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Sparse principal component analysis (PCA) aims at mapping large dimensionaldata to a linear subspace of lower dimension. By imposing loading vectors to besparse, it performs the double duty of dimension reduction and variableselection. Sparse PCA algorithms are usually expressed as a trade-off betweenexplained variance and sparsity of the loading vectors (i.e., number ofselected variables). As a high explained variance is not necessarily synonymouswith relevant information, these methods are prone to select irrelevantvariables. To overcome this issue, we propose an alternative formulation ofsparse PCA driven by the false discovery rate (FDR). We then leverage theTerminating-Random Experiments (T-Rex) selector to automatically determine anFDR-controlled support of the loading vectors. A major advantage of theresulting T-Rex PCA is that no sparsity parameter tuning is required. Numericalexperiments and a stock market data example demonstrate a significantperformance improvement.

Sparse PCA with False Discovery Rate Controlled Variable Selection