Zhaoshui He

Symmetric Nonnegative Matrix Factorization: Algorithms and Applications to Probabilistic Clustering

Nonnegative matrix factorization (NMF) is an unsupervised learning method useful in various applications including image processing and semantic analysis of documents. This paper focuses on symmetric NMF (SNMF), which is a special case of NMF decomposition. Three parallel multiplicative update algorithms using level 3 basic linear algebra subprograms directly are developed for this problem. First, by minimizing the Euclidean distance, a multiplicative update algorithm is proposed, and its convergence under mild conditions is proved. Based on it, we further propose another two fast parallel methods: α-SNMF and β -SNMF algorithms. All of them are easy to implement. These algorithms are applied to probabilistic clustering. We demonstrate their effectiveness for facial image clustering, document categorization, and pattern clustering in gene expression.

Minimum-Volume-Constrained Nonnegative Matrix Factorization: Enhanced Ability of Learning Parts

Nonnegative matrix factorization (NMF) with minimum-volume-constraint (MVC) is exploited in this paper. Our results show that MVC can actually improve the sparseness of the results of NMF. This sparseness is L0-norm oriented and can give desirable results even in very weak sparseness situations, thereby leading to the significantly enhanced ability of learning parts of NMF. The close relation between NMF, sparse NMF, and the MVC_NMF is discussed first. Then two algorithms are proposed to solve the MVC_NMF model. One is called quadratic programming_MVC_NMF (QP_MVC_NMF) which is based on quadratic programming and the other is called negative glow_MVC_NMF (NG_MVC_NMF) because it uses multiplicative updates incorporating natural gradient ingeniously. The QP_MVC_NMF algorithm is quite efficient for small-scale problems and the NG_MVC_NMF algorithm is more suitable for large-scale problems. Simulations show the efficiency and validity of the proposed methods in applications of blind source separation and human face images analysis.

Validating rationale of group-level component analysis based on estimating number of sources in EEG through model order selection.

This study addresses how to validate the rationale of group component analysis (CA) for blind source separation through estimating the number of sources in each individual EEG dataset via model order selection. Control children, typically reading children with risk for reading disability (RD), and children with RD participated in the experiment. Passive oddball paradigm was used for eliciting mismatch negativity during EEG data collection. Data were cleaned by two digital filters with pass bands of 1-30 Hz and 1-15 Hz and a wavelet filter with the pass band narrower than 1-12 Hz. Three model order selection methods were used to estimate the number of sources in each filtered EEG dataset. Under the filter with the pass band of 1-30 Hz, the numbers of sources were very similar among different individual EEG datasets and the group ICA would be suggested; regarding the other two filters with much narrower pass bands, the numbers of sources were relatively diverse, and then, applying group ICA would not be appropriate. Hence, before group ICA is performed, its rationale can be logically validated by the estimated number of sources in EEG data through model order selection.

Rate of Convergence of the FOCUSS Algorithm

Focal underdetermined system solver (FOCUSS) is a powerful method for basis selection and sparse representation, where it employs the <inline-formula> <tex-math notation=LaTeX>

Convergence Analysis of the FOCUSS Algorithm

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Canonical Polyadic Decomposition: From 3-way to N-Way

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Robust Latent Subspace Learning for Image Classification

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Low-Sparsity Unobservable Attacks Against Smart Grid: Attack Exposure Analysis and a Data-Driven Attack Scheme

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Nesterov's iterations for NMF-Based supervised classification of texture patterns

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Fast and effective model order selection method to determine the number of sources in a linear transformation model

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