Weighted principal component analysis

Abstract

In this paper, we proposed a weighted PCA (WPCA) method. This method first uses the distances between the test sample and each training sample to calculate the 'weighted' covariance matrix. It then exploits the obtained covariance matrix to perform feature extraction. The experimental results show that the proposed method can obtain a high accuracy than conventional PCA. WPCA has the underlying theoretical foundation: through the 'weighted' covariance matrix, WPCA takes emphasis on the training samples that are very close to the test sample and reduce the influence of the other training samples. As a result, it is likely that the test sample is easier to be classified into the same class as the training samples that are very close to it. The experimental results show the feasibility and effectiveness of WPCA. © 2011 Springer-Verlag.