Dimensionality reduction

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Dimensionality reduction

Ordination, Factor Analysis, Multivariate analysis

✎ This article/section is a stub — some half-sorted notes, not necessarily checked, not necessarily correct. Feel free to ignore, or tell me about it.

Correspondence Analysis (CA)

Conceptually similar to PCA, but uses a Chi-square distance, to be more appicable to nominal data (where PCA applies to continuous data).

See also:

• http://en.wikipedia.org/wiki/Correspondence_Analysis

Multi-dimensionsional scaling (MDS)

See also

• WS Torgerson (1958) Theory and Methods of Scaling
• JB Kruskal, and M Wish (1978) Multidimensional Scaling
• I Borg and P Groenen (2005) Modern Multidimensional Scaling: theory and applications
• TF Cox and MAA Cox (1994) Multidimensional Scaling

Generalizized MDS (GMDS)

A generalization of metric MDS where the target domain is non-Euclidean.

See also:

• http://en.wikipedia.org/wiki/Generalized_multidimensional_scaling_(GMDS)

Singular value decomposition (SVD)

See also:

• http://www.kwon3d.com/theory/jkinem/svd.html
• http://en.wikipedia.org/wiki/Singular_value_decomposition
• http://www.netlib.org/lapack/lug/node53.html
• http://public.lanl.gov/mewall/kluwer2002.html

Nonlinear dimensionality reduction / Manifold learning

UMAP

UMAP (Uniform manifold approximation and projection)

https://en.wikipedia.org/wiki/Nonlinear_dimensionality_reduction#Uniform_manifold_approximation_and_projection

Expectation Maximisation (EM)

✎ This article/section is a stub — some half-sorted notes, not necessarily checked, not necessarily correct. Feel free to ignore, or tell me about it.

A broadly applicable idea/method that iteratively uses the Maximum Likelihood (ML) idea and its estimation (MLE).