DreamNet: A Deep Riemannian Network based on SPD Manifold Learning for Visual Classification
This work addresses a specific bottleneck in visual classification for image sets using SPD manifolds, offering an incremental improvement over existing Riemannian networks.
The paper tackles the problem of image set classification by addressing the degradation of generalization ability in deeper Riemannian networks on SPD manifolds, proposing DreamNet which achieves improved accuracy with increased depth through a stacked Riemannian autoencoder and residual-like blocks.
Image set-based visual classification methods have achieved remarkable performance, via characterising the image set in terms of a non-singular covariance matrix on a symmetric positive definite (SPD) manifold. To adapt to complicated visual scenarios better, several Riemannian networks (RiemNets) for SPD matrix nonlinear processing have recently been studied. However, it is pertinent to ask, whether greater accuracy gains can be achieved by simply increasing the depth of RiemNets. The answer appears to be negative, as deeper RiemNets tend to lose generalization ability. To explore a possible solution to this issue, we propose a new architecture for SPD matrix learning. Specifically, to enrich the deep representations, we adopt SPDNet [1] as the backbone, with a stacked Riemannian autoencoder (SRAE) built on the tail. The associated reconstruction error term can make the embedding functions of both SRAE and of each RAE an approximate identity mapping, which helps to prevent the degradation of statistical information. We then insert several residual-like blocks with shortcut connections to augment the representational capacity of SRAE, and to simplify the training of a deeper network. The experimental evidence demonstrates that our DreamNet can achieve improved accuracy with increased depth of the network.