An extension to possibilistic fuzzy cluster analysis

Timm, Heiko; Borgelt, Christian; Döring, Christian; Kruse, Rudolf

doi:10.1016/j.fss.2003.11.009

Cited by 174 publications

(95 citation statements)

References 8 publications

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“…The special cases of this function include the ones used in: (i) the fuzzy c-means [17] (γ i = 0); (v) the extended possibilistic clustering model [25] (a = 0). In this work, we only focus on fuzzy c-means clustering and the original possibilistic clustering methodology.…”

Section: Objective Function-based Possibilistic Fuzzy Clustering For mentioning

confidence: 99%

Possibilistic Clustering for Crisis Prediction: Systemic Risk States and Membership Degrees

Mezei

Sarlin

2017

Proceedings of the 50th Hawaii International Conference on System Sciences (2017)

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Research on understanding and predicting systemic financial risk has been of increasing importance in the recent years. A common approach is to build predictive models based on macro-financial vulnerability indicators to identify systemic risk at an early stage. In this article, we outline an approach for identifying different systemic risk states through possibilistic fuzzy clustering. Instead of directly using a supervised classification method, we aim at identifying coherent groups of vulnerability with macrofinancial indicators for pre-crisis data, and determine the level of risk for a new observation based on its similarity to the identified groups. The approach allows for differentiating among different possible pre-crisis states, and using this information for estimating the possibility of systemic risk. In this work, we compare different fuzzy clustering methods, as well as conduct an empirical exercise for European systemic banking crises.

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Section: Objective Function-based Possibilistic Fuzzy Clustering For mentioning

confidence: 99%

Possibilistic Clustering for Crisis Prediction: Systemic Risk States and Membership Degrees

Mezei

Sarlin

2017

Proceedings of the 50th Hawaii International Conference on System Sciences (2017)

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“…Since the columns of partitions U 2 M f are independent, PCM-like algorithms tend to obtain concentrical clusters when the global minimum has been achieved [80,81]. To avoid this problem, the FPCM algorithm [15] finds memberships and typicalities simultaneously between the objects and clusters (i.e., one matrix U 2 M fp and another matrix P 2 M f ).…”

Section: Fpcm: Fuzzy-possibilistic C-meansmentioning

confidence: 99%

Fuzzy Clustering Algorithms and Validity Indices for Distributed Data

Vendramin

Naldi

Campello

2014

Partitional Clustering Algorithms

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This chapter presents a unified framework to generalize a number of fuzzy clustering algorithms to handle distributed data in an exact way, i.e., with no approximation of results with respect to their original centralized versions. The same framework allows the exact distribution of relative validity indices used to evaluate the quality of fuzzy clustering solutions. Complexity analyses for each distributed algorithm and index are reported in terms of space, time, and communication aspects. A general procedure to estimate the number of clusters in a non-centralized fashion using the proposed framework is also described. Such a procedure is directly applicable not only to distributed data, but to parallel data processing scenarios as well. Experimental results illustrate the speedup obtained when running algorithms under the proposed framework in multiple cores of a processor, when compared to their traditional, centralized counterparts running in a single core. Additionally, the quality of the results and amount of data transmitted are assessed and compared among different fuzzy clustering algorithms.

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“…Another important issue about PCM approach is that it is highly sensitive to K. Value of K In equation (9) together with in itial value of U can determine degree of convergence of the objective function. More ever, some groups of data are more sensitive to K than others.…”

Section: Analyzing Sensitivity Of Pcm Vs Hpcm With Respect To Kmentioning

confidence: 99%

“…The objective function proposed by Krishnapuram and Keller [3] is shown in equation (6). By min imizing the objective function, update formulas for ui,j , β i (center fo r cluster i) are indicated in equations (7,8,9). …”

Section: B Introduction To Possibilistic Clustering Approachesmentioning

confidence: 99%

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A Hierarchical Possibilistic Clustering

Haghighi¹,

Yazdi²,

Vahedian³

2009

IJCTE

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In this paper we propose to combine two clustering approaches, namely fuzzy and possibilistic c-means. While fuzzy c-means algorithm finds suitable clusters for groups of data points, obtained memberships of data, however, encounters a major deficiency caused by misinterpretation of membership values of data points. Therefore, membership values cannot correctly interpret compatibility or degree to which data points belong to clusters. As a result, noisy data will be misinterpreted by incorrect memberships assigned, as sum of memberships of each noisy data to all clusters is constrained to be equal to 1. To overcome this, a possibilistic approach has been proposed which removes this constraint. It has, however, caused another shortcoming as cluster centers converge to an identical point. Therefore, possibilities cannot correctly interpret the degrees of compatibilities. To correct this problem, a number of works have been carried out which all try to change possibilistic objective function proposed by Krishnapuram and James M. Keller.In this work, a hierarchical approach has been proposed based on properties of both fuzzy and possibilistic approaches to overcome this deficiency. Sensitivities of both methods have been studied together with analyzing results obtained by both methods. Superiority of the proposed method as opposed to conventional possibilistic c-means is shown to be conspicuous.

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An extension to possibilistic fuzzy cluster analysis

Cited by 174 publications

References 8 publications

Possibilistic Clustering for Crisis Prediction: Systemic Risk States and Membership Degrees

Possibilistic Clustering for Crisis Prediction: Systemic Risk States and Membership Degrees

Fuzzy Clustering Algorithms and Validity Indices for Distributed Data

A Hierarchical Possibilistic Clustering

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