Banded Pattern Mining Algorithms in Multi-dimensional Zero-One Data

Abstract

A zero-one high-dimensional data set is said to be banded if all the dimensions can be reorganised such that the “non zero” entries are arranged along the leading diagonal across the dimensions. Our goal is to develop effective algorithms that identify banded patterns in multi-dimensional zero-one data by automatically rearranging the ordering of all the dimensions. Rearranging zero-one data so as to feature “bandedness” allows for the identification of hidden information and enhances the operation of many data mining algorithms (and other algorithms) that work with zero-one data. In this paper two N-Dimensional Banded Pattern Mining (NDBPM) algorithms are presented. The first is an approximate algorithm (NDBPM$_{APPROX}$) and the second an exact algorithm (NDBPM$_{EXACT}$). Two variations of NDBPM$_{EXACT}$ are presented (Euclidean and Manhattan). Both algorithms are fully described together with evaluations of their operation.