{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,16]],"date-time":"2026-05-16T21:25:26Z","timestamp":1778966726459,"version":"3.51.4"},"reference-count":38,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2021,5,23]],"date-time":"2021-05-23T00:00:00Z","timestamp":1621728000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"the National Science Foundation Council of China","award":["61771006, 61976080, U1804149, 61701170"],"award-info":[{"award-number":["61771006, 61976080, U1804149, 61701170"]}]},{"name":"Key research projects of university in Henan province of China","award":["21A413002, 19A413006, 20B510001"],"award-info":[{"award-number":["21A413002, 19A413006, 20B510001"]}]},{"name":"the Programs for Science and Technology Development of Henan Province","award":["192102210254"],"award-info":[{"award-number":["192102210254"]}]},{"name":"the Talent Program of Henan University","award":["SYL19060110"],"award-info":[{"award-number":["SYL19060110"]}]},{"name":"the Postgraduate Quality Demonstration Courses of Henan University (English Professional Courses)","award":["SYL18030207"],"award-info":[{"award-number":["SYL18030207"]}]},{"name":"the Innovation and Quality Improvement ProgramProject for Graduate Education of Henan University","award":["SYL20060143"],"award-info":[{"award-number":["SYL20060143"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Identifying the key genes related to tumors from gene expression data with a large number of features is important for the accurate classification of tumors and to make special treatment decisions. In recent years, unsupervised feature selection algorithms have attracted considerable attention in the field of gene selection as they can find the most discriminating subsets of genes, namely the potential information in biological data. Recent research also shows that maintaining the important structure of data is necessary for gene selection. However, most current feature selection methods merely capture the local structure of the original data while ignoring the importance of the global structure of the original data. We believe that the global structure and local structure of the original data are equally important, and so the selected genes should maintain the essential structure of the original data as far as possible. In this paper, we propose a new, adaptive, unsupervised feature selection scheme which not only reconstructs high-dimensional data into a low-dimensional space with the constraint of feature distance invariance but also employs \u21132,1-norm to enable a matrix with the ability to perform gene selection embedding into the local manifold structure-learning framework. Moreover, an effective algorithm is developed to solve the optimization problem based on the proposed scheme. Comparative experiments with some classical schemes on real tumor datasets demonstrate the effectiveness of the proposed method.<\/jats:p>","DOI":"10.3390\/s21113627","type":"journal-article","created":{"date-parts":[[2021,5,24]],"date-time":"2021-05-24T00:01:20Z","timestamp":1621814480000},"page":"3627","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["An Adaptive Unsupervised Feature Selection Algorithm Based on MDS for Tumor Gene Data Classification"],"prefix":"10.3390","volume":"21","author":[{"given":"Bo","family":"Jin","sequence":"first","affiliation":[{"name":"School of Artificial Intelligence, Henan University, Kaifeng 475004, China"},{"name":"School of Computer and Information Engineering, Henan University, Kaifeng 475004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chunling","family":"Fu","sequence":"additional","affiliation":[{"name":"School of Physics and Electronics, Henan University, Kaifeng 475004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9325-5966","authenticated-orcid":false,"given":"Yong","family":"Jin","sequence":"additional","affiliation":[{"name":"School of Artificial Intelligence, Henan University, Kaifeng 475004, China"},{"name":"School of Computer and Information Engineering, Henan University, Kaifeng 475004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wei","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Computer and Information Engineering, Henan University, Kaifeng 475004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shengbin","family":"Li","sequence":"additional","affiliation":[{"name":"School of Artificial Intelligence, Henan University, Kaifeng 475004, China"},{"name":"School of Computer and Information Engineering, Henan University, Kaifeng 475004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guangyao","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Artificial Intelligence, Henan University, Kaifeng 475004, China"},{"name":"School of Computer and Information Engineering, Henan University, Kaifeng 475004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zheng","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Artificial Intelligence, Henan University, Kaifeng 475004, China"},{"name":"School of Computer and Information Engineering, Henan University, Kaifeng 475004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,5,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Sung, H., Ferlay, J., Siegel, R.L., Laversanne, M., Soerjomataram, I., Jemal, A., and Bray, F. (2021). Global cancer statistics 2020: GLOBOCAN estimates of incidence and mortality worldwide for 36 cancers in 185 countries. CA Cancer J. Clin.","DOI":"10.3322\/caac.21660"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Koul, N., and Manvi, S.S. (2019, January 21\u201322). A Scheme for Feature Selection from Gene Expression Data using Recursive Feature Elimination with Cross Validation and Unsupervised Deep Belief Network Classifier. Proceedings of the 2019 3rd International Conference on Computing and Communications Technologies (ICCCT), Chennai, India.","DOI":"10.1109\/ICCCT2.2019.8824943"},{"key":"ref_3","unstructured":"Duda, R.O., Hart, P.E., and Stork, D.G. (2001). Pattern Classification, Wiley. [2nd ed.]