Efficient Computation of the Tensor Chordal Kernels

In this paper new methods for fast computation of the chordal kernels are proposed. Two versions of the chordal kernels for tensor data are discussed. These are based on different projectors of the flattened matrices obtained from the input tensors. A direct transformation of multidimensional objects into the kernel feature space leads to better data separation which can result with a higher classification accuracy. Our approach to more efficient computation of the chordal distances between tensors is based on an analysis of the tensor projectors which exhibit different properties. Thanks to this an efficient eigen-decomposition becomes possible which is done with a version of the fixed-point algorithm. Experimental results show that our method allows significant speed-up factors, depending mostly on tensor dimensions