Efficient computation of higher order cumulant tensors

Author Domino K.; Gawron P.; Pawela Ł.
Title Efficient computation of higher order cumulant tensors
Journal SIAM J. SCI. COMPUT.
Year 2018
Status Published
Volume 40
Issue 3
Pages A1610
DOI 10.1137/17M1149365
URL https://epubs.siam.org/doi/abs/10.1137/17M1149365
Abstract <p>In this paper, we introduce a novel algorithm for calculating arbitrary order<br />
cumulants of multidimensional data. Since the d'th order<br />
cumulant can be presented in the form of an d-dimensional tensor, the<br />
algorithm is presented using tensor operations. The algorithm provided in the<br />
paper takes advantage of super-symmetry of cumulant and moment tensors.<br />
We show that the proposed algorithm considerably reduces the computational<br />
complexity and the computational memory requirement of cumulant calculation as<br />
compared with existing algorithms. For the sizes of interest, the<br />
reduction is of the order of d! compared to the naive algorithm.</p>