RF-PCA2: An Improvement on Robust Fuzzy PCA

摘要

Principal component analysis (PCA) is a well-known method for dimensionality reduction while maintaining most of the variation in data. Although PCA has been applied in many areas successfully, one of its main problems is the sensitivity to noise due to the use of sum-square-error. Several variants of PCA have been proposed to resolve the problem and, among the variants, robust fuzzy PCA (RF-PCA) demonstrated promising results, which uses fuzzy memberships to reduce noise sensitivity. However, there are also problems in RF-PCA and convergence property is one of them. RF-PCA uses two different objective functions to update memberships and principal components, which is the main reason of the lack of convergence property. The difference between two objective functions also slows convergence and deteriorates the solutions of RF-PCA. In this paper, a variant of RF-PCA, called improved robust fuzzy PCA (RF-PCA2), is proposed. RF-PCA2 uses an integrated objective function both for memberships and principal components, which guarantees RF-PCA2 to converge on a local optimum. Furthermore, RF-PCA2 converges faster than RF-PCA and the solutions are more similar to desired ones than those of RF-PCA. Experimental results with artificial data sets also support this.