Another Variant of Robust Fuzzy PCA with Initial Membership Estimation

Abstract

Principal component analysis (PCA) is a well-known method for dimensionality reduction and feature extraction. PCA has been applied in many areas successfully, however, one of its problems is noise sensitivity due to the use of sum-square-error. Several variants of PCA have been proposed to resolve the problem and, among the variants, improved robust fuzzy PCA (RF-PCA2) demonstrated promising results. RF-PCA2, however, still can be affected by noise due to equal initial membership values for all data points. The fact that RF-PCA2 is still based on sum-square-error is another reason for noise sensitivity.In this paper, a variant of RF-PCA2 called RF-PCA3 is proposed. The proposed algorithm modifies the objective function of RF-PCA2 to allow some increase of sum-square-error and calculates initial membership values using data distribution. RF-PCA3 outperforms RF-PCA2, which is supported by experimental results.Keywordsprincipal component analysisnoise sensitivitymembership initializationnearest neighborKD-tree