# Kernel Alignment for Unsupervised Feature Selection via Matrix Factorization

arXiv: https://arxiv.org/abs/2403.14688 · HTML: https://mlsanity.com/paper/2403.14688/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 42 references that are in the map.
- First posted on arXiv 13 Mar 2024.

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

- [Deep Unsupervised Feature Selection by Discarding Nuisance and Correlated Features](https://mlsanity.com/paper/2110.05306/) (2021)
- [Fairness-Aware Unsupervised Feature Selection](https://mlsanity.com/paper/2106.02216/) (2021)
- [Unsupervised Feature Selection based on Adaptive Similarity Learning and Subspace Clustering](https://mlsanity.com/paper/1912.05458/) (2019)
- [Graph Convolutional Network-based Feature Selection for High-dimensional and Low-sample Size Data](https://mlsanity.com/paper/2211.14144/) (2022)
- [Unsupervised feature selection via self-paced learning and low-redundant regularization](https://mlsanity.com/paper/2112.07227/) (2021)
- [Unsupervised Feature Selection for Tumor Profiles using Autoencoders and Kernel Methods](https://mlsanity.com/paper/2007.06106/) (2020)

## Abstract (arXiv)

By removing irrelevant and redundant features, feature selection aims to find a good representation of the original features. With the prevalence of unlabeled data, unsupervised feature selection has been proven effective in alleviating the so-called curse of dimensionality. Most existing matrix factorization-based unsupervised feature selection methods are built upon subspace learning, but they have limitations in capturing nonlinear structural information among features. It is well-known that kernel techniques can capture nonlinear structural information. In this paper, we construct a model by integrating kernel functions and kernel alignment, which can be equivalently characterized as a matrix factorization problem. However, such an extension raises another issue: the algorithm performance heavily depends on the choice of kernel, which is often unknown a priori. Therefore, we further propose a multiple kernel-based learning method. By doing so, our model can learn both linear and nonlinear similarity information and automatically generate the most appropriate kernel. Experimental analysis on real-world data demonstrates that the two proposed methods outperform other classic and state-of-the-art unsupervised feature selection methods in terms of clustering results and redundancy reduction in almost all datasets tested.