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Annual Review of Statistics and Its Application

Volume 11, 2024

Manifold Learning: What, How, and Why

Abstract

Manifold learning (ML), also known as nonlinear 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, denoise, and interpret them. This review presents the underlying principles of ML, its representative methods, and their statistical foundations, all 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.

Keyword(s): embedding, manifold learning, nonlinear dimension reduction
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2024-04-22
2024-04-30
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Manifold Learning: What, How, and Why
Annual Review of Statistics and Its Application 11, 393 (2024); https://doi.org/10.1146/annurev-statistics-040522-115238
/content/journals/10.1146/annurev-statistics-040522-115238
/content/journals/10.1146/annurev-statistics-040522-115238
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