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Principal component analysis (PCA) has been widely used as an effectivetechnique for feature extraction and dimension reduction. In the High DimensionLow Sample Size (HDLSS) setting, one may prefer modified principal components,with penalized loadings, and automated penalty selection by implementing modelselection among these different models with varying penalties. The earlier work[1, 2] has proposed penalized PCA, indicating the feasibility of modelselection in $L_2$- penalized PCA through the solution path of Ridgeregression, however, it is extremely time-consuming because of the intensivecalculation of matrix inverse. In this paper, we propose a fast model selectionmethod for penalized PCA, named Approximated Gradient Flow (AgFlow), whichlowers the computation complexity through incorporating the implicitregularization effect introduced by (stochastic) gradient flow [3, 4] andobtains the complete solution path of $L_2$-penalized PCA under varying$L_2$-regularization. We perform extensive experiments on real-world datasets.AgFlow outperforms existing methods (Oja [5], Power [6], and Shamir [7] and thevanilla Ridge estimators) in terms of computation costs.

AgFlow: Fast Model Selection of Penalized PCA via Implicit Regularization Effects of Gradient Flow