Superparamagnetic Clustering of Data
Physical Review LettersPublished 29 April 1996
Marcelo Blatt, Shai Wiseman, Eytan Domany
Citations544
SJR quartileQ1
SJR score2.86
SNIP2.41
Generate an AI Snapshot to get a quick, structured summary of this paper.
Study Snapshot
ObjectiveStudy objective
MethodsResearch methodology
PopulationPopulation studied
Sample sizeSample sizes
OutcomesStudy outcomes here
ResultsStudy results comes here
LimitationsResearch study limitations comes here
A concise AI-generated summary of the paper will appear here once you click Generate AI Snapshot.
TL;DR
This work presents a new approach for clustering, based on the physical properties of an inhomogeneous ferromagnetic model, which outperforms other algorithms for toy problems as well as for real 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.
Keywords
Computer SciencePhysics and Astronomy
ScienceOptimization by Simulated Annealing
44,600 Citations1983Scott Kirkpatrick, C. D. Gelatt +1 more
A detailed analogy with annealing in solids provides a framework for optimization of the properties of very large and complex systems.
Pattern classification and scene analysis
12,643 Citations1973Richard O. Duda, Peter E. Hart
Elsevier eBooksIntroduction to Statistical Pattern Recognition
11,121 Citations1990Keinosuke Fukunaga
A system to determine the sex of fish from their length, as accurately as possible, using a set of labelled data, together with the class label (male or female), as a training set.
Neural ComputationFast Learning in Networks of Locally-Tuned Processing Units
4,219 Citations1989John Moody, Christian J. Darken
This work proposes a network architecture which uses a single internal layer of locally-tuned processing units to learn both classification tasks and real-valued function approximations (Moody and Darken 1988).
Journal of the Royal Statistical Society Series A (General)Pattern Classification and Scene Analysis.
3,240 Citations1974Mairi Clarke, Richard O. Duda +1 more
PhysicaOn the random-cluster model
1,772 Citations1972C.M. Fortuin, Piet Kasteleyn
It is shown that the function which for the random-cluster model plays the role of a partition function, is a generalization of the dichromatic polynomial earlier introduced by Tutte, and related polynomials.
Journal of Physics A Mathematical and GeneralClusters and Ising critical droplets: a renormalisation group approach
552 Citations1980Antonio Coniglio, W. Klein
Physical Review LettersStatistical mechanics and phase transitions in clustering
463 Citations1990Kenneth Rose, E. Gurewitz +1 more
Journal of Physics A Mathematical and GeneralApplication of statistical mechanics to NP-complete problems in combinatorial optimisation
326 Citations1986Yuchen Fu, Philip W. Anderson
The authors find a spin glass transition in the system, and the low temperature phase space has an ultrametric structure, which sheds light on the nature of hard computation problems.
Physica A Statistical Mechanics and its ApplicationsCluster Monte Carlo algorithms
280 Citations1990Jian‐Sheng Wang, Robert H. Swendsen
The Swendsen-Wang and Wolff Monte Carlo algorithms are described in some detail, using the Potts model as an example, and various generalizations are reviewed.
Journal de physiqueA replica analysis of the travelling salesman problem
139 Citations1986Marc Mézard, Giorgio Parisi
Neural ComputationStatistical Physics Algorithms That Converge
124 Citations1994Alan Yuille, J.J. Kosowsky
Close connections are demonstrated between mean field theory methods and other approaches, in particular, barrier function and interior point methods, for obtaining approximate solutions to optimization problems.
IEEE Transactions on Information TheoryVector quantization with complexity costs
98 Citations1993Joachim M. Buhmann, H. Kühnel
The approach establishes a unifying framework for different quantization methods like K-means clustering and its fuzzy version, entropy constrained vector quantization or topological feature maps, and competitive neural networks.
Physics Letters ATwo-dimensional eight-state Potts model on random lattices: A Monte Carlo study
44 Citations1995Wolfhard Janke, Ramon Villanova
The Astrophysical JournalOn percolation as a cosmological test
41 Citations1985Avishai Dekel, M. J. West
Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topicsStatistical mechanics of the maximum-likelihood density estimation
28 Citations1994Naama Barkai, Haim Sompolinsky
It is shown numerically that estimating the centers by slowly reducing the estimated Gaussian width yields a good agreement with the theory even in the presence of many local minima.
SIAM Journal on Scientific ComputingConstruction of <i>K</i>-Dimensional Delaunay Triangulations Using Local Transformations
25 Citations1993Barry Joe
It is proved that local transformations can be used to construct a Delaunay triangulation of a set of nk-dimensional points for any $k \geq 2$ and algorithms using this approach are presented.
Physics Letters BImproving the improved estimator in O(N) spin models
21 Citations1990Ferenc Niedermayer
It is pointed out that the improved estimator in the popular cluster updating algorithm for O(N) spin models works well only at large distances, while for strongly correlated spins it has larger dispersin than the scalar product itself.