Nonnegative Matrix and Tensor Factorizations

Applications to Exploratory Multi-way Data Analysis and Blind Source Separation

Shun-ichi Amari author Andrzej Cichocki author Anh Huy Phan author Rafal Zdunek author

Format:Hardback

Publisher:John Wiley & Sons Inc

Published:11th Sep '09

Currently unavailable, and unfortunately no date known when it will be back

Nonnegative Matrix and Tensor Factorizations cover

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.

"[A] focus on the algorithms that are most useful in practice and aim to derive and implement, in MATLAB, efficient and simple iterative algorithms that work with real-world data." (Book News, December 2009)

ISBN: 9780470746660

Dimensions: 252mm x 173mm x 31mm

Weight: 1202g

504 pages