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Hubs and Hyperspheres: Reducing Hubness and Improving Transductive Few-shot Learning with Hyperspherical Embeddings

Daniel J. TrostenRwiddhi ChakrabortySigurd L{\o}kseKristoffer Knutsen Wickstr{\o}mRobert JenssenMichael C. Kampffmeyer
Mar 2023
摘要
Distance-based classification is frequently used in transductive few-shotlearning (FSL). However, due to the high-dimensionality of imagerepresentations, FSL classifiers are prone to suffer from the hubness problem,where a few points (hubs) occur frequently in multiple nearest neighbour listsof other points. Hubness negatively impacts distance-based classification whenhubs from one class appear often among the nearest neighbors of points fromanother class, degrading the classifier's performance. To address the hubnessproblem in FSL, we first prove that hubness can be eliminated by distributingrepresentations uniformly on the hypersphere. We then propose two newapproaches to embed representations on the hypersphere, which we prove optimizea tradeoff between uniformity and local similarity preservation -- reducinghubness while retaining class structure. Our experiments show that the proposedmethods reduce hubness, and significantly improves transductive FSL accuracyfor a wide range of classifiers.
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