."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Liu, H., Wu, X., and Zhang, S. (2011, January 24\u201328). Feature selection using hierarchical feature clustering. Proceedings of the 20th ACM Conference on Information and Knowledge Management, CIKM 2011, Glasgow, UK.","DOI":"10.1145\/2063576.2063716"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"971","DOI":"10.1109\/TCBB.2015.2478454","article-title":"Supervised, Unsupervised, and Semi-Supervised Feature Selection: A Review on Gene Selection","volume":"13","author":"Ang","year":"2016","journal-title":"IEEE\/ACM Trans. Comput. Biol. Bioinform."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Song, L., Smola, A.J., Gretton, A., Borgwardt, K.M., and Bedo, J. (2007). Supervised Feature Selection via Dependence Estimation. arXiv.","DOI":"10.1145\/1273496.1273600"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"3913","DOI":"10.1109\/TNNLS.2017.2740341","article-title":"Self-Weighted Supervised Discriminative Feature Selection","volume":"29","author":"Zhang","year":"2018","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"301","DOI":"10.1109\/34.990133","article-title":"Unsupervised feature selection using feature similarity","volume":"24","author":"Mitra","year":"2002","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1587","DOI":"10.1109\/TNNLS.2018.2868847","article-title":"Generalized Uncorrelated Regression with Adaptive Graph for Unsupervised Feature Selection","volume":"30","author":"Li","year":"2019","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"619","DOI":"10.1109\/TKDE.2011.222","article-title":"On Similarity Preserving Feature Selection","volume":"25","author":"Zhao","year":"2013","journal-title":"IEEE Trans. Knowl. Data Eng."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1610","DOI":"10.1109\/TPAMI.2009.190","article-title":"Local-Learning-Based Feature Selection for High-Dimensional Data Analysis","volume":"32","author":"Sun","year":"2010","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1226","DOI":"10.1109\/TPAMI.2005.159","article-title":"Feature selection based on mutual information criteria of max-dependency, max-relevance, and min-redundancy","volume":"27","author":"Peng","year":"2005","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_13","unstructured":"Lafferty, J.D., Williams, C.K.I., Shawe-Taylor, J., Zemel, R.S., and Culotta, A. (2010). 1-Norms Minimization. Advances in Neural Information Processing Systems 23, Proceedings of the 24th Annual Conference on Neural Information Processing Systems 2010, Vancouver, BC, Canada, 6\u20139 December 2010, Curran Associates, Inc."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1738","DOI":"10.1109\/TNNLS.2012.2212721","article-title":"Discriminative Least Squares Regression for Multiclass Classification and Feature Selection","volume":"23","author":"Xiang","year":"2012","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Kim, Y., and Kim, J. (2004). Gradient LASSO for Feature Selection. ICML \u201904, Proceedings of the Twenty-First International Conference on Machine Learning, Banff, AB, Canada, 4\u20138 July 2004, Association for Computing Machinery.","DOI":"10.1145\/1015330.1015364"},{"key":"ref_16","first-page":"2777","article-title":"Structured Variable Selection with Sparsity-Inducing Norms","volume":"12","author":"Jenatton","year":"2011","journal-title":"J. Mach. Learn. Res."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1083","DOI":"10.1109\/TNNLS.2013.2287275","article-title":"Global and Local Structure Preservation for Feature Selection","volume":"25","author":"Liu","year":"2014","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"154354","DOI":"10.1109\/ACCESS.2020.3018480","article-title":"Adaptive Unsupervised Feature Learning for Gene Signature Identification in Non-Small-Cell Lung Cancer","volume":"8","author":"Ye","year":"2020","journal-title":"IEEE Access"},{"key":"ref_19","first-page":"1151","article-title":"Spectral feature selection for supervised and unsupervised learning","volume":"Volume 227","author":"Ghahramani","year":"2007","journal-title":"Machine Learning, Proceedings of the Twenty-Fourth International Conference (ICML 2007), Corvallis, OR, USA, 20\u201324 June 2007"},{"key":"ref_20","unstructured":"Walsh, T. (2011). Joint Feature Selection and Subspace Learning. IJCAI 2011, Proceedings of the 22nd International Joint Conference on Artificial Intelligence, Barcelona, Catalonia, Spain, 16\u201322 July 2011, IJCAI\/AAAI."