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.
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