Manifold learning: what, how, and why

Marina Meilă; Hanyu Zhang

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arXiv · 2311.03757

Manifold learning: what, how, and why

Marina Meilă·Hanyu Zhang

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Abstract

Manifold learning (ML), known also as non-linear dimension reduction, is a set of methods to find the low dimensional structure of data. Dimension reduction for large, high dimensional data is not merely a way to reduce the data; the new representations and descriptors obtained by ML reveal the geometric shape of high dimensional point clouds, and allow one to visualize, de-noise and interpret them. This survey presents the principles underlying ML, the representative methods, as well as their statistical foundations from a practicing statistician's perspective. It describes the trade-offs, and what theory tells us about the parameter and algorithmic choices we make in order to obtain reliable conclusions.

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stat.ML cs.LG

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Marina Meilă, Hanyu Zhang. 2023-11-07. Manifold learning: what, how, and why. https://arxiv.org/abs/2311.03757

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