Supervised Dimension Reduction

Tools for dimension reduction with auxiliary information (generalization of PCA)

This package provides several useful functions for dimension reduction of a primary data matrix with the presence of an auxiliary data matrix, which potentially drives some underlying structure of the primary data (therefore, referred to as supervision). The goal is to obtain a more interpretable and accurate low-rank approximation of the primary data with the help of supervision. More details about the methods can be found in "Supervised singular value decomposition and its asymptotic properties" by Li et al. (2016) in JMVA and "Supervised sparse and functional principal component analysis" by Li et al. (2016+) in JCGS.
The SupPCA function decomposes an auxiliary data into a few low-rank components as the standard principal component analysis (PCA) does. But SupPCA can accommodate auxiliary information measured on the same set of samples to further refine dimension reduction results. SupSFPCA further enhances the results by incorporating smoothness and sparsity to accommodate high dimensional data and functional data. It subsumes the standard PCA, sparse PCA, functional PCA, supervised PCA as special cases through special specification of tuning parameters.

The output of SupPCA and SupSFPCA is similar to that of the standard PCA (i.e., loadings and scores). Thus it can be easily used in statistical analysis such as visualization, prediction, clustering, and inference. Besides, the functions also provide insights into how the auxiliary data drive the underlying structure of the primary data.

We provide a call center arrival rate example (data and code) to illustrate the usage of different methods. We find that both SupPCA and SupSFPCA outperform the standard PCA in terms of interpretation and forecasting accuracy. More details can be found in Li et al. (2016) JMVA paper.