Dictionary construction for patch-to-tensor embedding

The incorporation of matrix relation, which can encompass multidimensional similarities between local neighborhoods of points in the manifold, can improve kernel based data analysis. However, the utilization of multidimensional similarities results in a larger kernel and hence the computational cost of the corresponding spectral decomposition increases dramatically. In this paper, we propose dictionary construction to approximate the kernel in this case and its respected embedding. The proposed dictionary construction is demonstrated on a relevant example of a super kernel that is based on the utilization of the diffusion maps kernel together with linear-projection operators between tangent spaces of the manifold.