Book
Nonnegative matrix factorization (NMF) in its modern form has become a standard tool in the analysis of high-dimensional data sets. This book provides a comprehensive and up-to-date account of the most important aspects of the NMF problem and is the first to detail its theoretical aspects, including geometric interpretation, nonnegative rank, complexity, and uniqueness. It explains why understanding these theoretical insights is key to using this computational tool effectively and meaningfully. The book also presents models, algorithms and applications of NMF. It contains 2 parts and is divided into 9 chapters:
Nonnegative matrix factorization (NMF) in its modern form has become a standard tool in the analysis of high-dimensional data sets. This book provides a comprehensive and up-to-date account of the most important aspects of the NMF problem and is the first to detail its theoretical aspects, including geometric interpretation, nonnegative rank, complexity, and uniqueness. It explains why understanding these theoretical insights is key to using this computational tool effectively and meaningfully. The book also presents models, algorithms and applications of NMF. It contains 2 parts and is divided into 9 chapters:
- Introduction
Part I - Exact factorizations
Part I - Exact factorizations
- Exact NMF
- Nonnegative Rank
- Identifiability
Part II - Approximate factorizations
Part II - Approximate factorizations
- Models
- Computational Complexity of NMF
- Near-separable NMF
- Iterative algorithms for NMF
- Applications
The book can be ordered on the SIAM website and it is available in the SIAM digital library (see here), and on Google Play.
The book can be ordered on the SIAM website and it is available in the SIAM digital library (see here), and on Google Play.
MATLAB
MATLAB
The MATLAB codes presented and used in the book can be downloaded here, and include a documentation.
The MATLAB codes presented and used in the book can be downloaded here, and include a documentation.
Any feedback on the code or on the book is more than welcome!
Any feedback on the code or on the book is more than welcome!
Errata and additional material
Errata and additional material
In this document, you can find the errata of the first version of the book (so far, there are mostly minor errors -- please report to me any error you may find). A new version (reprint from January 2024) is available here.
In this document, you can find the errata of the first version of the book (so far, there are mostly minor errors -- please report to me any error you may find). A new version (reprint from January 2024) is available here.
I have also prepared some useful additional material: an illustrative example of the use of NMF to extract topics automatically in a set of documents (such an example is not present in the book), another comparison of minimum-volume NMF models on the Moffet data set, and a new accelerated version of the multiplicative updates (MU) for β-NMF; see this document.
I have also prepared some useful additional material: an illustrative example of the use of NMF to extract topics automatically in a set of documents (such an example is not present in the book), another comparison of minimum-volume NMF models on the Moffet data set, and a new accelerated version of the multiplicative updates (MU) for β-NMF; see this document.
Reviews
Reviews
A review of the book in zbMATH Open by John D. Dixon (Carleton University) is available here, including
"The book is clearly written and the geometric parts are attractively illustrated. The book has a bibliography of over 500 items (about half published in the last 10 years), a good index and an important index of notation including a full page of acronyms. It surveys a wide range of material. It is helpful that the chapters are largely independent and that the author is careful to stop and summarize from time to time."
A review of the book in zbMATH Open by John D. Dixon (Carleton University) is available here, including
"The book is clearly written and the geometric parts are attractively illustrated. The book has a bibliography of over 500 items (about half published in the last 10 years), a good index and an important index of notation including a full page of acronyms. It surveys a wide range of material. It is helpful that the chapters are largely independent and that the author is careful to stop and summarize from time to time."
Another one in SIAM Review by Arvind K. Saibaba (North Carolina State University) is available here, including
"This book is a one-stop shop for the theory, algorithms, and applications of NMF."
"These chapters weave foundational results with a ton of insight from linear algebra, optimization, and geometry. The proofs are easy to follow, and the main results are illuminated with examples (or counterexamples) and illustrations."
"It is not common to find a book that is good in theory, algorithms, and applications, but this book manages to find a good balance."
Another one in SIAM Review by Arvind K. Saibaba (North Carolina State University) is available here, including
"This book is a one-stop shop for the theory, algorithms, and applications of NMF."
"These chapters weave foundational results with a ton of insight from linear algebra, optimization, and geometry. The proofs are easy to follow, and the main results are illuminated with examples (or counterexamples) and illustrations."
"It is not common to find a book that is good in theory, algorithms, and applications, but this book manages to find a good balance."
A third one from Mathematical Reviews by Elena Pelican (Ovidius University) is available here, including
"The book is organized in 9 chapters, each of them a survey of the announced topic, and as self-contained as possible, so that the reader is able to understand the material without the necessity of reading the previous chapters. A plus of the book is the fact that at the end of each chapter, the reader can find some take-home messages that summarize and highlight the most important aspects of the topic covered."
"...for the huge amount of work necessary to put together all the results, the author should be congratulated."
A third one from Mathematical Reviews by Elena Pelican (Ovidius University) is available here, including
"The book is organized in 9 chapters, each of them a survey of the announced topic, and as self-contained as possible, so that the reader is able to understand the material without the necessity of reading the previous chapters. A plus of the book is the fact that at the end of each chapter, the reader can find some take-home messages that summarize and highlight the most important aspects of the topic covered."
"...for the huge amount of work necessary to put together all the results, the author should be congratulated."