{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,16]],"date-time":"2025-10-16T06:58:31Z","timestamp":1760597911446,"version":"build-2065373602"},"reference-count":39,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2019,8,12]],"date-time":"2019-08-12T00:00:00Z","timestamp":1565568000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Graph-based embedding methods receive much attention due to the use of graph and manifold information. However, conventional graph-based embedding methods may not always be effective if the data have high dimensions and have complex distributions. First, the similarity matrix only considers local distance measurement in the original space, which cannot reflect a wide variety of data structures. Second, separation of graph construction and dimensionality reduction leads to the similarity matrix not being fully relied on because the original data usually contain lots of noise samples and features. In this paper, we address these problems by constructing two adjacency graphs to stand for the original structure featuring similarity and diversity of the data, and then impose a rank constraint on the corresponding Laplacian matrix to build a novel adaptive graph learning method, namely locality sensitive discriminative unsupervised dimensionality reduction (LSDUDR). As a result, the learned graph shows a clear block diagonal structure so that the clustering structure of data can be preserved. Experimental results on synthetic datasets and real-world benchmark data sets demonstrate the effectiveness of our approach.<\/jats:p>","DOI":"10.3390\/sym11081036","type":"journal-article","created":{"date-parts":[[2019,8,12]],"date-time":"2019-08-12T06:38:02Z","timestamp":1565591882000},"page":"1036","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Locality Sensitive Discriminative Unsupervised Dimensionality Reduction"],"prefix":"10.3390","volume":"11","author":[{"given":"Yun-Long","family":"Gao","sequence":"first","affiliation":[{"name":"Department of Automation, Xiamen University, Xiamen 361005, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0024-3101","authenticated-orcid":false,"given":"Si-Zhe","family":"Luo","sequence":"additional","affiliation":[{"name":"Department of Automation, Xiamen University, Xiamen 361005, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhi-Hao","family":"Wang","sequence":"additional","affiliation":[{"name":"Department of Automation, Xiamen University, Xiamen 361005, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chih-Cheng","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Information Engineering, Jimei University, Xiamen 361021, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jin-Yan","family":"Pan","sequence":"additional","affiliation":[{"name":"School of Information Engineering, Jimei University, Xiamen 361021, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,8,12]]},"reference":[{"doi-asserted-by":"crossref","unstructured":"Everitt, B.S., Dunn, G., Everitt, B.S., and Dunn, G. (2011). Cluster Analysis, Wiley.","key":"ref_1","DOI":"10.1002\/9780470977811"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"645","DOI":"10.1109\/TNN.2005.845141","article-title":"Survey of clustering algorithms","volume":"16","author":"Xu","year":"2005","journal-title":"IEEE Trans. Neural Netw."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1217","DOI":"10.1109\/TPAMI.2010.195","article-title":"The Fisher-Markov Selector: Fast Selecting Maximally Separable Feature Subset for Multiclass Classification with Applications to High-Dimensional Data","volume":"33","author":"Cheng","year":"2011","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"doi-asserted-by":"crossref","unstructured":"Dash, M., and Liu, H. (2000, January 17\u201320). Feature selection for clustering. Proceedings of the Pacific-Asia Conference on Knowledge Discovery and Data Mining, Keihanna Plaza, Japan.","key":"ref_4","DOI":"10.1007\/3-540-45571-X_13"},{"key":"ref_5","first-page":"773","article-title":"Pattern recognition and reduction of dimensionality","volume":"2","year":"1982","journal-title":"Handb. Stat."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1016\/0169-7439(87)80084-9","article-title":"Principal component analysis","volume":"2","author":"Wold","year":"1987","journal-title":"Chemom. Intell. Lab. Syst."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1111\/j.1469-1809.1936.tb02137.x","article-title":"The use of multiple measurements in taxonomic problems","volume":"7","author":"FISHER","year":"1936","journal-title":"Ann. Eugen."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1287\/mnsc.17.3.219","article-title":"Anr-Dimensional Quadratic Placement Algorithm","volume":"17","author":"Hall","year":"1970","journal-title":"Manag. Sci."