Efficient computation of higher order cumulant tensors
This work addresses the computational bottleneck of higher-order cumulant calculation for researchers in signal processing and statistics, offering a significant efficiency gain.
The paper introduces a novel algorithm for computing arbitrary order cumulant tensors that exploits super-symmetry, reducing computational complexity and memory requirements by a factor of d! compared to naive methods.
In this paper, we introduce a novel algorithm for calculating arbitrary order cumulants of multidimensional data. Since the $d^\text{th}$ order cumulant can be presented in the form of an $d$-dimensional tensor, the algorithm is presented using tensor operations. The algorithm provided in the paper takes advantage of super-symmetry of cumulant and moment tensors. We show that the proposed algorithm considerably reduces the computational complexity and the computational memory requirement of cumulant calculation as compared with existing algorithms. For the sizes of interest, the reduction is of the order of $d!$ compared to the naive algorithm.