Matrix-Based Kernel Subspace Methods

It is a common practice that a matrix, the de facto image representation, is first converted into a vector before fed into subspace analysis or kernel method; however, the conversion ruins the spatial structure of the pixels that defines the image. In this paper, we propose two kernel subspace methods that are directly based on the matrix representation, namely matrix-based kernel principal component analysis (matrix KPCA) and matrix-based kernel linear discriminant component analysis (matrix KLDA). We show that, through an extended Gram matrix, the two proposed matrix-based kernel subspace methods generalize their vector-based counterparts and contain richer information. Our experiments also confirm the advantages of the matrix-based kernel subspace methods over the vector-based ones.