Preface

Nonnegative Matrix Factorization (NMF) is one of the widely used matrix
factorization techniques for revealing hidden factors that underlie sets of random variables, measurements, or signals. NMF is essentially a method for extracting individual signals from mixtures of signals. The concept of a matrix factorization arises in a variety of significant applications and each matrix factorization task makes a different assumption regarding factor matrices and their underlying configurations. Therefore choosing the appropriate one is important in each application domain. In most instances, the data to be analyzed are nonnegative, and sometimes they also have sparse representations. For such applications, it is preferable to take these constraints into account in the analysis to extract nonnegative and sparse/smooth components or factors with physical meaning or reasonable interpretation, and thereby avoid absurd or unpredictable results. NMF research can be motivated by the open problems and continuing research on these problems, and hence a need to edit this book to report the latest results on the topic. These challenges motivate further research in the area of NMF, and this book intends to put together all the innovative ideas and new results in this research area.