Data Clustering Using a Model Granular Magnet
- 1 November 1997
- journal article
- Published by MIT Press in Neural Computation
- Vol. 9 (8), 1805-1842
- https://doi.org/10.1162/neco.1997.9.8.1805
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.Keywords
This publication has 34 references indexed in Scilit:
- Superparamagnetic Clustering of DataPhysical Review Letters, 1996
- A neural network for unsupervised categorization of multivalued input patterns: an application to satellite image clusteringIEEE Transactions on Geoscience and Remote Sensing, 1995
- Vector quantization with complexity costsIEEE Transactions on Information Theory, 1993
- Randomness-induced second-order transition in the two-dimensional eight-state Potts model: A Monte Carlo studyPhysical Review Letters, 1992
- Dynamics near a first-order phase transition with the Metropolis and Swendsen-Wang algorithmsNuclear Physics B, 1991
- Generalization of the Fortuin-Kasteleyn-Swendsen-Wang representation and Monte Carlo algorithmPhysical Review D, 1988
- On percolation as a cosmological testThe Astrophysical Journal, 1985
- Dot Pattern Processing Using Voronoi NeighborhoodsIeee Transactions On Pattern Analysis and Machine Intelligence, 1982
- Thermal phase transitions at the percolation thresholdPhysics Letters A, 1981
- A clustering technique for summarizing multivariate dataBehavioral Science, 1967