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- W4300587783 abstract "Topological data analysis offers a rich source of valuable information to study vision problems. Yet, so far we lack a theoretically sound connection to popular kernel-based learning techniques, such as kernel SVMs or kernel PCA. In this work, we establish such a connection by designing a multi-scale kernel for persistence diagrams, a stable summary representation of topological features in data. We show that this kernel is positive definite and prove its stability with respect to the 1-Wasserstein distance. Experiments on two benchmark datasets for 3D shape classification/retrieval and texture recognition show considerable performance gains of the proposed method compared to an alternative approach that is based on the recently introduced persistence landscapes." @default.
- W4300587783 created "2022-10-03" @default.
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- W4300587783 date "2014-12-21" @default.
- W4300587783 modified "2023-10-12" @default.
- W4300587783 title "A Stable Multi-Scale Kernel for Topological Machine Learning" @default.
- W4300587783 doi "https://doi.org/10.48550/arxiv.1412.6821" @default.
- W4300587783 hasPublicationYear "2014" @default.
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