OPTEC Seminar on Tensors, Computing, Optimization and Signal Processing location:Leuven, Belgium date:May 2-3, 2012
We present an alternative strategy to truncate the higher-order singular value decomposition (T-HOSVD), called the sequentially truncated HOSVD (ST-HOSVD). It requires less operations to compute and often improves the approximation error with respect to the T-HOSVD. Whenever a tensor is truncated to its multilinear rank, the basis computed by the T-HOSVD and ST-HOSVD coincide. In one experiment we performed, the results of a numerical simulation of a partial differential equation were compressed by T-HOSVD and ST-HOSVD. At the same truncation rank, the approximation errors were similar, and the bases computed by both algorithms were indistinguishable. The execution time, on the other hand, was reduced from 2h45 for T-HOSVD to one minute for ST-HOSVD, representing a speedup of 133. In another experiment, we compare T-HOSVD and ST-HOSVD for constructing a multilinear model for classifying handwritten digits.