PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

The Discrete Basis Problem
Pauli Miettinen, Taneli Mielikäinen, Aristides Gionis, Gautam Das and Heikki Mannila
In: PKDD 2006, September 18-22, Berlin, Germany.

Abstract

Matrix decomposition methods represent a data matrix as a product of two smaller matrices: one containing basis vectors that represent meaningful concepts in the data, and another describing how the observed data can be expressed as combinations of the basis vectors. Decomposition methods have been studied extensively, but many methods return real-valued matrices. If the original data is binary, the interpretation of the basis vectors is hard. We describe a matrix decomposition formulation, the Discrete Basis Problem. The problem seeks for a Boolean decomposition of a binary matrix, thus allowing the user to easily interpret the basis vectors. We show that the problem is computationally difficult and give a simple greedy algorithm for solving it. We present experimental results for the algorithm. The method gives intuitively appealing basis vectors. On the other hand, the continuous decomposition methods often give better reconstruction accuracies. We discuss the reasons for this behavior.

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EPrint Type:Conference or Workshop Item (Paper)
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Theory & Algorithms
Information Retrieval & Textual Information Access
ID Code:2158
Deposited By:Taneli Mielikäinen
Deposited On:03 August 2006