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Recent studies have shown that aggregating convolutional features of apre-trained Convolutional Neural Network (CNN) can obtain impressiveperformance for a variety of visual tasks. The symmetric Positive Definite(SPD) matrix becomes a powerful tool due to its remarkable ability to learn anappropriate statistic representation to characterize the underlying structureof visual features. In this paper, we propose to aggregate deep convolutionalfeatures into an SPD matrix representation through the SPD generation and theSPD transformation under an end-to-end deep network. To this end, several newlayers are introduced in our network, including a nonlinear kernel aggregationlayer, an SPD matrix transformation layer, and a vectorization layer. Thenonlinear kernel aggregation layer is employed to aggregate the convolutionalfeatures into a real SPD matrix directly. The SPD matrix transformation layeris designed to construct a more compact and discriminative SPD representation.The vectorization and normalization operations are performed in thevectorization layer for reducing the redundancy and accelerating theconvergence. The SPD matrix in our network can be considered as a mid-levelrepresentation bridging convolutional features and high-level semanticfeatures. To demonstrate the effectiveness of our method, we conduct extensiveexperiments on visual classification. Experiment results show that our methodnotably outperforms state-of-the-art methods.

Learning a Robust Representation via a Deep Network on Symmetric Positive Definite Manifolds