Dimensionality reduction

A process of reducing the dimension of data while keeping as much “useful” information as possible. The useful information can be operationalized as the covariance structure (e.g., PCA) or identification of manifold on which data points lives.

It implicitly assumes that the data manifold in the High dimensional space has a low Effective dimensionality or a low-dimensional manifold.

• https://en.wikipedia.org/wiki/Dimensionality_reduction

Methods

Common methods

• PCA
  • PredPCA: Isomura2021dimensionality
• Isomap
• MDS
• t SNE
• UMAP

Kobak2021initialization argues that initialization is critical for obtaining more representative results from t-SNE and UMAP.

Others

• LargeVis

Books

• Modern Dimension Reduction

Tutorials

• The Beginner’s Guide to Dimensionality Reduction
• Nguyen2019ten - Ten quick tips for effective dimensionality reduction
• A Bluffers Guide to Dimension Reduction By Leland McInnes
• https://www.youtube.com/watch?v=4cZEccwm8WY