01097nas a2200157   4500000000100000000000100001008004100002100002100043700001700064700001900081245005900100856005400159300001000213490000700223520070900230       2018                            d1 aKrzysztof Domino1 aPiotr Gawron1 aŁukasz Pawela00aEfficient computation of higher order cumulant tensors  uhttps://epubs.siam.org/doi/abs/10.1137/17M1149365  aA16100 v403 a<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>