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.
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Hong Kong Inst Educ, Dept Int Educ & Lifelong Learning, Tai Po, Hong Kong, Peoples R ChinaHong Kong Inst Educ, Dept Int Educ & Lifelong Learning, Tai Po, Hong Kong, Peoples R China
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Univ Tasmania, Sch Clin, Sch Nursing & Midwifery, Hobart, Tas 7000, AustraliaUniv Tasmania, Sch Clin, Sch Nursing & Midwifery, Hobart, Tas 7000, Australia
Andrews, Christine E.
Ford, Karen
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Royal Hobart Hosp, Practice Dev Unit, Hobart, Tas, Australia
Univ Tasmania, Sch Nursing & Midwifery, Hobart, Tas 7001, AustraliaUniv Tasmania, Sch Clin, Sch Nursing & Midwifery, Hobart, Tas 7000, Australia
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CALIF POLYTECH STATE UNIV SAN LUIS OBISPO,KENNEDY LIB,SAN LUIS OBISPO,CA 93407CALIF POLYTECH STATE UNIV SAN LUIS OBISPO,KENNEDY LIB,SAN LUIS OBISPO,CA 93407