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 $\ell_1$-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.

本研究提出了一种新颖的特征选择技术，称为稀疏线性质心编码器（SLCE），它使用线性变换重构点，同时使用l1范数惩罚去除输入数据中不必要的特征，并通过凸优化问题解决方案该问题。我们通过实证分析表明，SLCE在各种数据集上促进了稀疏性。与某些基于神经网络的特征选择技术相比，SLCE具有性能优势。

稀疏线性质心编码器:一种特征选择的凸方法