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, ......
This thoroughly revised second edition provides an updated treatment of numerical linear algebra techniques for solving problems in data mining and pattern recognition. Adopting an application-oriented approach, the author introduces matrix theory and decompositions, describes how modern matrix methods can be applied in real life scenarios, and ......
Many fundamental combinatorial problems, arising in such diverse fields as artificial intelligence, logic, graph theory, and linear algebra, can be formulated as Boolean constraint satisfaction problems (CSP). This volume is devoted to the study of the complexity of such problems. The authors' goal is to develop a framework for classifying the ......
New proofs of classical results are presented and difficult results are made accessible in this monograph. The integer programming models known as set packing and set covering have a wide range of applications. Sometimes, owing to the special structure of the constraint matrix, the natural linear programming relaxation yields an optimal solution ......
An encyclopaedia for the literature on graph classes, this volume contains a survey of more than 200 classes of graphs, organized by types of properties used to define and characterize the classes, citing key theorems and literature references for each. The authors state results without proof, providing readers with access to a wide selection of ......
A book that presents real applications of graph theory in a unified format. This book is the only source for an extended, concentrated focus on the theory and techniques common to various types of intersection graphs. It is a concise treatment of the aspects of intersection graphs that interconnect many standard concepts and form the foundation ......
This monograph provides an introduction to the state of the art of the probability theory that is most directly applicable to combinatorial optimization. Much attention is paid to those questions dealing with discrete optimization problems for points in Euclidean space, such as the minimum spanning tree, the travelling-salesman tour and ......
This monograph is a survey of some of the work that has been done since the appearance of the second edition of Combinatorial Algorithms. Topics include progress in: Gray Codes, listing of subsets of given size of a given universe, listing rooted and free trees, selecting free trees and unlabeled graphs uniformly at random, and ranking and ......
A study of how complexity questions in computing interact with classical mathematics in the numerical analysis of issues in algorithm design. Algorithmic designers concerned with linear and nonlinear combinatorial optimization will find this volume especially useful. Two algorithms are studied in detail: the ellipsoid method and the simultaneous ......
