On Fuzzy Clustering based Correlation

This paper presents a fuzzy clustering based correlation which measures the similarity of the ordinary correlation of objects and the correlation of the classification structures of the objects. This correlation is derived from self- organized dissimilarity which measures dissimilarity of a pair of objects and classification structures of the objects. It is known that this dissimilarity performs better for noisy data. In this paper, we first describe the performance of the self-organized dissimilarity in the framework of the clustering model. Next, we show how to obtain the fuzzy clustering based correlation from the self-organized dissimilarity. Finally, we provide a numerical example of the use of fuzzy clustering based correlation. Our target data is high-dimension and low-sample size (HDLSS) data in which the number of variables is much larger than the number of objects. Recently the analysis of this type of data has gained tremendous interest. However, with this data, since we cannot obtain the correct solution as eigen-values of the covariance matrix of variables, we cannot obtain a result of the ordinary principal component analysis (PCA). We show that by exploiting the proposed fuzzy clustering based correlation, we can solve this problem and obtain the result of PCA with better performance.