Stress Functions for Unsupervised Dimensionality Reduction

Sylvain Lespinats, Benoit Colange and Denys Dutykh
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Sylvain Lespinats: Grenoble Alpes University, National Institute of Solar Energy (INES)
Benoit Colange: Grenoble Alpes University, National Institute of Solar Energy (INES)
Denys Dutykh: Université Grenoble Alpes, Université Savoie Mont Blanc, Campus Scientifique, CNRS - LAMA UMR 5127

Chapter Chapter 5 in Nonlinear Dimensionality Reduction Techniques, 2022, pp 89-118 from Springer

Abstract: Abstract Dimensionality Reduction (DR) represents a set of points {ξ i} in a high dimensional metric data space D $$\mathcal {D}$$ by associated points {x i} in a low-dimensional embedding space ℰ $$\mathcal {E}$$ . This representation defines a mapping Φ : D → ℰ $$\Phi : \mathcal {D} \longrightarrow \mathcal {E}$$ such that Φ(ξ i) = x i for all i. This mapping must preserve as much as possible the structure of data.

Date: 2022
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DOI: 10.1007/978-3-030-81026-9_5

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