Sparse non-symmetrical correspondence analysis
Abstract
Sparse methods inspired by the Lasso have been successfully applied to principal components analysis and only recently to correspondence analysis in its multiple and contingency table versions. The principle consists in forcing a significant number of row and column weights to be zero to facilitate the interpretation of the components, in the spirit of the search for simple structures, especially for large arrays. This simplicity comes at the expense of the loss of characteristic properties such as orthogonality and double barycentric relations, hence the need for a trade-off.
Liu et al. (2023) developed a specific deflation algorithm to obtain orthogonal successive weight vectors, in a constrained generalized SVD. Although it is possible to sparsify only the rows (or columns) of a contingency table, their method remains fundamentally symmetric.
We propose here a sparse version of the non-symmetric correspondence analysis (NSCA) introduced by Lauro and D’Ambra (1984), cf Beh and Lombardo (2021). Since NSCA is a weighted PCA of centered column profiles, or a generalized SVD, both row (the responses) and column (the predictors) weights may be sparsified, or only one set according to user’s choice. Sparse NSCA will be illustrated on several data sets and compared to standard CA, sparse CA and standard NSCA.
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