To further improve the formulation of the skew term in SID and better capture the nuances of the feature distributions, several approaches can be considered:
Alternative Skewness Measures: Instead of using the cube root of the coskewness tensor, exploring other skewness measures like Mardia skewness or Kollo skewness could provide a more accurate representation of the skew in the data.
Weighted Skew Term: Introducing a weighted skew term that assigns different weights to different dimensions based on their importance or contribution to the overall skewness could enhance the sensitivity of SID to subtle variations in the feature distributions.
Non-linear Transformations: Applying non-linear transformations to the skew term, such as logarithmic or exponential transformations, could help in capturing non-linear relationships and variations in the feature distributions more effectively.
Incorporating Higher-Order Moments: Extending the skew term to include higher-order moments beyond the third moment, such as kurtosis or higher-order cumulants, could provide a more comprehensive characterization of the feature distributions and improve the discriminative power of SID.