# Feature Grouping and Sparse Principal Component Analysis with Truncated Regularization

arXiv: https://arxiv.org/abs/2106.13685 · HTML: https://mlsanity.com/paper/2106.13685/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 48 references that are in the map.
- First posted on arXiv 25 Jun 2021.

## Builds on (most cited first, 6 of 6)

- [A Survey on Nonconvex Regularization Based Sparse and Low-Rank Recovery in Signal Processing, Statistics, and Machine Learning](https://mlsanity.com/paper/1808.05403/) (2018)
- [An efficient Hessian based algorithm for solving large-scale sparse group Lasso problems](https://mlsanity.com/paper/1712.05910/) (2017)
- [Sparse Principal Component Analysis via Variable Projection](https://mlsanity.com/paper/1804.00341/) (2018)
- [Learning Feature Sparse Principal Components](https://mlsanity.com/paper/1904.10155/) (2019)
- [Two-Layer Feature Reduction for Sparse-Group Lasso via Decomposition of Convex Sets](https://mlsanity.com/paper/1410.4210/) (2014)
- [Principal Component Projection and Regression in Nearly Linear Time through Asymmetric SVRG](https://mlsanity.com/paper/1910.06517/) (2019)

## Built on by (most cited first, 1 of 1)

- [SparCA: Sparse Compressed Agglomeration for Feature Extraction and Dimensionality Reduction](https://mlsanity.com/paper/2302.10776/) (2023)

## Abstract (arXiv)

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}.