Pattern-based clustering and attribute analysis

The Logical Analysis of Data (LAD) is a combinatorics, optimization and logic based methodology for the analysis of datasets with binary or numerical input variables, and binary outcomes. It has been established in previous studies that LAD provides a competitive classification tool comparable in efficiency with the top classification techniques available. The goal of this paper is to show that the methodology of LAD can be useful in the discovery of new classes of observations and in the analysis of attributes. After a brief description of the main concepts of LAD, two efficient combinatorial algorithms are described for the generation of all prime, respectively all spanned, patterns (rules) satisfying certain conditions. It is shown that the application of classic clustering techniques to the set of observations represented in prime pattern space leads to the identification of a subclass of, say positive, observations, which is accurately recognizable, and is sharply distinct from the observations in the opposite, say negative, class. It is also shown that the set of all spanned patterns allows the introduction of a measure of significance and of a concept of monotonicity in the set of attributes. Acknowledgements: The partial support provided by ONR grant N00014-92-J-1375 and DIMACS is gratefully acknowledged.