Kernel Alignment for Unsupervised Feature Selection via Matrix Factorization

• URL: http://arxiv.org/abs/2403.14688v1
• Date: Wed, 13 Mar 2024 20:35:44 GMT
• Title: Kernel Alignment for Unsupervised Feature Selection via Matrix Factorization
• Authors: Ziyuan Lin, Deanna Needell,
• Abstract summary: 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. In this paper, we construct a model by integrating kernel functions and kernel alignment, which can be equivalently characterized as a matrix factorization problem. By doing so, our model can learn both linear and nonlinear similarity information and automatically generate the most appropriate kernel.
• Score: 8.020732438595905
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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