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 classification, 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 artificial and real-life problems, such as classification of flowers, processing of satellite images, speech recognition and identification of textures and images. We are currently involved in several collaborations, applying the method to image classification, fMRI data analysis and classification of protein structures.