FastPSA: A Fast Version of the Principal Skewness Analysis

Recently, principal skewness analysis (PSA) has been introduced into the domain of feature extraction. It is equivalent to the skewness version of Fast independent component analysis (FastICA). Unlike FastICA, PSA does not require all sample points when searching for the projection directions, making it faster. However, for the data of dimension $L$, PSA needs to calculate the eigenvectors of $L$ tensors, each of size $L\times L\times L$. When $L$ is large, PSA still requires significant computational time to find all projection directions. In this letter, we find that the $(m+1)$th projection direction in PSA can be obtained by calculating the eigenvector of a tensor of size $(L-m)\times (L-m)\times (L-m)$. Furthermore, we propose a fast version of PSA (FastPSA) that is mathematically equivalent to PSA. The experimental results demonstrate that FastPSA has lower computational complexity than PSA.