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