  The sole aim of this book is to give a self-contained introduction to
concepts and mathematical tools in Bayesian matrix decomposition in order to
seamlessly introduce matrix decomposition techniques and their applications in
subsequent sections. However, we clearly realize our inability to cover all the
useful and interesting results concerning Bayesian matrix decomposition and
given the paucity of scope to present this discussion, e.g., the separated
analysis of variational inference for conducting the optimization. We refer the
reader to literature in the field of Bayesian analysis for a more detailed
introduction to the related fields.
  This book is primarily a summary of purpose, significance of important
Bayesian matrix decomposition methods, e.g., real-valued decomposition,
nonnegative matrix factorization, Bayesian interpolative decomposition, and the
origin and complexity of the methods which shed light on their applications.
The mathematical prerequisite is a first course in statistics and linear
algebra. Other than this modest background, the development is self-contained,
with rigorous proof provided throughout.
