Supervised LogEuclidean Metric Learning for Symmetric Positive Definite Matrices

Log-Euclidean Metric Learning on Symmetric Positive Definite Manifold with Application to Image Set Classification

The manifold of Symmetric Positive Definite (SPD) matrices has been successfully used for data representation in image set classification. By endowing the SPD manifold with LogEuclidean Metric, existing methods typically work on vector-forms of SPD matrix logarithms. This however not only inevitably distorts the geometrical structure of the space of SPD matrix logarithms but also brings low eff...

CMSC 828J: Linear Subspaces and Manifolds for Computer Vision and Machine Learning Riemannian Metric Learning for Symmetric Positive Definite Matrices

Riemannian Metric Learning for Symmetric Positive Definite Matrices

Over the past few years, symmetric positive definite matrices (SPD) have been receiving considerable attention from computer vision community. Though various distance measures have been proposed in the past for comparing SPD matrices, the two most widely-used measures are affine-invariant distance and log-Euclidean distance. This is because these two measures are true geodesic distances induced...

Composite Kernel Optimization in Semi-Supervised Metric

Machine-learning solutions to classification, clustering and matching problems critically depend on the adopted metric, which in the past was selected heuristically. In the last decade, it has been demonstrated that an appropriate metric can be learnt from data, resulting in superior performance as compared with traditional metrics. This has recently stimulated a considerable interest in the to...

Approximating Sets of Symmetric and Positive-Definite Matrices by Geodesics

We formulate a generalized version of the classical linear regression problem on Riemannian manifolds and derive the counterpart to the normal equations for the manifold of symmetric and positive definite matrices, equipped with the only metric that is invariant under the natural action of the general linear group.