engleski

Recompression of Hadamard Products of Tensors in Tucker Format

The Hadamard product features prominently in tensor-based algorithms in scientificcomputing and data analysis. Due to its tendency to significantly increase ranks, the Hadamard product can represent a major computational obstacle in algorithmsbased on low-rank tensor representations. It is therefore of interest to develop re-compression techniques that mitigate the effects of this rank increase. In this work, we investigate such techniques for the case of the Tucker format, which is well suitedfor tensors of low order and small to moderate multilinear ranks. Fast algorithmsare attained by combining iterative methods, such as the Lanczos method and rand-omized algorithms, with fast matrix-vector products that exploit the structure ofHadamard products. The resulting complexity reduction is particularly relevant fortensors featuring large mode sizes I and small to moderate multilinear ranks R. Toimplement our algorithms, we have created a new Julia library for tensors in Tuckerformat.

tensors ; recompression ; Tucker format

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