Journal
PATTERN RECOGNITION
Volume 46, Issue 6, Pages 1604-1615Publisher
ELSEVIER SCI LTD
DOI: 10.1016/j.patcog.2012.12.007
Keywords
Fuzzy scatter matrix; Fuzzy Linear Discriminant Analysis; Optimal transformation matrix; Maximum entropy fuzzy clustering algorithm
Funding
- National Science Foundation of China [61102095]
- Science Plan Foundation of the Education Bureau of Shaanxi Province [2010JK835, 11JK1051]
- Natural Science Basic Research Plan in Shaanxi Province of China [2012JQ8045]
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Linear Discriminant Analysis (LDA) is a classical statistical approach for supervised feature extraction and dimensionality reduction, hard c-means (HCM) is a classical unsupervised learning algorithm for clustering. Based on the analysis of the relationship between LDA and HCM, Linear Discriminant Analysis-guided adaptive subspace hard c-means clustering algorithm (LDA-HCM) had been proposed. LDA-HCM combines LDA and HCM into a coherent framework and can adaptively reduce the dimension of data while performing data clustering simultaneously. Seeing that LDA-HCM is still a hard clustering algorithm, we consider the fuzzy extension version of LDA-HCM in this paper. To this end, firstly, we propose a new optimization criterion of Fuzzy Linear Discriminant Analysis (FLDA) by extending the value of membership function in classical LDA from binary 0 or 1 into closed interval [0, 1]. In the meantime, we present an efficient algorithm for the proposed FLDA. Secondly, we show the close relationship between FLDA and Maximum Entropy Fuzzy Clustering Algorithm (MEFCA): they both are maximizing fuzzy between-class scatter and minimizing within-class scatter simultaneously. Finally, based on the above analysis, combining FLDA and MEFCA into a joint framework, we propose fuzzy Linear Discriminant Analysis-guided maximum entropy fuzzy clustering algorithm (FLDA-MEFCA). LDA-MEFCA is a natural and effective fuzzy extension of LDA-HCM. Due to the introduction of soft decision strategy, FLDA-MEFCA can yield fuzzy partition of data set and is more flexible than LDA-HCM. We also give the convergence proof of FLDA-MEFCA. Extensive experiments on a collection of benchmark data sets are presented to show the effectiveness of the proposed algorithm. (c) 2012 Elsevier Ltd. All rights reserved.
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