The Emergence of Prototypicality: Unsupervised Feature Learning in Hyperbolic Space

Yunhui Guo, Yubei Chen, Stella Yu

Keywords: Unsupervised Learning, Prototypicality, Hyperbolic Space

TL;DR: We propose a novel unsupervised learning method by leveraging the property of hyperbolic space for organizing images based on prototypicality and semantics.

Abstract: Prototypicality is extensively studied in machine learning and computer vision. However, there is still no widely accepted definition of prototypicality. In this paper, we first propose to define prototypicality based on the concept of congealing. Then, we develop a novel method called HACK to automatically discover prototypical examples from the dataset. HACK conducts unsupervised \pt\ learning in \underline{H}yperbolic space with sphere p\underline{ACK}ing. HACK first generates uniformly packed particles in the Poincar\'e ball of hyperbolic space and then assigns the image uniquely to each particle. Due to the geometrical property of hyperbolic space, prototypical examples naturally emerge and tend to locate in the center of the Poincar\'e ball. HACK naturally leverages hyperbolic space to discover prototypical examples in a data-driven fashion. We verify the effectiveness of the method with synthetic dataset and natural image datasets. Extensive experiments show that HACK can naturally discover the prototypical examples without supervision. The discovered prototypical examples and atypical examples can be used to reduce sample complexity and increase model robustness.

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