Algorithms for Internal Validation Clustering Measures in the Post Genomic Era

TL;DR

This paper evaluates and compares internal validation measures for clustering microarray data, proposing a new algorithmic framework and approximation techniques to balance accuracy and computational efficiency.

Contribution

It introduces a general algorithmic paradigm for stability-based validation measures and develops fast approximation algorithms to improve their practical applicability.

Findings

Hierarchy of measures in terms of accuracy and speed

Fast approximation algorithms significantly reduce computation time

Trade-off between speed and accuracy is minimized with new techniques

Abstract

Inferring cluster structure in microarray datasets is a fundamental task for the -omic sciences. A fundamental question in Statistics, Data Analysis and Classification, is the prediction of the number of clusters in a dataset, usually established via internal validation measures. Despite the wealth of internal measures available in the literature, new ones have been recently proposed, some of them specifically for microarray data. In this dissertation, a study of internal validation measures is given, paying particular attention to the stability based ones. Indeed, this class of measures is particularly prominent and promising in order to have a reliable estimate the number of clusters in a dataset. For those measures, a new general algorithmic paradigm is proposed here that highlights the richness of measures in this class and accounts for the ones already available in the literature. Moreover, some of the most representative validation measures are also considered. Experiments on 12 benchmark datasets are performed in order to assess both the intrinsic ability of a measure to predict the correct number of clusters in a dataset and its merit relative to the other measures. The main result is a hierarchy of internal validation measures in terms of precision and speed, highlighting some of their merits and limitations not reported before in the literature. This hierarchy shows that the faster the measure, the less accurate it is. In order to reduce the time performance gap between the fastest and the most precise measures, the technique of designing fast approximation algorithms is systematically applied. The end result is a speed-up of many of the measures studied here that brings the gap between the fastest and the most precise within one order of magnitude in time, with no degradation in their prediction power. Prior to this work, the time gap was at least two orders of magnitude.