Unsupervised Feature Selection via a Dual-Graph Autoencoder with <inline-formula><math display="inline"><semantics><mrow><msub><mi mathvariant="bold-script">l</mi><mrow><mn mathvariant="bold">2</mn><mo mathvariant="bold">,</mo><mn mathvariant="bold">1</mn><mo mathvariant="bold">/</mo><mn mathvariant="bold">2</mn></mrow></msub></mrow></semantics></math></inline-formula>-Norm for [<sup>68</sup>Ga]Ga-Pentixafor PET Imaging of Glioma
In the era of big data, high-dimensional datasets have become increasingly common in fields such as biometrics, computer vision, and medical imaging. While such data contain abundant information, they are often accompanied by substantial noise, high redundancy, and complex intrinsic structures, posi...
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-05-01
|
| Series: | Applied Sciences |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2076-3417/15/11/6177 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849722571509989376 |
|---|---|
| author | Zhichao Song Meiling Chen Liang Xie Xi Fang |
| author_facet | Zhichao Song Meiling Chen Liang Xie Xi Fang |
| author_sort | Zhichao Song |
| collection | DOAJ |
| description | In the era of big data, high-dimensional datasets have become increasingly common in fields such as biometrics, computer vision, and medical imaging. While such data contain abundant information, they are often accompanied by substantial noise, high redundancy, and complex intrinsic structures, posing significant challenges for analysis and modeling. To address these issues, unsupervised feature selection has attracted growing interest due to its ability to handle unlabeled, noisy, and unstructured data. This paper proposes a novel unsupervised feature selection algorithm based on a dual-graph autoencoder (DGA), which combines the powerful data reconstruction capability of autoencoders with the structural preservation strengths of graph regularization. Specifically, the algorithm introduces the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="script">l</mi><mrow><mn>2</mn><mo>,</mo><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msub></mrow></semantics></math></inline-formula>-norm and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="script">l</mi><mrow><mn>2</mn><mo>,</mo><mn>1</mn></mrow></msub></mrow></semantics></math></inline-formula>-norm constraints on the encoder and decoder weight matrices, respectively, to promote feature sparsity and suppress redundancy. Furthermore, an <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="script">l</mi><mrow><mn>2</mn><mo>,</mo><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msub></mrow></semantics></math></inline-formula>-norm loss term is introduced to enhance robustness against noise and outliers. Two separate adjacency graphs are constructed to capture the local geometric relationships among samples and among features, and their corresponding graph regularization terms are embedded in the training process to retain the intrinsic structure of the data. Experiments on multiple benchmark datasets and [<sup>68</sup>Ga]Ga-Pentixafor PET/CT glioma imaging data demonstrate that the proposed DGA significantly improves clustering performance and accurately identifies features associated with lesion regions. From a clinical perspective, DGA facilitates more accurate lesion characterization and biomarker identification in glioma patients, thereby offering potential utility in aiding diagnosis, treatment planning, and personalized prognosis assessment. |
| format | Article |
| id | doaj-art-ed87b0d06fcd4ee2ac12fa482729fe02 |
| institution | DOAJ |
| issn | 2076-3417 |
| language | English |
| publishDate | 2025-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Applied Sciences |
