# Sparse Linear Centroid-Encoder: A Convex Method for Feature Selection

arXiv: https://arxiv.org/abs/2306.04824 · HTML: https://mlsanity.com/paper/2306.04824/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 29 references that are in the map.
- First posted on arXiv 7 Jun 2023.

## Builds on (most cited first, 7 of 7)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Concrete Autoencoders for Differentiable Feature Selection and Reconstruction](https://mlsanity.com/paper/1901.09346/) (2019)
- [Group Sparse Regularization for Deep Neural Networks](https://mlsanity.com/paper/1607.00485/) (2016)
- [FsNet: Feature Selection Network on High-dimensional Biological Data](https://mlsanity.com/paper/2001.08322/) (2020)
- [Supervised Dimensionality Reduction and Visualization using Centroid-encoder](https://mlsanity.com/paper/2002.11934/) (2020)
- [The Trimmed Lasso: Sparsity and Robustness](https://mlsanity.com/paper/1708.04527/) (2017)

## Abstract (arXiv)

We present a novel feature selection technique, Sparse Linear Centroid-Encoder (SLCE). The algorithm uses a linear transformation to reconstruct a point as its class centroid and, at the same time, uses the ℓ1-norm penalty to filter out unnecessary features from the input data. The original formulation of the optimization problem is nonconvex, but we propose a two-step approach, where each step is convex. In the first step, we solve the linear Centroid-Encoder, a convex optimization problem over a matrix A. In the second step, we only search for a sparse solution over a diagonal matrix B while keeping A fixed. Unlike other linear methods, e.g., Sparse Support Vector Machines and Lasso, Sparse Linear Centroid-Encoder uses a single model for multi-class data. We present an in-depth empirical analysis of the proposed model and show that it promotes sparsity on various data sets, including high-dimensional biological data. Our experimental results show that SLCE has a performance advantage over some state-of-the-art neural network-based feature selection techniques.