Database Transposition for Constrained (Closed) Pattern Mining

TL;DR

This paper introduces a theoretical framework for transposing databases and constraints to efficiently mine constrained closed patterns in databases with many attributes but few objects, such as in genome biology.

Contribution

It provides a formal approach for transposing databases and constraints, enabling efficient pattern mining in high-dimensional, sparse datasets.

Findings

Framework for database and constraint transposition

Method to generate original constrained patterns from transposed data

Analysis of properties of constraint transposition

Abstract

Recently, different works proposed a new way to mine patterns in databases with pathological size. For example, experiments in genome biology usually provide databases with thousands of attributes (genes) but only tens of objects (experiments). In this case, mining the "transposed" database runs through a smaller search space, and the Galois connection allows to infer the closed patterns of the original database. We focus here on constrained pattern mining for those unusual databases and give a theoretical framework for database and constraint transposition. We discuss the properties of constraint transposition and look into classical constraints. We then address the problem of generating the closed patterns of the original database satisfying the constraint, starting from those mined in the "transposed" database. Finally, we show how to generate all the patterns satisfying the constraint from the closed ones.