Chapter 7: Proximities in dimensionality reduction
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Dimensionality reduction aims at representing high-dimensional data in a lower-dimensional representation, while preserving their structure (clusters, outliers, manifold). Dimensionality reduction can be used for exploratory data visualization, data compression, or as a preprocessing to some other analysis in order to alleviate the curse of dimensionality. Data structure is usually quantified with indicators, like covariance between variables, or pairwise proximity relationships, like scalar products, distances, similarities, or neighbourhoods. One objective of this chapter is to provide an overview of some classical and more recent methods of dimensionality reduction, to shed some light on them from the perspective of analyzing proximities, and to illustrate them with multivariate data that could be typically encountered in social sciences. Complementary aspects like quality assessment and alternative metrics are briefly developed.

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