Multiple correspondence analysis - Wikipedia

Abstraction: PCA counterpart for nominal categorical data using chi-square distances

Key points:

• MCA detects and represents structure in nominal categorical data by projecting into low-dimensional Euclidean space; counterpart of PCA for categorical variables
• Applied to indicator matrix (complete disjunctive table, CDT) or Burt table (symmetric matrix of all pairwise cross-tabulations, analogous to covariance matrix)
• Uses SVD of normalized CDT; factor decomposition gives coordinates for both observations and variables in the same factor space
• Axes ranked by variance explained (eigenvalues); number of axes retained determined by modified eigenvalue criterion
• Famously applied by Pierre Bourdieu in La Distinction and Homo Academicus to map social fields geometrically
• Implemented in R's FactoMineR package; can be viewed as unstandardized PCA on transformed CDT

Connections: Pierre Bourdieu · Multiple Correspondence Analysis · Correspondence Analysis · Dimensionality Reduction

Source: http://en.wikipedia.org/wiki/Multiple_correspondence_analysis