Superparamagnetic clustering of data

Abstract

We present a new approach for clustering, based on the physical properties of an inhomogeneous ferromagnetic model. We do not assume any structure of the underlying distribution of the data. A Potts spin is assigned to each data point and short range interactions between neighboring points are introduced. Spin-spin correlations, measured (by Monte Carlo procedure) in a superparamagnetic regime in which aligned domains appear, serve to partition the data points into clusters. Our method outperforms other algorithms for toy problems as well as for real data. [S0031-9007(96)00104-4]

Functional connectivity mapping using the ferromagnetic Potts spin model

“…The effect of the form of the interaction kernel on algorithm performance has been experimentally shown to be negligible by previous researchers [Wiseman et al, 1998]. In particular, the standard deviation trajectories for the power law interactions, interactions specified by the Gaussian kernel, and interactions specified by the exponential kernel were found to be similar and differ only in the range of temperatures where the changes in the system occur.…”

“…Choosing K too big or too small would either smooth out the important features in the data or make its structure appear too noisy. The effect of K was not found to be crucial to the performance of the clustering procedure for a many-cluster model with noise [Wiseman et al, 1998], however, the size of the neighborhood considered in that paper did not vary considerably (K ¼ 6, 12, 14, 18, and the Voronoi cell structure were studied), the contrast to noise ratio of the image, though not specified, appeared to be reasonably high, and the performance of the algorithm was measured in terms of accuracy, a measure that is less conservative than the adjusted Rand index.…”

“…The method was originally developed by Blatt et al [1996] and its physical aspects and performance were rigorously studied in successive publications [Blatt et al, 1997;Domany, 1999;Wiseman et al, 1998]. The Potts model is native of statistical physics [Wu, 1982] and models an inhomogeneous ferromagnetic system where each data point is viewed as a marked vertex on the graph.…”

The Structure of an Oral Tradition ? Mapping of Hungarian Folk Music to a Metric Space

“…Dynamic programming, which is widely used in control theory, has been successfully applied to characterise the diversity of a couple of melodies by a scalar measure (Vicsi, Mattila, & Berényi, 1990;Sachira & Milan, 1997). Further classification methods, like supermagnetic clustering, may also be able for musical aims (Wiesman & Domany, 1998).…”

Macrostate data clustering

“…A number have used analogies to statistical mechanical phase transitions [11,12,13,14,15], while others have used chaotic [16] or quantum mechanical [17] systems as analogs. Most of these have the advantage of being "fuzzy"-in addition to assigning items to clusters, they provide a continuous measure of the probability or strength of the assignment of each item.…”