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Image set-based visual classification methods have achieved remarkableperformance, via characterising the image set in terms of a non-singularcovariance matrix on a symmetric positive definite (SPD) manifold. To adapt tocomplicated visual scenarios better, several Riemannian networks (RiemNets) forSPD matrix nonlinear processing have recently been studied. However, it ispertinent to ask, whether greater accuracy gains can be achieved by simplyincreasing the depth of RiemNets. The answer appears to be negative, as deeperRiemNets tend to lose generalization ability. To explore a possible solution tothis issue, we propose a new architecture for SPD matrix learning.Specifically, to enrich the deep representations, we adopt SPDNet [1] as thebackbone, with a stacked Riemannian autoencoder (SRAE) built on the tail. Theassociated reconstruction error term can make the embedding functions of bothSRAE and of each RAE an approximate identity mapping, which helps to preventthe degradation of statistical information. We then insert severalresidual-like blocks with shortcut connections to augment the representationalcapacity of SRAE, and to simplify the training of a deeper network. Theexperimental evidence demonstrates that our DreamNet can achieve improvedaccuracy with increased depth of the network.

DreamNet: A Deep Riemannian Network based on SPD Manifold Learning for Visual Classification