MILP approach to pattern generation in logical analysis of data

General Set Covering for Feature Selection in Data Mining

“…In this section, with two small examples, we illustrate the usefulness of (gSC) for support feature selection, in comparison with (sSC), the standard approach in the literature (e.g., Boros et al, 2000;Kim and Ryoo, 2008;Ryoo and Jang, 2009). …”

“…As seen, however, (gSC) selects support features based on combinatorial interplay among all variables, hence is better suited for the purpose of support feature selection in data mining than the standard approach of using SC k times successively (e.g., Boros et al, 2000;Kim and Ryoo, 2008;Ryoo and Jang, 2009). …”

“…Therefore, the degree of difficulty associated with finding an accurate classification theory is closely related to the number of support features used. For support feature selection, which is a combinatorial optimization problem in nature, set covering has widely been accepted as a staple tool (e.g., Boros et al, 1997;Boros et al, 2000), and the common practice is to apply SC k times in succession to ensure selecting small but enough number of features for an accurate analysis of data on hand (e.g., Boros et al, 2000;Kim and Ryoo, 2008;Ryoo and Jang, 2009). In short, support features are the building blocks of a classification theory and, therefore, the quality of a classification theory can be said to be only as good as the quality of the features selected for use.…”

Logical analysis of multi-class data

“…The research area of LAD was introduced and developed by Peter L. Hammer [28] whose vision expanded the LAD methodology from theory to successful data applications in numerous biomedical, industrial, and economics case studies (see, e.g., [13,51] and the references therein). The implementation of LAD algorithm was described in [12], and several further developments of the original algorithm were presented in [4,11,30,27,52]. An overview of standard LAD algorithm can be found in [3,11].…”

“…Since the problem is of practical importance, there have been several attempts to extend binary classification algorithms to multi-class problems in literature. Here are some of them: multiclass classification [8,59,26,32], discriminant analysis for multi-class classification [43,42], multiclass learning [6,23], combining many two-class classifiers into a multiclass classifier [50,58,56,55,25], multi-class classfication with applications [54] , mixed-integer programming approach to multi-class data classification, [57,27,52], general multiclass classfication methods reviews [5], and multiclass classfication by using support vector machines [2].…”