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

• URL: http://arxiv.org/abs/2306.04824v2
• Date: Fri, 9 Jun 2023 04:06:36 GMT
• Title: Sparse Linear Centroid-Encoder: A Convex Method for Feature Selection
• Authors: Tomojit Ghosh, Michael Kirby, Karim Karimov
• Abstract summary: We present Sparse Centroid-Encoder (SLCE) over a novel feature selection technique. The algorithm uses a linear network to reconstruct a neural feature at the same time.
• Score: 1.057079240576682
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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