Boolean Matrix Decomposition Problem: Theory, Variations and Applications to Data Engineering

Abstract

With the ubiquitous nature and sheer scale of data collection, the problem of data summarization is most critical for effective data management. Classical matrix decomposition techniques have often been used for this purpose, and have been the subject of much study. In recent years, several other forms of decomposition, including Boolean Matrix Decomposition have become of significant practical interest. Since much of the data collected is categorical in nature, it can be viewed in terms of a Boolean matrix. Boolean matrix decomposition (BMD), wherein a boolean matrix is expressed as a product of two Boolean matrices, can be used to provide concise and interpretable representations of Boolean data sets. The decomposed matrices give the set of meaningful concepts and their combination which can be used to reconstruct the original data. Such decompositions are useful in a number of application domains including role engineering, text mining as well as knowledge discovery from databases. In this seminar, we look at the theory underlying the BMD problem, study some of its variants and solutions, and examine different practical applications.