Nonnegative Matrix and Tensor Factorizations (PDF)

This book provides a broad survey of models and efficient
algorithms for Nonnegative Matrix Factorization (NMF). This
includes NMF's 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.