| spelling | doaj-art-ed87b0d06fcd4ee2ac12fa482729fe022025-08-20T03:11:18ZengMDPI AGApplied Sciences2076-34172025-05-011511617710.3390/app15116177Unsupervised Feature Selection via a Dual-Graph Autoencoder with <inline-formula><math display="inline"><semantics><mrow><msub><mi mathvariant="bold-script">l</mi><mrow><mn mathvariant="bold">2</mn><mo mathvariant="bold">,</mo><mn mathvariant="bold">1</mn><mo mathvariant="bold">/</mo><mn mathvariant="bold">2</mn></mrow></msub></mrow></semantics></math></inline-formula>-Norm for [<sup>68</sup>Ga]Ga-Pentixafor PET Imaging of GliomaZhichao Song0Meiling Chen1Liang Xie2Xi Fang3School of Mathematics and Statistics, Wuhan University of Technology, Wuhan 430070, ChinaSchool of Mathematics and Statistics, Wuhan University of Technology, Wuhan 430070, ChinaSchool of Mathematics and Statistics, Wuhan University of Technology, Wuhan 430070, ChinaSchool of Mathematics and Statistics, Wuhan University of Technology, Wuhan 430070, ChinaIn the era of big data, high-dimensional datasets have become increasingly common in fields such as biometrics, computer vision, and medical imaging. While such data contain abundant information, they are often accompanied by substantial noise, high redundancy, and complex intrinsic structures, posing significant challenges for analysis and modeling. To address these issues, unsupervised feature selection has attracted growing interest due to its ability to handle unlabeled, noisy, and unstructured data. This paper proposes a novel unsupervised feature selection algorithm based on a dual-graph autoencoder (DGA), which combines the powerful data reconstruction capability of autoencoders with the structural preservation strengths of graph regularization. Specifically, the algorithm introduces the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="script">l</mi><mrow><mn>2</mn><mo>,</mo><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msub></mrow></semantics></math></inline-formula>-norm and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="script">l</mi><mrow><mn>2</mn><mo>,</mo><mn>1</mn></mrow></msub></mrow></semantics></math></inline-formula>-norm constraints on the encoder and decoder weight matrices, respectively, to promote feature sparsity and suppress redundancy. Furthermore, an <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="script">l</mi><mrow><mn>2</mn><mo>,</mo><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msub></mrow></semantics></math></inline-formula>-norm loss term is introduced to enhance robustness against noise and outliers. Two separate adjacency graphs are constructed to capture the local geometric relationships among samples and among features, and their corresponding graph regularization terms are embedded in the training process to retain the intrinsic structure of the data. Experiments on multiple benchmark datasets and [<sup>68</sup>Ga]Ga-Pentixafor PET/CT glioma imaging data demonstrate that the proposed DGA significantly improves clustering performance and accurately identifies features associated with lesion regions. From a clinical perspective, DGA facilitates more accurate lesion characterization and biomarker identification in glioma patients, thereby offering potential utility in aiding diagnosis, treatment planning, and personalized prognosis assessment.https://www.mdpi.com/2076-3417/15/11/6177unsupervised feature selectionautoencoderdual-graph regularizationnorm[<sup>68</sup>Ga]Ga-Pentixafor PET |
| spellingShingle | Zhichao Song Meiling Chen Liang Xie Xi Fang Unsupervised Feature Selection via a Dual-Graph Autoencoder with <inline-formula><math display="inline"><semantics><mrow><msub><mi mathvariant="bold-script">l</mi><mrow><mn mathvariant="bold">2</mn><mo mathvariant="bold">,</mo><mn mathvariant="bold">1</mn><mo mathvariant="bold">/</mo><mn mathvariant="bold">2</mn></mrow></msub></mrow></semantics></math></inline-formula>-Norm for [<sup>68</sup>Ga]Ga-Pentixafor PET Imaging of Glioma Applied Sciences unsupervised feature selection autoencoder dual-graph regularization norm [<sup>68</sup>Ga]Ga-Pentixafor PET |
