Superparamagnetic clustering of data: application to computer vision

Domany, Eytan; Blatt, Marcelo; Gdalyahu, Yoram; Weinshall, Daphna

doi:10.1016/s0010-4655(99)00267-2

Cited by 8 publications

(6 citation statements)

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“…Stanberry, Murua, and Cordes (2007) applied the method to study functional connectivity patterns in fMRI data and examined the dependence of the method on neighborhood structure, signal-to-noise ratio, and spatial dependence in the data. Potts model clustering has been applied to different fields such as computer vision (Domany et al 1999), gene expression data (Getz et al 2000;Einav et al 2005), high-dimensional chemical data (Ott et al 2004(Ott et al , 2005 and neuronal spike detection (Quiroga, Nadasdy, and Ben-Shaul 2004).…”

Section: Maximizing (13) Is Equivalent To Minimizingmentioning

confidence: 99%

On Potts Model Clustering, KernelK-Means and Density Estimation

Murua

Stanberry

Stuetzle

2008

Journal of Computational and Graphical Statistics

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Many clustering methods, such as K -means, kernel K -means, and MNcut clustering, follow the same recipe: (i) choose a measure of similarity between observations; (ii) define a figure of merit assigning a large value to partitions of the data that put similar observations in the same cluster; and (iii) optimize this figure of merit over partitions. Potts model clustering represents an interesting variation on this recipe. Blatt, Wiseman, and Domany defined a new figure of merit for partitions that is formally similar to the Hamiltonian of the Potts model for ferromagnetism, extensively studied in statistical physics. For each temperature T , the Hamiltonian defines a distribution assigning a probability to each possible configuration of the physical system or, in the language of clustering, to each partition. Instead of searching for a single partition optimizing the Hamiltonian, they sampled a large number of partitions from this distribution for a range of temperatures. They proposed a heuristic for choosing an appropriate temperature and from the sample of partitions associated with this chosen temperature, they then derived what we call a consensus clustering: two observations are put in the same consensus cluster if they belong to the same cluster in the majority of the random partitions. In a sense, the consensus clustering is an "average" of plausible configurations, and we would expect it to be more stable (over different samples) than the configuration optimizing the Hamiltonian.The goal of this article is to contribute to the understanding of Potts model clustering and to propose extensions and improvements: (1) We show that the Hamiltonian used in Potts model clustering is closely related to the kernel K -means and MNCut criteria. (2) We propose a modification of the Hamiltonian penalizing unequal cluster sizes and show that it can be interpreted as a weighted version of the kernel K -means criterion. (3) We introduce a new version of the Wolff algorithm to simulate configurations from the distribution defined by the penalized Hamiltonian, leading to penalized Potts model clustering. (4) We note a link between kernel based clustering methods and nonparametric density estimation and exploit it to automatically determine locally adaptive kernel bandwidths. (5) We propose a new simple rule for selecting a good temperature T .As an illustration we apply Potts model clustering to gene expression data and compare our results to those obtained by model based clustering and a nonparametric dendrogram sharpening method.

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Section: Maximizing (13) Is Equivalent To Minimizingmentioning

confidence: 99%

On Potts Model Clustering, KernelK-Means and Density Estimation

Murua

Stanberry

Stuetzle

2008

Journal of Computational and Graphical Statistics

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“…The superparamagnetic clustering method, as it was dubbed in the original paper, has been successfully applied to different research problems [Agrawal and Domany, 2003;Domany, 2003;Domany et al, 1999;Einav et al, 2005;Getz et al, 2000a;Kullmann et al, 2000;Ott et al, 2004Ott et al, , 2005Quiroga et al, 2004] and various extensions of the method were proposed, including the iterative coupled two-way clustering [Getz et al, 2000b;Getz and Domany, 2003], the modified Hamiltonian and an improved version of the cluster update algorithm for the image segmentation problem [von Ferber and Woergoetter, 2000], a sequential extension for inhomogeneous clusters [Ott et al, 2004[Ott et al, , 2005, and a spin-glass Hamiltonian for complex networks data [Reichardt and Bornholdt, 2004]. Murua et al (On Potts model clustering, kernel K-means and density estimation, J Comput Graph Stat, under review) related the Potts model based clustering to kernel-based clustering methods and density estimation and introduced yet another penalized Hamiltonian to favor clusters of equal sizes.…”

Section: Introductionmentioning

confidence: 99%

Functional connectivity mapping using the ferromagnetic Potts spin model

Stanberry

Murua

Cordes

2007

Human Brain Mapping

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An unsupervised stochastic clustering method based on the ferromagnetic Potts spin model is introduced as a powerful tool to determine functionally connected regions. The method provides an intuitively simple approach to clustering and makes no assumptions of the number of clusters in the data or their underlying distribution. The performance of the method and its dependence on the intrinsic parameters (size of the neighborhood, form of the interaction term, etc.) is investigated on the simulated data and real fMRI data acquired during a conventional periodic finger tapping task. The merits of incorporating Euclidean information into the connectivity analysis are discussed. The ability of the Potts model clustering to uncover the hidden structure in the complex data is demonstrated through its application to the resting-state data to determine functional connectivity networks of the anterior and posterior cingulate cortices for the group of nine healthy male subjects.

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“…SPC was used in a variety of contexts, ranging from computer vision (Domany et al, 1999) to speech recognition (Blatt et al, 1997). Its first direct application to gene expression data has been for analysis of the temporal dependence of the expression levels in a synchronized yeast culture (Eisen et al, 1998), identifying gene clusters whose variation reflects the cell cycle.…”

Section: Superparamagnetic Clustering -Spcmentioning

confidence: 99%