A tensor is a multidimensional array which can represent data with multidimensional relationships. When considering such data, it is common to 'flatten' it into a matrix, which can lead to a loss of information about the relationships between different data points. We want to consider these higher dimensional objects with all their structure, but this can be costly in terms of both space and computing power. We can approximate a tensor via the semidiscrete decomposition as proposed by Kolda and O'Leary, but this approximation, which is based on the CANDECOMP/PARAFAC model of tensor decomposition, converges very slowly and does not take advantage of orientation dependence that may be present in the data. We propose utilizing a new tensor multiplication as defined by Kilmer and Martin to increase accuracy, decrease storage space, and provide the potential for parallelization. We illustrate the potential of our algorithm for increased compression relative to the existing tensor SDD for the same, or less, computational work.
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