Manifold learning via quantum dynamics

Akshat Kumar; Mohan Sarovar

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arXiv · 2112.11161

Manifold learning via quantum dynamics

Akshat Kumar·Mohan Sarovar

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Abstract

We introduce an algorithm for computing geodesics on sampled manifolds that relies on simulation of quantum dynamics on a graph embedding of the sampled data. Our approach exploits classic results in semiclassical analysis and the quantum-classical correspondence, and forms a basis for techniques to learn the manifold from which a dataset is sampled, and subsequently for nonlinear dimensionality reduction of high-dimensional datasets. We illustrate the new algorithm with data sampled from model manifolds and also by a clustering demonstration based on COVID-19 mobility data. Finally, our method reveals interesting connections between the discretization provided by data sampling and quantization.

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quant-ph cs.LG math.ST stat.ML stat.TH

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BibTeX RIS

Akshat Kumar, Mohan Sarovar. 2021-12-20. Manifold learning via quantum dynamics. https://arxiv.org/abs/2112.11161

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