GrasNet: A Simple Grassmannian Network for Image Set Classification

Representing image sets on the Grassmann manifold has been widely used in visual classification tasks, and the existing Grassmannian learning methods have shown powerful ability in feature representation. In order to develop the ideology of conventional deep learning to the Grassmann manifold, we devise a simple Grassmann manifold feature learning network (GrasNet) in this paper, which provides a new way for image set classification. For the proposed GrasNet, we design a fully mapping layer to transform the input Grassmannian data into more appropriate representations. In view of the consistency of the data space, orthonormal maintaining layer is exploited to normalize the input matrices to form a valid Grassmann manifold. To perform Grassmannian computing on the resulting Grassmann manifold-valued features, we also introduce a projection mapping layer. For the sake of further reducing the dimensionality and redundancy of the learned geometric features, we devise a projection pooling layer. The log-map layer is finally adopted to embed the resulting data manifold into a tangent space via Riemannian matrix logarithm map, such that the Euclidean computations apply. To learn the multistage connection weights for the proposed GrasNet, we utilize the Principal Component Analysis (PCA) algorithm rather than the complex Riemannian matrix backpropagation optimizer, which makes it be built and trained extremely easy and efficient. We evaluate our model on three different visual classification tasks: face recognition, object categorization and cell identification, respectively. Extensive classification results verify its feasibility and effectiveness.