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Kernel Alignment for Unsupervised Feature Selection via Matrix Factorization
Machine Learning · Submitted 13 Mar 2024
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim 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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The abstract, sentence by sentence
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.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | By removing irrelevant and redundant features, feature selection aims to find a good representation of the original features. | background 1.00 | 0.04 | 0.02 | asserted 1.00 |
| s1 | With the prevalence of unlabeled data, unsupervised feature selection has been proven effective in alleviating the so-called curse of dimensionality. | background 1.00 | 0.06 | 0.02 | asserted 1.00 |
| s2 | 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. | gap 0.76 | 0.05 | 0.03 | asserted 1.00 |
| s3 | It is well-known that kernel techniques can capture nonlinear structural information. | background 1.00 | 0.04 | 0.02 | asserted 1.00 |
| s4 | In this paper, we construct a model by integrating kernel functions and kernel alignment, which can be equivalently characterized as a matrix factorization problem. | method 0.64 | 0.94 | 0.07 | asserted 1.00 |
| s5 | However, such an extension raises another issue: the algorithm performance heavily depends on the choice of kernel, which is often unknown a priori. | limitation 0.89 | 0.26 | 0.02 | asserted 0.99 |
| s6 | Therefore, we further propose a multiple kernel-based learning method. | contribution 0.81 | 0.83 | 0.04 | asserted 0.97 |
| s7 | By doing so, our model can learn both linear and nonlinear similarity information and automatically generate the most appropriate kernel. | method 0.59 | 0.79 | 0.12 | asserted 0.95 |
| s8 | 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. | result 1.00 | 0.96 | 0.88 | asserted 1.00 |
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Original 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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