Theoretical analysis on feature extraction capability of class-augmented PCA

In this paper, we present a theoretical analysis on a novel supervised feature extraction method called class-augmented principal component analysis (CA-PCA), which is composed of processes for encoding the class information, augmenting the encoded information to data, and extracting features from class-augmented data by applying PCA. Through a combination of these processes, CA-PCA can extract features appropriate for classification. Our theoretical analysis aims to clarify the role of these processes and to provide an explanation on how CA-PCA can extract good features. Experimental results for various datasets are provided in order to show the validity of the proposed method for real problems. The effect of parameters on the quality of extracted features is also investigated and the rules of thumb for determining the appropriate parameters are provided.