Comment on “Enhanced soft subspace clustering integrating within-cluster and between-cluster information” by Z. Deng et al. (Pattern Recognition, vol. 43, pp. 767–781, 2010)

doi:10.1016/j.patcog.2017.10.011

Pattern Recognition

Volume 77, May 2018, Pages 456-457

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Highlights

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This paper comments on the published work dealing with "Enhanced soft subspace clustering integrating within-cluster and between-cluster information" (Pattern Recognition, vol. 43, pp. 767–781, 2010) proposed by Z. Deng et al.
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Their clustering approach is based on a new mathematical model with two groups of variables: cluster centers and clusters memberships.
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In each iteration of their proposed approach, they fixed cluster centers and used some conditions to obtain the optimal clusters memberships.
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We further analysis their approach and show that the mentioned conditions are necessary and sufficient condition for optimality of clusters memberships when cluster centers are fixed.

Abstract

This paper comments on the published work dealing with "Enhanced soft subspace clustering integrating within-cluster and between-cluster information" (Pattern Recognition, vol. 43, pp. 767–781, 2010) proposed by Z. Deng et al. Their clustering approach is based on a new mathematical model with two groups of variables: cluster centers and clusters memberships. They proposed an iterative algorithm to obtain the solution of this model. In each iteration, they fixed cluster centers and used some conditions to obtain the optimal clusters memberships. In this paper, we further analysis their approach and show that the mentioned conditions are necessary and sufficient condition for optimality of clusters memberships when cluster centers are fixed.

Section snippets

Comment

Let $X = {x_{1}, x_{2}, \dots, x_{N}}$ be a set of n objects, where x_j ∈ R^D. The basic fuzzy c-means model [1] clusters these N objects to C clusters by using the following mathematical model: $\begin{matrix} min_{u, v} \sum_{i = 1}^{C} \sum_{j = 1}^{N} u_{i j}^{m} \sum_{k = 1}^{D} {(x_{j k} - v_{i k})}^{2} \\ subject to {\begin{matrix} \sum_{i = 1}^{C} u_{i j} = 1, j = 1, 2, \dots, N; \\ 0 \leq u_{i j} \leq 1, j = 1, 2, \dots, N; i = 1, 2, \dots, C . \end{matrix} \end{matrix}$ where m > 1 is the predefined fuzzifier parameter, v_i is ith cluster center, and $u_{i j} = 1$ indicates that x_j is the member of ith cluster. The basic fuzzy c-means model minimizes intra-cluster compactness. The following model proposed

References (3)

Z. Deng et al.
Enhanced soft subspace clustering integrating within-cluster and between-cluster information
Pattern Recognit.
(2010)

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Cited by (1)

An entropy regularization k-means algorithm with a new measure of between-cluster distance in subspace clustering
2019, Entropy

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Comment on “Enhanced soft subspace clustering integrating within-cluster and between-cluster information” by Z. Deng et al. (Pattern Recognition, vol. 43, pp. 767–781, 2010)

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Abstract

Section snippets

Comment

Pattern Recognit.