| title | Unsupervised Feature Selection via a Dual-Graph Autoencoder with <inline-formula><math display="inline"><semantics><mrow><msub><mi mathvariant="bold-script">l</mi><mrow><mn mathvariant="bold">2</mn><mo mathvariant="bold">,</mo><mn mathvariant="bold">1</mn><mo mathvariant="bold">/</mo><mn mathvariant="bold">2</mn></mrow></msub></mrow></semantics></math></inline-formula>-Norm for [<sup>68</sup>Ga]Ga-Pentixafor PET Imaging of Glioma |
| title_full | Unsupervised Feature Selection via a Dual-Graph Autoencoder with <inline-formula><math display="inline"><semantics><mrow><msub><mi mathvariant="bold-script">l</mi><mrow><mn mathvariant="bold">2</mn><mo mathvariant="bold">,</mo><mn mathvariant="bold">1</mn><mo mathvariant="bold">/</mo><mn mathvariant="bold">2</mn></mrow></msub></mrow></semantics></math></inline-formula>-Norm for [<sup>68</sup>Ga]Ga-Pentixafor PET Imaging of Glioma |
| title_fullStr | Unsupervised Feature Selection via a Dual-Graph Autoencoder with <inline-formula><math display="inline"><semantics><mrow><msub><mi mathvariant="bold-script">l</mi><mrow><mn mathvariant="bold">2</mn><mo mathvariant="bold">,</mo><mn mathvariant="bold">1</mn><mo mathvariant="bold">/</mo><mn mathvariant="bold">2</mn></mrow></msub></mrow></semantics></math></inline-formula>-Norm for [<sup>68</sup>Ga]Ga-Pentixafor PET Imaging of Glioma |
| title_full_unstemmed | Unsupervised Feature Selection via a Dual-Graph Autoencoder with <inline-formula><math display="inline"><semantics><mrow><msub><mi mathvariant="bold-script">l</mi><mrow><mn mathvariant="bold">2</mn><mo mathvariant="bold">,</mo><mn mathvariant="bold">1</mn><mo mathvariant="bold">/</mo><mn mathvariant="bold">2</mn></mrow></msub></mrow></semantics></math></inline-formula>-Norm for [<sup>68</sup>Ga]Ga-Pentixafor PET Imaging of Glioma |
| title_short | Unsupervised Feature Selection via a Dual-Graph Autoencoder with <inline-formula><math display="inline"><semantics><mrow><msub><mi mathvariant="bold-script">l</mi><mrow><mn mathvariant="bold">2</mn><mo mathvariant="bold">,</mo><mn mathvariant="bold">1</mn><mo mathvariant="bold">/</mo><mn mathvariant="bold">2</mn></mrow></msub></mrow></semantics></math></inline-formula>-Norm for [<sup>68</sup>Ga]Ga-Pentixafor PET Imaging of Glioma |
| title_sort | unsupervised feature selection via a dual graph autoencoder with inline formula math display inline semantics mrow msub mi mathvariant bold script l mi mrow mn mathvariant bold 2 mn mo mathvariant bold mo mn mathvariant bold 1 mn mo mathvariant bold mo mn mathvariant bold 2 mn mrow msub mrow semantics math inline formula norm for sup 68 sup ga ga pentixafor pet imaging of glioma |
| topic | unsupervised feature selection autoencoder dual-graph regularization norm [<sup>68</sup>Ga]Ga-Pentixafor PET |
| url | https://www.mdpi.com/2076-3417/15/11/6177 |
| work_keys_str_mv | AT zhichaosong unsupervisedfeatureselectionviaadualgraphautoencoderwithinlineformulamathdisplayinlinesemanticsmrowmsubmimathvariantboldscriptlmimrowmnmathvariantbold2mnmomathvariantboldmomnmathvariantbold1mnmomathvariantboldmomnmathvariantbold2mnmrowmsubmrowsemanticsmat AT meilingchen unsupervisedfeatureselectionviaadualgraphautoencoderwithinlineformulamathdisplayinlinesemanticsmrowmsubmimathvariantboldscriptlmimrowmnmathvariantbold2mnmomathvariantboldmomnmathvariantbold1mnmomathvariantboldmomnmathvariantbold2mnmrowmsubmrowsemanticsmat AT liangxie unsupervisedfeatureselectionviaadualgraphautoencoderwithinlineformulamathdisplayinlinesemanticsmrowmsubmimathvariantboldscriptlmimrowmnmathvariantbold2mnmomathvariantboldmomnmathvariantbold1mnmomathvariantboldmomnmathvariantbold2mnmrowmsubmrowsemanticsmat AT xifang unsupervisedfeatureselectionviaadualgraphautoencoderwithinlineformulamathdisplayinlinesemanticsmrowmsubmimathvariantboldscriptlmimrowmnmathvariantbold2mnmomathvariantboldmomnmathvariantbold1mnmomathvariantboldmomnmathvariantbold2mnmrowmsubmrowsemanticsmat |