Data Clustering Using a Model Granular Magnet

Abstract

We present a new approach to clustering, based on the physical properties of an inhomogeneous ferromagnet. No assumption is made regarding the underlying distribution of the data. We assign a Potts spin to each data point and introduce an interaction between neighboring points, whose strength is a decreasing function of the distance between the neighbors. This magnetic system exhibits three phases. At very low temperatures, it is completely ordered; all spins are aligned. At very high temperatures, the system does not exhibit any ordering, and in an intermediate regime, clusters of relatively strongly coupled spins become ordered, whereas different clusters remain uncorrelated. This intermediate phase is identified by a jump in the order parameters. The spin-spin correlation function is used to partition the spins and the corresponding data points into clusters. We demonstrate on three synthetic and three real data sets how the method works. Detailed comparison to the performance of other techniques clearly indicates the relative success of our method.

Seismic Image Segmentation

“…The image segmentation method is adapted from a data clustering method [9], both of which solve similar problems. Briefly, the segmentation method is outlined as follows.…”

“…The data clustering method on which this image segmentation method is based is described in detail in [9]. The method was successfully applied to speech recognition, land-cover clsss.ification, and more [9].…”

Learning and inferring image segmentations using the GBP typical cut algorithm

“…The criterion was first introduced by Blatt et al [1] in the framework of statistical physics, and was reformulated by Gdalyahu et al [5] in terms of graph partitioning and image segmentation. Unlike most graph partitioning algorithms, this one is directly based on a probability distribution over partitions.…”

“…Thus performing MAP inference under this probability distribution will still lead to trivial segmentations. However, as pointed out by [1,5], there is far more information in the full probability distribution over partitions than solely in the MAP partition. For example, consider the pairwise correlation Ô´ µ defined for any two neighboring nodes in the graph as the probability that they belong to the same segment:…”

“…While efficient approximate algorithms for normalized cut are available through eigensolvers, to this day, there has been no similar algorithm for typical cuts. Both [1,5] used sophisticated stochastic algorithms whose behavior for finite samples is difficult to analyze. In fact, the problem of determining the equilibrium distribution over segmentations from which the algorithm used in [5] samples from, is an open one.…”