Paper:

# Variable Weighting in PCA-Guided *k*-Means and its Connection with Information Summarization

## Katsuhiro Honda, Akira Notsu, and Hidetomo Ichihashi

Graduate School of Engineering, Osaka Prefecture University, 1-1 Gakuen-cho, Nakaku, Sakai, Osaka 599-8531, Japan

*k*-means clustering, principal component analysis, variable weighting

In the present paper, a variable selection model in *k*-Means is proposed, in which a variable weighting mechanism is introduced to PCA-guided *k*-Means. Variable weights are estimated in a manner similar to FCM clustering, while the membership indicator is derived using a PCA-guided method, in which the principal component scores are calculated by considering the variable weights. The variable weights emphasize the variables that have meaningful cluster information in the calculation of the membership indicators, and the absolute responsibility of each variable is revealed by soft transition to possibilistic values. It is also shown that the variable weights are derived in a manner similar to variable selection for PCA, with the goal being information summarization. The characteristics of the proposed method are demonstrated in an application to document clustering.

*k*-Means and its Connection with Information Summarization,”

*J. Adv. Comput. Intell. Intell. Inform.*, Vol.15, No.1, pp. 83-89, 2011.

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