Weighted Principal Component Analysis Based on Fuzzy Clustering

In this paper, we propose a weighted principal component analysis (WPCA) using the result of fuzzy clustering [4]. The principal component analysis (PCA) [1], [7] is one widely used and well-known data analysis method. However there is a problem, when the data does not have a structure that the PCA can capture we cannot obtain any satisfactory results. For the most part, this is due to the uniformity of the data structure, which means we cannot find any significant proportion or accumulated proportion for the obtained principal components. In order to solve this problem, we use the cluster structure and degree of belongingness of objects to clusters, which is obtained as the fuzzy clustering result. By the introduction of the pre-classification and the degree of belongingness to the data, we can transform the data into a clearer structured data, so avoiding the noise in the data.