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Conference Papers Year : 2019

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

Abstract

Symmetric Positive Definite (SPD) matrices have been widelyused in medical data analysis and a number of different Riemannian met-rics were proposed to compute with them. However, there are very fewmethodological principles guiding the choice of one particular metric fora given application. Invariance under the action of the affinetransfor-mations was suggested as a principle. Another concept is based on sym-metries. However, the affine-invariant metric and the recently proposedpolar-affine metric are both invariant and symmetric. Comparing thesetwo cousin metrics leads us to introduce much wider families: power-affineand deformed-affine metrics. Within this continuum, we investigate otherprinciples to restrict the family size.
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Dates and versions

hal-02147020 , version 1 (04-06-2019)

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Yann Thanwerdas, Xavier Pennec. Is affine invariance well defined on SPD matrices? A principled continuum of metrics. GSI 2019 - 4th conference on Geometric Science of Information, Aug 2019, Toulouse, France. pp.502-510, ⟨10.1007/978-3-030-26980-7_52⟩. ⟨hal-02147020⟩
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