Pattern Synthesis for Large - Scale Pattern Recognition

Micro-arrays technology has marked a substantial improvement in making available a huge amount of data about gene expression in pathophysiological conditions; among the many papers and books recently devoted to the topic, see, for instance, Hardimann (2003) for a discussion on such a tool. The availability of so many data attracted the attention of the scientific community much on how to extract significant and directly understandable information in an easy and fast automatic way from such a big quantity of measurements. Many papers and books have been devoted as well to various ways to process micro-arrays data; Knudsen (2004) is a recent re-edition of a book pointing to some of the approaches of interest to the topic. When such opportunity to have many measurements on several subjects arises, one of the typical goals one has in mind is to classify subjects on the basis of a hopefully reduced meaningful subset of the measured variables. The complexity of the problem makes it worthwhile to resort to automatic classification procedures. A quite general data-mining approach that proved to be useful also in this context is described elsewhere in this encyclopedia (Liberati, 2004), where different techniques also are referenced, and where a clustering approach to piecewise affine model identification also is reported. In this contribution, we will resort to a different recently developed unsupervised clustering approach, the PDDP algorithm, proposed in Boley (1998). According to the analysis provided in Savaresi & Boley (2004), PDDP is able to provide a significant improvement of the performances of a classical k-means approach (Hand et al., 2001; MacQueen, 1967), when PDDP is used to initialize the kmeans clustering procedure. Such cascading of PDDP and k-means was, in fact, already successfully applied in a totally different context for analyzing the data regarding a large virtual community of Internet users (Garatti et al., 2004). The approach taken herein may be summarized in the following four steps, the third of which is the core of the method, while the first two constitute a preprocessing phase useful to ease the following task, and the fourth one a post-processing designed to focus back on the original variables, found to be meaningful after the transforms operated in the previous steps: