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Adaptive indefinite kernels in hyperbolic spaces
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DOI：10.1016/j.neunet.2024.106803.png)
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摘要
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Learning embeddings in hyperbolic space has gained increasing interest in the community, due to its property of negative curvature, as a way of encoding data hierarchy. Recent works investigate the improvement of the representation power of hyperbolic embeddings through kernelization. However, existing developments focus on defining positive definite (pd) kernels, which may affect the intriguing property of hyperbolic spaces. This is due to the structures of hyperbolic spaces being modeled in indefinite spaces (e.g., Krein space). This paper addresses this issue by developing adaptive indefinite kernels, which can better utilize the structures in the Krein space. To this end, we first propose an adaptive embedding function in the Lorentz model and define indefinite Lorentz kernels (iLks) via the embedding function. Due to the isometric relationship between the Lorentz model and the Poincare ball, these iLks are further extended to the Poincare ball, resulting in the development of what are termed indefinite Poincare kernels (iPKs). We evaluate the proposed indefinite kernels on a diversity of learning scenarios, including image classification, few-shot learning, zero-shot learning, person re-identification, knowledge distillation, etc. We show that the proposed indefinite kernels can bring significant performance gains over the baselines and enjoy better representation power from RKKSs than pd kernels.
Keyword:
Hyperbolic space
Data hierarchy
Indefinite Lorentz kernels
Indefinite Poincare kernels
期刊
IF:
6.3
论文数:
8.2K
被引数:
3.0W
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