Xuejing Yuan
ABSTRACT
The bilinear transformation of symmetric positive definite (SPD) matrix is currently the most common SPD data dimensionality reduction framework. The transformation matrix can be determined according to different criteria to produce different SPD data dimensionality reduction algorithms. The bilinear transformation of SPD matrix is essentially a transformation between two Riemannian manifolds. Since Riemannian manifolds are not linear spaces, most SPD data bilinear transformation dimensionality reduction algorithms now avoid linear operations between SPD matrices. This paper proposes a SPD data dimensionality reduction algorithm based on SPD manifold tangent space and local LDA. The main contributions are as follows: (1) This paper adopts the affine invariant Riemann metric, the tangent space of the unit matrix and the log transformation to transform the SPD The data is transformed from the Riemannian manifold to the unit matrix tangent space, so that the geodesic distance between the SPD and the unit matrix and the Euclidean distance transformation between the tangent vector and the origin of the tangent space after the transformation remain unchanged; (2) The so-called local discriminant difference of SPD is to first The SPD data is decomposed into one part, and then the local discriminant difference of the SPD data is calculated according to the category (label) of the SPD data. The local discriminant difference of SPD data better realizes the combination of internal and external attributes of SPD data.
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