Locality preserving projection on SPD matrix Lie group: algorithm and analysis
Abstract
Symmetric positive definite (SPD) matrices used as feature descriptors in image recognition are usually high dimensional. Traditional manifold learning is only applicable for reducing the dimension of highdimensional vectorform data. For highdimensional SPD matrices, directly using manifold learning algorithms to reduce the dimension of matrixform data is impossible. The SPD matrix must first be transformed into a long vector, and then the dimension of this vector must be reduced. However, this approach breaks the spatial structure of the SPD matrix space. To overcome this limitation, we propose a new dimension reduction algorithm on SPD matrix space to transform highdimensional SPD matrices into lowdimensional SPD matrices. Our work is based on the fact that the set of all SPD matrices with the same size has a Lie group structure, and we aim to transform the manifold learning to the SPD matrix Lie group. We use the basic idea of the manifold learning algorithm called locality preserving projection (LPP) to construct the corresponding Laplacian matrix on the SPD matrix Lie group. Thus, we call our approach LieLPP to emphasize its Lie group character. We present a detailed algorithm analysis and show through experiments that LieLPP achieves effective results on human action recognition and human face recognition.
 Publication:

arXiv eprints
 Pub Date:
 March 2017
 arXiv:
 arXiv:1703.09499
 Bibcode:
 2017arXiv170309499L
 Keywords:

 Computer Science  Computer Vision and Pattern Recognition;
 Computer Science  Numerical Analysis;
 F.2.2
 EPrint:
 15 pages, 3 tables