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> |