On the ℓ₁ Procrustes problem

Trendafilov, Nickolay T. (2003). On the ℓ₁ Procrustes problem. Future Generation Computer Systems, 19(7) pp. 1177–1186.

DOI: https://doi.org/10.1016/S0167-739X(03)00043-8

Abstract

In this paper, the well-known Procrustes problem is reconsidered. The usual least squares objective function is replaced by more robust one, based on a smooth approximation of the ℓ ₁ matrix norm. This smooth approximation to the ℓ₁ Procrustes problem is solved making use of the projected gradient method. The Procrustes problem with partially specified target is treated and solved as well. Several classical numerical examples from factor analysis (well-known with their least squares Procrustes solutions) are solved with respect to the smooth approximation of the ℓ ₁ matrix norm goodness-of-fit measure.

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