Accelerated algorithm for pattern detection in logical analysis of data

Authors:
Sorin Alexe;Peter L. Hammer
Affiliations:
Rutgers University, RUTCOR, 640 Bartholomew Road, Piscataway, NJ 08854-8003, United States;Rutgers University, RUTCOR, 640 Bartholomew Road, Piscataway, NJ 08854-8003, United States
Venue:
Discrete Applied Mathematics - Special issue: Discrete mathematics & data mining II (DM & DM II)
Year:
2006

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Abstract

Sets of ''positive'' and ''negative'' points (observations) in n-dimensional discrete space given along with their non-negative integer multiplicities are analyzed from the perspective of the Logical Analysis of Data (LAD). A set of observations satisfying upper and/or lower bounds imposed on certain components is called a positive pattern if it contains some positive observations and no negative one. The number of variables on which such restrictions are imposed is called the degree of the pattern. A total polynomial algorithm is proposed for the enumeration of all patterns of limited degree, and special efficient variants of it for the enumeration of all patterns with certain ''sign'' and ''coverage'' requirements are presented and evaluated on a publicly available collection of benchmark datasets.