System and Merhod for Log Euclidean Metric Learning using Riemannian Submanifold Framework on Symmetric Positive Definite Manifolds

摘要

The present invention removes nonlinear constraints by performing a linear transformation on a normal coordinate of a positive definite matrix (SPD matrix) to improve speed and accuracy during training. A log Euclidean metric learning apparatus and method using a sub-manifold framework, comprising: a tangent space mapping unit that maps data represented by a symmetric positive definite (SPD) matrix to a tangent space; A Euclidean point processing unit representing the points mapped in the unit as Euclidean points (R ^D ); a subspace mapping unit mapping to subspaces (R ^K ) through the parameter W; By re-mapping from Tangent space to SPD(n) through Expm(matrix exponential), the points of the same class are reduced by using the objective function, while the points of other classes are distanced. It includes a; re-mapping unit to increase the metric learning.