In this paper, we aim to construct a deep neural network which embeds high dimensional symmetric positive definite (SPD) matrices into a more discriminative low dimensional SPD manifold. To this end, we develop two types of basic layers: a 2D fully connected layer which reduces the dimensionality of the SPD matrices, and a symmetrically clean layer which achieves non-linear mapping. Specifically, we extend the classical fully connected layer such that it is suitable for SPD matrices, and we further show that SPD matrices with symmetric pair elements setting zero operations are still symmetric positive definite. Finally, we complete the construction of the deep neural network for SPD manifold learning by stacking the two layers. Experiments on several face datasets demonstrate the effectiveness of the proposed method.

Retrieving faces from large mess of videos is an attractive research topic with wide range of applications. Its challenging problems are large intra-class variations, and tremendous time and space complexity. In this paper, we develop a new deep convolutional neural network (deep CNN) to learn discriminative and compact binary representations of faces for face video retrieval. The network integrates feature extraction and hash learning into a unified optimization framework for the optimal compatibility of feature extractor and hash functions. In order to better initialize the network, the low-rank discriminative binary hashing is proposed to pre-learn hash functions during the training procedure. Our method achieves excellent performances on two challenging TV-Series datasets.