Comparison and Weighted Summation Type of Fuzzy Cluster Validity Indices

Abstract

Finding the optimal cluster number and validating the partition results of a data set are difficult tasks since clustering is an unsupervised learning process. Cluster validity index (CVI) is a kind of criterion function for evaluating the clustering results and determining the optimal number of clusters. In this paper, we present an extensive comparison of ten well-known CVIs for fuzzy clustering. Then we extend traditional single CVIs by introducing the weighted method and propose a weighted summation type of CVI (WSCVI). Experiments on nine synthetic data sets and four real-world UCI data sets demonstrate that no one CVI performs better on all data sets than others. Nevertheless, the proposed WSCVI is more effective by properly setting the weights.

Peer Review #1 of "Clustering of fMRI data: the elusive optimal number of clusters (v0.1)"

“…Our findings are in line with previous studies that compared several CV indices on different simulated datasets and found that CV indices may fail to indicate the true number of clusters in noisy data that have high number of classes (Suleman 2017;Wang & Zhang 2007;Zhou et al 2014a). It might be the case their effectiveness might even be lesser given the complex nature of noise in MRI images with significant correlations between voxels (Gudbjartsson & Patz 1995;Parrish et al 2000).…”

“…Previous work suggested that, when CV indices fail to agree on the true number of clusters for high-dimensional datasets, a combination of different indices into a single index should be considered (Sheng et al 2005;Zhou et al 2014a). Specifically, by using a weighted sum of several normalized CV indices, it has been shown that this weighted sum can improve the confidence of clustering solutions.…”

“…Ultimately, this approach aims to force an agreement between CV indices so that one optimal single c-partition is selected. However, this approach may not be applicable to all contexts because (i) the number and types of CV indices to be combined are arbitrary, (ii) there is no objective procedure to set optimal weights, and previous empirical work showed that such weights are data-dependent (Zhou et al 2014a), (iii) the weighted sum does not properly deal with redundant information, given that CV indices are likely to share similar compactness or separation measures, (iv) the relationships of some CV indices with the number of expected clusters can take any arbitrary shape (e.g. Figure 5B), hence linear combinations may not be suitable, and (v) this approach implicitly assumes that there must be one unique 'true' explanation of the data.…”

“…In a preliminary analysis (results not shown here), about 20 selected CV indices were first tested on several simulated datasets (as defined in (Bezdek & Pal 1998;Bouguessa et al 2006;Dave 1996;Fukuyama & Sugeno 1989;Geva et al 2000;Kim et al 2001;Kim et al 2003;Kim & Ramakrishna 2005;Kwon 1998;Pakhira et al 2004;Pakhira et al 2005;Pal & Bezdek 1995;Rezaee et al 1998;Rhee & Oh 1996;Sun et al 2004;Tsekouras & Sarimveis 2004;Wu & Yang 2005;Xie & Beni 1991;Yu & Li 2006;Zahid et al 1999a;Zahid et al 1999b)). These CV indices were selected from earlier studies (for a similar rationale, see recent comparison study (Zhou et al 2014a during CV computation; (iv) be fast to compute when n is expected to be very high (e.g.…”

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