Few-shot learning (FSL) attempts to learn with limited data. In this work, we perform the feature extraction in the Euclidean space and the geodesic distance metric on the Oblique Manifold (OM). Specially, for better feature extraction, we propose a non-parametric Region Self-attention with Spatial Pyramid Pooling (RSSPP), which realizes a trade-off between the generalization and the discriminative ability of the single image feature. Then, we embed the feature to OM as a point. Furthermore, we design an Oblique Distance-based Classifier (ODC) that achieves classification in the tangent spaces which better approximate OM locally by learnable tangency points. Finally, we introduce a new method for parameters initialization and a novel loss function in the transductive settings. Extensive experiments demonstrate the effectiveness of our algorithm and it outperforms state-of-the-art methods on the popular benchmarks: mini-ImageNet, tiered-ImageNet, and Caltech-UCSD Birds-200-2011 (CUB).
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