On image matrix based feature extraction algorithms

Principal component analysis (PCA) and linear discriminant analysis (LDA) are two important feature extraction methods and have been widely applied in a variety of areas. A limitation of PCA and LDA is that when dealing with image data, the image matrices must be first transformed into vectors, which are usually of very high dimensionality. This causes expensive computational cost and sometimes the singularity problem. Recently two methods called two-dimensional PCA (2DPCA) and two-dimensional LDA (2DLDA) were proposed to overcome this disadvantage by working directly on 2-D image matrices without a vectorization procedure. The 2DPCA and 2DLDA significantly reduce the computational effort and the possibility of singularity in feature extraction. In this paper, we show that these matrices based 2-D algorithms are equivalent to special cases of image block based feature extraction, i.e., partition each image into several blocks and perform standard PCA or LDA on the aggregate of all image blocks. These results thus provide a better understanding of the 2-D feature extraction approaches.