},{"key":"ref_21","unstructured":"Walsh, T. (2011). Feature Selection via Joint Embedding Learning and Sparse Regression. IJCAI 2011, Proceedings of the 22nd International Joint Conference on Artificial Intelligence, Barcelona, Catalonia, Spain, 16\u201322 July 2011, IJCAI\/AAAI."},{"key":"ref_22","unstructured":"Getoor, L., and Scheffer, T. (2011). Eigenvalue Sensitive Feature Selection. ICML 2011, Proceedings of the 28th International Conference on Machine Learning, Bellevue, WA, USA, 28 June\u20132 July 2011, Omnipress."},{"key":"ref_23","unstructured":"He, X., Cai, D., and Niyogi, P. (2005). Laplacian Score for Feature Selection. Advances in Neural Information Processing Systems 18, Proceedings of the Neural Information Processing Systems, NIPS 2005, Vancouver, BC, Canada, 5\u20138 December 2005, MIT Press."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"2210","DOI":"10.1109\/TSP.2004.831130","article-title":"Geodesic entropic graphs for dimension and entropy estimation in manifold learning","volume":"52","author":"Costa","year":"2004","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_25","unstructured":"Walsh, T. (2011). l2, 1-Norm Regularized Discriminative Feature Selection for Unsupervised Learning. IJCAI 2011, Proceedings of the 22nd International Joint Conference on Artificial Intelligence, Barcelona, Catalonia, Spain, 16\u201322 July 2011, IJCAI\/AAAI."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"2013","DOI":"10.1109\/TPAMI.2011.44","article-title":"A Variance Minimization Criterion to Feature Selection Using Laplacian Regularization","volume":"33","author":"He","year":"2011","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"793","DOI":"10.1109\/TCYB.2013.2272642","article-title":"Joint Embedding Learning and Sparse Regression: A Framework for Unsupervised Feature Selection","volume":"44","author":"Hou","year":"2014","journal-title":"IEEE Trans. Cybern."},{"key":"ref_28","unstructured":"Hoffmann, J., and Selman, B. (2012, January 22\u201326). Unsupervised Feature Selection Using Nonnegative Spectral Analysis. Proceedings of the Twenty-Sixth AAAI Conference on Artificial Intelligence, Toronto, ON, Canada."},{"key":"ref_29","unstructured":"Cao, L., Zhang, C., Joachims, T., Webb, G.I., Margineantu, D.D., and Williams, G. (2015, January 10\u201313). Unsupervised Feature Selection with Adaptive Structure Learning. Proceedings of the 21th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, Sydney, NSW, Australia."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1921","DOI":"10.1109\/TIP.2010.2044958","article-title":"Flexible Manifold Embedding: A Framework for Semi-Supervised and Unsupervised Dimension Reduction","volume":"19","author":"Nie","year":"2010","journal-title":"IEEE Trans. Image Process."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1007\/s11263-014-0722-8","article-title":"Sparse Representation Based Fisher Discrimination Dictionary Learning for Image Classification","volume":"109","author":"Yang","year":"2014","journal-title":"Int. J. Comput. Vis."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Vu, T.H., and Monga, V. (2016, January 25\u201328). Learning a low-rank shared dictionary for object classification. Proceedings of the 2016 IEEE International Conference on Image Processing (ICIP), Hoenix, AZ, USA.","DOI":"10.1109\/ICIP.2016.7533197"},{"key":"ref_33","unstructured":"Boyd, S.P., and Vandenberghe, L. (2014). Convex Optimization, Cambridge University Press."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Qiu, Y., Jiang, H., and Ching, W.K. (2020). Unsupervised learning framework with multidimensional scaling in predicting epithelial-mesenchymal transitions. IEEE\/ACM Trans. Comput. Biol. Bioinform.","DOI":"10.1109\/TCBB.2020.2992605"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1532","DOI":"10.1109\/TPAMI.2010.215","article-title":"Feature Selection and Kernel Learning for Local Learning-Based Clustering","volume":"33","author":"Zeng","year":"2011","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"8097","DOI":"10.1109\/TIP.2020.3011253","article-title":"Unsupervised Feature Selection via Data Reconstruction and Side Information","volume":"29","author":"Zhang","year":"2020","journal-title":"IEEE Trans. Image Process."},{"key":"ref_37","first-page":"583","article-title":"Cluster Ensembles\u2014A Knowledge Reuse Framework for Combining Multiple Partitions","volume":"3","author":"Strehl","year":"2003","journal-title":"J. Mach. Learn. Res."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1109\/TSMCB.2011.2161607","article-title":"Initialization Independent Clustering with Actively Self-Training Method","volume":"42","author":"Nie","year":"2012","journal-title":"IEEE Trans. Syst. Man Cybern. Part (Cybern.)"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/11\/3627\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T06:06:24Z","timestamp":1760162784000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/11\/3627"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,5,23]]},"references-count":38,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2021,6]]}},"alternative-id":["s21113627"],"URL":"https:\/\/doi.org\/10.3390\/s21113627","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,5,23]]}}}