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arXiv · 1906.01349

Is affine invariance well defined on SPD matrices? A principled continuum of metrics

Yann Thanwerdas·Xavier Pennec
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Abstract

Symmetric Positive Definite (SPD) matrices have been widely used in medical data analysis and a number of different Riemannian met-rics were proposed to compute with them. However, there are very few methodological principles guiding the choice of one particular metric for a given application. Invariance under the action of the affine transformations was suggested as a principle. Another concept is based on symmetries. However, the affine-invariant metric and the recently proposed polar-affine metric are both invariant and symmetric. Comparing these two cousin metrics leads us to introduce much wider families: power-affine and deformed-affine metrics. Within this continuum, we investigate other principles to restrict the family size.

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Yann Thanwerdas, Xavier Pennec. 2019-06-04. Is affine invariance well defined on SPD matrices? A principled continuum of metrics. https://arxiv.org/abs/1906.01349

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