Superparamagnetic Clustering of Data - the Definitive Solution of an Ill-posed Problem

Clustering is an important technique in exploratory data analysis, with applications in image processing, object classiication, target recognition, data mining etc. The aim is to partition data according to natural classes present in it, assigning data points that are "more similar" to the same "cluster". We solved this ill-posed problem without making any assumptions about the structure of the data, by using a physical system as an analog computer. The physical system we use is a disordered (granular) magnet. The method was tested successfully on a variety of artiicial and real-life problems, such as classiication of owers, processing of satellite images, speech recognition and identiication of textures and images. We are currently involved in several collaborations, applying the method to image classiication, fMRI data analysis and classiication of protein structures.