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Star products and dimension reduction

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  • Loperfido, Nicola

Abstract

The star product of two matrices is the linear combination of the blocks in the second matrix, with the corresponding elements of the first matrix as coefficients. In probability and statistics, the star product appeared in conjunction with measures of multivariate skewness and kurtosis, within the frameworks of model-based clustering, multivariate normality testing, outlier detection, invariant coordinate selection and independent component analysis. In this paper, we investigate some properties of the star product and their applications to dimension reduction techniques, including common principal components and invariant coordinate selection. The connections of the star product with tensor concepts and three-way data are also considered. The theoretical results are illustrated with the Iris Flowers and the Swiss Banknotes datasets.

Suggested Citation

  • Loperfido, Nicola, 2026. "Star products and dimension reduction," Journal of Multivariate Analysis, Elsevier, vol. 211(C).
    • Handle: RePEc:eee:jmvana:v:211:y:2026:i:c:s0047259x25001186
    DOI: 10.1016/j.jmva.2025.105523
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