Titlebook: Nonlinear Dimensionality Reduction Techniques; A Data Structure Pre Sylvain Lespinats,Benoit Colange,Denys Dutykh Book 2022 The Editor(s) (

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Conclusions,Dimensionality Reduction (DR) enables analysts to perform visual exploration of high dimensional data by providing a low-dimensional representation. On its own, it allows, for instance, to identify at a glance data structures such as clusters, hierarchies or outliers.

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Intrinsic Dimensionality,umed to live in a manifold whose dimensionality is lower than that of the data space dimensionality. The effective dimensionality of data is called intrinsic dimensionality. Its estimation is detailed Sect. 2.2.

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Stress Functions for Supervised Dimensionality Reduction,tion for which the desired output must be provided for a training set. Yet, DR is sometimes applied to datasets for which such annotations are available (e.g., class-information). In this context, supervised dimensionality reduction methods seek to take advantage of that information to improve the representation of the data structure.

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Optimization, Acceleration and Out of Sample Extensions, effectively used (Sect. 7.1). It then addresses the issue of time and space complexity and DR techniques acceleration (Sect. 7.2). Finally, it dives into out of sample extension of the mapping, which allows to position new data points a posteriori onto a given map (Sect. 7.3).