ArticlePNAS nexus2024
Hierarchical simplicial manifold learning.
Article in PNAS nexus, 2024. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Not yet cited in PubMed.
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The abstract states no effect estimate the extractor could read, or names no intervention and outcome on the map, so this paper lights no cell and moves no belief. It is still indexed, cited and linked below.
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3 authors.
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Abstract
Learning global structures, i.e. topological properties, inherent in complex data is an essential yet challenging task that spans across various scientific and engineering disciplines. A fundamental approach is to extract local data representations and use them to assemble the global structure. This conjunction of local and global operations catalyzes the integration of tools from algebraic and computational topology with machine learning. In this article, we propose a hierarchical simplicial manifold learning algorithm, constituted by nested clustering and topological reduction, for constructing simplicial complexes and decoding their topological properties. We show that the learned complex possesses the same topology as the original embedding manifold from which the data were sampled. We demonstrate applicability, convergence, and computational efficiency of the algorithm on both synthetic and real-world data.
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