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In this paper, we consider a new variant for principal component analysis(PCA), aiming to capture the grouping and/or sparse structures of factorloadings simultaneously. To achieve these goals, we employ a non-convextruncated regularization with naturally adjustable sparsity and groupingeffects, and propose the Feature Grouping and Sparse Principal ComponentAnalysis (FGSPCA). The proposed FGSPCA method encourages the factor loadingswith similar values to collapse into disjoint homogeneous groups for featuregrouping or into a special zero-valued group for feature selection, which inturn helps reducing model complexity and increasing model interpretation.Usually, existing structured PCA methods require prior knowledge to constructthe regularization term. However, the proposed FGSPCA can simultaneouslycapture the grouping and/or sparse structures of factor loadings without anyprior information. To solve the resulting non-convex optimization problem, wepropose an alternating algorithm that incorporates the difference-of-convexprogramming, augmented Lagrange method and coordinate descent method.Experimental results demonstrate the promising performance and efficiency ofthe new method on both synthetic and real-world datasets. An R implementationof FGSPCA can be found on github {https://github.com/higeeks/FGSPCA}.

Feature Grouping and Sparse Principal Component Analysis with Truncated Regularization