (ISS) characterized by electroencephalogram (EEG) recordings exhibiting hypsarrythmia (HYPS) are a severe form of epilepsy. Many clinicians have been trying to improve ISS outcomes; however, quantification of discharges from hypsarrythmic EEG readings remains challenging. This thesis describes the development of a novel method that assists clinicians to successfully localize the epileptic discharges associated with ISS in HYPS. The approach includes: construct the time-frequency domain (TFD) of the EEG recording using matching pursuit TFD (MP-TFD), decompose the TFD matrix into two submatrices using nonnegative matrix factorizations (NMF), and employ the decomposed vectors to locate the spikes. The proposed method was employed to an EEG dataset of five ISS individuals, and identification of spikes was compared with those which were identified by the epileptologists and those obtained using clinical software (Persyst). Performance evaluations showed results based on classification techniques: thresholdings, and support vector machine (SVM). Using the thresholdings, average true positive (TP) and false negative (FN) percentages of 86% and 14% were achieved, which represented a significant improvement over the use of Persyst, which only achieved average TP and FN percentages of 4% and 96%, respectively. Using SVM, the percentage of area under curve (AUC) of receiver operating characteristic (ROC) was significantly improved up to 98.56%. In summary, the proposed novel algorithm based on MP-TFD and NMF was able to successfully detect the epileptic discharges from the dataset. The development of the proposed automated method can potentially assist clinicians to successfully localize the epileptic discharges associated with ISS in HYPS. The quantitative assessment of spike detection, as well as other features of HYPS, is expected to allow a more accurate assessment of the relevance of EEG to clinical outcomes, which is significant in therapy management of ISS

Adaptive Graph via Multiple Kernel Learning for Nonnegative Matrix Factorization

Nonnegative Matrix Factorization (NMF) has been continuously evolving in several areas like pattern recognition and information retrieval methods. It factorizes a matrix into a product of 2 low-rank non-negative matrices that will define parts-based, and linear representation of nonnegative data. Recently, Graph regularized NMF (GrNMF) is proposed to find a compact representation,which uncovers the hidden semantics and simultaneously respects the intrinsic geometric structure. In GNMF, an affinity graph is constructed from the original data space to encode the geometrical information. In this paper, we propose a novel idea which engages a Multiple Kernel Learning approach into refining the graph structure that reflects the factorization of the matrix and the new data space. The GrNMF is improved by utilizing the graph refined by the kernel learning, and then a novel kernel learning method is introduced under the GrNMF framework. Our approach shows encouraging results of the proposed algorithm in comparison to the state-of-the-art clustering algorithms like NMF, GrNMF, SVD etc.Comment: This paper has been withdrawn by the author due to the terrible writin

Decorrelation of Neutral Vector Variables: Theory and Applications

In this paper, we propose novel strategies for neutral vector variable decorrelation. Two fundamental invertible transformations, namely serial nonlinear transformation and parallel nonlinear transformation, are proposed to carry out the decorrelation. For a neutral vector variable, which is not multivariate Gaussian distributed, the conventional principal component analysis (PCA) cannot yield mutually independent scalar variables. With the two proposed transformations, a highly negatively correlated neutral vector can be transformed to a set of mutually independent scalar variables with the same degrees of freedom. We also evaluate the decorrelation performances for the vectors generated from a single Dirichlet distribution and a mixture of Dirichlet distributions. The mutual independence is verified with the distance correlation measurement. The advantages of the proposed decorrelation strategies are intensively studied and demonstrated with synthesized data and practical application evaluations

Single-Trial Decoding of Bistable Perception Based on Sparse Nonnegative Tensor Decomposition

The study of the neuronal correlates of the spontaneous alternation in perception elicited by bistable visual stimuli is promising for understanding the mechanism of neural information processing and the neural basis of visual perception and perceptual decision-making. In this paper, we develop a sparse nonnegative tensor factorization-(NTF)-based method to extract features from the local field potential (LFP), collected from the middle temporal (MT) visual cortex in a macaque monkey, for decoding its bistable structure-from-motion (SFM) perception. We apply the feature extraction approach to the multichannel time-frequency representation of the intracortical LFP data. The advantages of the sparse NTF-based feature extraction approach lies in its capability to yield components common across the space, time, and frequency domains yet discriminative across different conditions without prior knowledge of the discriminating frequency bands and temporal windows for a specific subject. We employ the support vector machines (SVMs) classifier based on the features of the NTF components for single-trial decoding the reported perception. Our results suggest that although other bands also have certain discriminability, the gamma band feature carries the most discriminative information for bistable perception, and that imposing the sparseness constraints on the nonnegative tensor factorization improves extraction of this feature