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I've got bit confused about dimensionality reduction and clustering . whether all clustering algorithms (k-means, affinity propagation, spectral clustering,...) do kind of dimensionality reduction ?

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    $\begingroup$ When compared to methods like principal components analysis and factor analysis, I've always viewed the methods of clustering I am most familiar with (model based) as a way to maintain and exploit the dimensionality of the data. $\endgroup$
    – D L Dahly
    Dec 24, 2013 at 10:38

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Clustering algorithms such as K-means work on distances. By dimensionality reduction, the data is projected from a large amount of components to only a few key components, at the same time, the distance metric that helps differentiate different clusters maximally is retained in dimensionality reduction. Such strategy is not only to reduce the computational efficiency in clustering, but may also reduce the local minima (may not though) and increase the robustness to the initializations.

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They somehow do; yet the space to which the reduce is "local" which means that only a single cluster is active.

If you want to use this as a preprocessing step (e.g. for a classifier), it often works to use the distances to the clusters (possibly transformed) as features. This is often done in the case of radial basis functions. For some more recent work on this with applications to natural images, see Adam Coates work, who relates this to sparse coding.

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