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Cheng-Hsuan Li, Bor-Chen Kuo, and Chin-Teng Lin, "LDA-based Clustering Algorithm and Its Application to an Unsupervised Feature Extraction," IEEE Transactions on Fuzzy Systems, Vol. 19, No. 1, pp.152-163, Feb. 2011. (SCI, Impact Factor=3.343)
Cheng-Hsuan Li, Bor-Chen Kuo, Chin-Teng Lin, and Hsin-Hua Ho, "An Unsupervised Linear Discriminant Analysis and Its Application for Clustering," 21th Computer Vision, Graphics, and Image Processing, August, 24-26, 2008
Research has shown fuzzy c-means (FCM) clustering to be a powerful tool for partitioning samples into different categories. However, the objective function of FCM is based only on the sum of distances of samples to their cluster centers, which is equal to the trace of the within-cluster scatter matrix. In this study, we propose a clustering algorithm based on both within- and between-cluster scatter matrices, extended from linear discriminant analysis (LDA), and its application to an unsupervised feature extraction. Our proposed methods comprise between-cluster and within-cluster scatter matrices modified from the between-class and within-class scatter matrices of LDA. The scatter matrices of LDA are special cases of our proposed unsupervised scatter matrices. The results of experiments on both synthetic and real data show that the proposed clustering algorithm can generate similar or better clustering results than eleven popular clustering algorithms: K-means, K-medoid, FCM, the Gustafson-Kessel, Gath-Geva, possibilistic c-means, fuzzy-possibilistic c-means, possibilistic fuzzy c-means, fuzzy compactness and separation, a fuzzy clustering algorithm based on a fuzzy treatment of finite mixtures of multivariate Student’s-t distributions algorithms, and a fuzzy mixture of Student’s t factor analyzers model. The results also show that the proposed feature extraction outperforms principal component analysis and independent component analysis.