Distance Functions, Clustering Algorithms and Microarray Data Analysis

Distance functions are a fundamental ingredient of classification and clustering procedures, and this holds true also in the particular case of microarray data. In the general data mining and classification literature, functions such as Euclidean distance or Pearson correlation have gained their status of de facto standards thanks to a considerable amount of experimental validation. For microarray data, the issue of which distance function "works best" has been investigated, but no final conclusion has been reached. The aim of this paper is to shed further light on that issue. Indeed, we present an experimental study, involving several distances, assessing (a) their intrinsic separation ability and (b) their predictive power when used in conjunction with clustering algorithms. The experiments have been carried out on six benchmark microarray datasets, where the "gold solution" is known for each of them. We have used both Hierarchical and K-means clustering algorithms and external validation criteria as evaluation tools. From the methodological point of view, the main result of this study is a ranking of those measures in terms of their intrinsic and clustering abilities, highlighting also the correlations between the two. Pragmatically, based on the outcomes of the experiments, one receives the indication that Minkowski, cosine and Pearson correlation distances seems to be the best choice when dealing with microarray data analysis.