Principle Component Analysis Based on New Symmetric Similarity Measures for Heavy-Tailed Data

摘要

We consider the principal component analysis (PCA) for the heavy-tailed distributions. A traditional measure for the classical PCA is the covariance measure. Due to the non-existence of variance of many heavy-tailed distributions, this measure cannot be used for them. We will clarify how to perform PCA in heavy-tailed data by extending a similarity measure based on covariance. We introduce similarity measures based on a new dependence coefficient of heavy-tailed distributions. Using real and artificial datasets, the performance of the proposed PCA is evaluated and compared with the classical one.