A least biased fuzzy clustering method

Beni, G.; Liu, Xiaomin

doi:10.1109/34.310694

Cited by 77 publications

(40 citation statements)

References 8 publications

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“…If a limitation on the number of clusters is imposed, then at zero temperature a hard clustering solution, or a quantizer, is obtained. The basic DA approach to clustering has since inspired modifications, extensions, and related work by numerous researchers including [6], [14], [47], [64], [70], [72], [73], [82], [91], [103], [106].…”

Section: Introductionmentioning

confidence: 99%

Deterministic annealing for clustering, compression, classification, regression, and related optimization problems

1998

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The deterministic annealing approach to clustering and its extensions has demonstrated substantial performance improvement over standard supervised and unsupervised learning methods in a variety of important applications including compression, estimation, pattern recognition and classification, and statistical regression. The method offers three important features: 1) the ability to avoid many poor local optima; 2) applicability to many different structures/architectures; and 3) the ability to minimize the right cost function even when its gradients vanish almost everywhere, as in the case of the empirical classification error. It is derived within a probabilistic framework from basic information theoretic principles (e.g., maximum entropy and random coding). The application-specific cost is minimized subject to a constraint on the randomness (Shannon entropy) of the solution, which is gradually lowered. We emphasize intuition gained from analogy to statistical physics, where this is an annealing process that avoids many shallow local minima of the specified cost and, at the limit of zero "temperature," produces a nonrandom (hard) solution. Alternatively, the method is derived within rate-distortion theory, where the annealing process is equivalent to computation of Shannon's rate-distortion function, and the annealing temperature is inversely proportional to the slope of the curve. This provides new insights into the method and its performance, as well as new insights into rate-distortion theory itself. The basic algorithm is extended by incorporating structural constraints to allow optimization of numerous popular structures including vector quantizers, decision trees, multilayer perceptrons, radial basis functions, and mixtures of experts. Experimental results show considerable performance gains over standard structure-specific and application-specific training methods. The paper concludes with a brief discussion of extensions of the method that are currently under investigation.

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Section: Introductionmentioning

confidence: 99%

Deterministic annealing for clustering, compression, classification, regression, and related optimization problems

1998

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“…For example, we can use the FCM [6] membership model given by (2) ( 1) where m e [1, oo) is the "fuzzifier." Another possibility is [5] The above equations generate a fuzzy partition of X in the sense that the sum of the memberships of an object x^-across classes is equal to one. If we desire possibilistic memberships [29], we could use functions of the following type [30]:…”

Section: The Fuzzy C Medoids Algorithm (Fcmdd)mentioning

confidence: 99%

Low-complexity fuzzy relational clustering algorithms for Web mining

Krishnapuram

Joshi

Nasraoui

et al. 2001

IEEE Trans. Fuzzy Syst.

335

180

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Abstract-This paper presents new algorithms-fuzzy cmedoids (FCMdd) and robust fuzzy c-medoids (RFCMdd)-for fuzzy clustering of relational data. The objective functions are based on selecting c representative objects (medoids) from the data set in such a way that the total fuzzy dissimilarity within each cluster is minimized. A comparison of FCMdd with the wellknown relational fuzzy c-means algorithm (RFCM) shows that FCMdd is more efficient. We present several applications of these algorithms to Web mining, including Web document clustering, snippet clustering, and Web access log analysis.

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“…The Maximum Entropy Principle [14] and Renyi's entropy [15] have been proposed as information-theoretic distance measures between centroids and data points. Butte and Kohane [16] computed entropy between gene pairs and used thresholding to build clusters.…”

Section: A Distance Measuresmentioning

confidence: 99%

Clustering by a genetic algorithm with biased mutation operator

Auffarth

2010

IEEE Congress on Evolutionary Computation

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Abstract-In this paper we propose a genetic algorithm that partitions data into a given number of clusters. The algorithm can use any cluster validity function as fitness function. Cluster validity is used as a criterion for cross-over operations. The cluster assignment for each point is accompanied by a temperature and points with low confidence are preferentially mutated. We present results applying this genetic algorithm to several UCI machine learning data sets and using several objective cluster validity functions for optimization. It is shown that given an appropriate criterion function, the algorithm is able to converge on good cluster partitions within few generations. Our main contributions are: 1. to present a genetic algorithm that is fast and able to converge on meaningful clusters for real-world data sets, 2. to define and compare several cluster validity criteria.

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A least biased fuzzy clustering method

Cited by 77 publications

References 8 publications

Deterministic annealing for clustering, compression, classification, regression, and related optimization problems

Deterministic annealing for clustering, compression, classification, regression, and related optimization problems

Low-complexity fuzzy relational clustering algorithms for Web mining

Clustering by a genetic algorithm with biased mutation operator

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