Fuzzy Clustering for Extracting Principal Components Independent of Dominant Factors

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  • 支配的要因と独立な主成分を摘出するファジィクラスタリング法
  • 支配的要因と独立な主成分を抽出するファジィクラスタリング法
  • シハイテキ ヨウイン ト ドクリツ ナ シュセイブン オ チュウシュツ スル ファジィクラスタリングホウ

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Abstract

Fuzzy clustering algorithms are useful vehicles to search for structure in data sets by handling fuzzy clusters and have a lot of varieties. Fuzzy c-varieties(FCV)is one of those algorithms in which the prototypes are multi-dimensional linear varieties. The linear varieties are spanned by some local principal component vectors and the FCV clustering algorithm can be regarded as a simultaneous algorithm of fuzzy clustering and principal component analysis. Even though the FCV has the advantage of finding local principal components, they are sometimes strongly influenced by the dominant factors. To eliminate the influence, we propose a new method of fuzzy clustering which extracts local principal components independent of subsidiary variables. In the algorithm, subsidiary variables are regarded as dominant factors. A certain constraint which represents that principal components and subsidiary variables are uncorrelated is added to the objective function for the sake of realization of the proposed method, The solution algorithm is based on an iterative procedure through necessary conditions of optimality of Lagragian function. As numerical examples, first we apply the conventional FCV and the proposed method to an artificial data set and examine their performance. Next, we apply them to a POS(Point of Sales)transaction data set in order to discover associations among items without being influenced by the explicit dominant factors.

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