Anh Huy Phan

Nonnegative Matrix and Tensor Factorizations

This book provides a broad survey of models and efficient algorithms for Nonnegative Matrix Factorization (NMF). This includes NMFs various extensions and modifications, especially Nonnegative Tensor Factorizations (NTF) and Nonnegative Tucker Decompositions (NTD). NMF/NTF and their extensions are increasingly used as tools in signal and image processing, and data analysis, having garnered interest due to their capability to provide new insights and relevant information about the complex latent relationships in experimental data sets. It is suggested that NMF can provide meaningful components with physical interpretations; for example, in bioinformatics, NMF and its extensions have been successfully applied to gene expression, sequence analysis, the functional characterization of genes, clustering and text mining. As such, the authors focus on the algorithms that are most useful in practice, looking at the fastest, most robust, and suitable for large-scale models. Key features: Acts as a single source reference guide to NMF, collating information that is widely dispersed in current literature, including the authors own recently developed techniques in the subject area. Uses generalized cost functions such as Bregman, Alpha and Beta divergences, to present practical implementations of several types of robust algorithms, in particular Multiplicative, Alternating Least Squares, Projected Gradient and Quasi Newton algorithms. Provides a comparative analysis of the different methods in order to identify approximation error and complexity. Includes pseudo codes and optimized MATLAB source codes for almost all algorithms presented in the book. The increasing interest in nonnegative matrix and tensor factorizations, as well as decompositions and sparse representation of data, will ensure that this book is essential reading for engineers, scientists, researchers, industry practitioners and graduate students across signal and image processing; neuroscience; data mining and data analysis; computer science; bioinformatics; speech processing; biomedical engineering; and multimedia.

Noninvasive BCIs: Multiway Signal-Processing Array Decompositions

In addition to helping better understand how the human brain works, the brain-computer interface neuroscience paradigm allows researchers to develop a new class of bioengineering control devices and robots, offering promise for rehabilitation and other medical applications as well as exploring possibilities for advanced human-computer interfaces.

Low Complexity Damped Gauss--Newton Algorithms for CANDECOMP/PARAFAC

The damped Gauss--Newton (dGN) algorithm for CANDECOMP/PARAFAC (CP) decomposition can handle the challenges of collinearity of factors and different magnitudes of factors; nevertheless, for factorization of an order-

PARAFAC algorithms for large-scale problems

N

MULTI-DOMAIN FEATURE EXTRACTION FOR SMALL EVENT-RELATED POTENTIALS THROUGH NONNEGATIVE MULTI-WAY ARRAY DECOMPOSITION FROM LOW DENSE ARRAY EEG

tensor of size

Fast Alternating LS Algorithms for High Order CANDECOMP/PARAFAC Tensor Factorizations

I_1\times\cdots\times I_N

Nonsmooth Optimization for Efficient Beamforming in Cognitive Radio Multicast Transmission

with rank

Extended HALS algorithm for nonnegative Tucker decomposition and its applications for multiway analysis and classification

R

Flexible HALS algorithms for sparse non-negative matrix/tensor factorization

, the algorithm is computationally demanding due to construction of a large approximate Hessian of size

Cramér-Rao-Induced Bounds for CANDECOMP/PARAFAC Tensor Decomposition

(RT \times RT)