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1373","DOI":"10.1162\/089976603321780317","article-title":"Laplacian Eigenmaps for Dimensionality Reduction and Data Representation","volume":"15","author":"Belkin","year":"2003","journal-title":"Neural Comput."},{"doi-asserted-by":"crossref","unstructured":"Luo, D., Ding, C., Huang, H., and Li, T. (2009, January 6\u20139). Non-negative Laplacian Embedding. Proceedings of the 2009 Ninth IEEE International Conference on Data Mining, Miami, FL, USA.","key":"ref_10","DOI":"10.1109\/ICDM.2009.74"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"2323","DOI":"10.1126\/science.290.5500.2323","article-title":"Nonlinear Dimensionality Reduction by Locally Linear Embedding","volume":"290","author":"Roweis","year":"2000","journal-title":"Science"},{"unstructured":"He, X., and Niyogi, P. (2004). Locality preserving projections. Advances in Neural Information Processing Systems, MIT Press.","key":"ref_12"},{"unstructured":"Nie, F., Xiang, S., and Zhang, C. (2007, January 8). Neighborhood MinMax Projections. Proceedings of the International Joint Conference on Artificial Intelligence (IJCAI), Hyderabad, India.","key":"ref_13"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"2319","DOI":"10.1126\/science.290.5500.2319","article-title":"A Global Geometric Framework for Nonlinear Dimensionality Reduction","volume":"290","author":"Tenenbaum","year":"2000","journal-title":"Science"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1016\/j.knosys.2012.02.014","article-title":"Face recognition using discriminant sparsity neighborhood preserving embedding","volume":"31","author":"Lu","year":"2012","journal-title":"Knowl.-Based Syst."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1016\/j.knosys.2016.05.008","article-title":"Multiple empirical kernel learning with locality preserving constraint","volume":"105","author":"Fan","year":"2016","journal-title":"Knowl.-Based Syst."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1016\/j.knosys.2017.09.034","article-title":"Local graph based correlation clustering","volume":"138","author":"Pandove","year":"2017","journal-title":"Knowl.-Based Syst."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1016\/j.knosys.2017.01.019","article-title":"Efficient Locality Weighted Sparse Representation for Graph-Based Learning","volume":"121","author":"Feng","year":"2017","journal-title":"Knowl.-Based Syst."},{"doi-asserted-by":"crossref","unstructured":"Du, L., and Shen, Y.D. (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, Australia.","key":"ref_19","DOI":"10.1145\/2783258.2783345"},{"unstructured":"Nie, F., Wang, H., Huang, H., and Ding, C. (2011, January 6\u201313). Unsupervised and semi-supervised learning via L1-norm graph. Proceedings of the 2011 International Conference on Computer Vision, Barcelona, Spain.","key":"ref_20"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"626","DOI":"10.1109\/TIFS.2013.2246786","article-title":"Joint Global and Local Structure Discriminant Analysis","volume":"8","author":"Gao","year":"2013","journal-title":"IEEE Trans. Inf. Forensics Secur."},{"doi-asserted-by":"crossref","unstructured":"Nie, F., Wang, X., Jordan, M.I., and Huang, H. (2016, January 12\u201317). The Constrained Laplacian Rank Algorithm for Graph-Based Clustering. Proceedings of the Thirtieth AAAI Conference on Artificial Intelligence, Phoenix, AZ, USA.","key":"ref_22","DOI":"10.1609\/aaai.v30i1.10302"},{"unstructured":"Luo, D., Nie, F., Huang, H., and Ding, C.H. (July, January 28). Cauchy graph embedding. Proceedings of the 28th International Conference on Machine Learning (ICML-11), Bellevue, WA, USA.","key":"ref_23"},{"doi-asserted-by":"crossref","unstructured":"Nie, F., Wang, X., and Huang, H. (2014, January 24\u201327). Clustering and projected clustering with adaptive neighbors. Proceedings of the 20th ACM SIGKDD international conference on Knowledge discovery and data mining, New York, NY, USA.","key":"ref_24","DOI":"10.1145\/2623330.2623726"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1016\/j.neucom.2014.11.018","article-title":"A novel semi-supervised learning for face recognition","volume":"152","author":"Gao","year":"2015","journal-title":"Neurocomputing"},{"key":"ref_26","first-page":"12","article-title":"The Laplacian spectrum of graphs","volume":"2","author":"Mohar","year":"1991","journal-title":"Graph Theory Comb. Appl."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"652","DOI":"10.1073\/pnas.35.11.652","article-title":"On a Theorem of Weyl Concerning Eigenvalues of Linear Transformations I","volume":"35","author":"Fan","year":"1949","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"2615","DOI":"10.1016\/j.patcog.2009.04.001","article-title":"Semi-supervised orthogonal discriminant analysis via label propagation","volume":"42","author":"Nie","year":"2009","journal-title":"Pattern Recognit."},{"key":"ref_29","first-page":"351","article-title":"Convergence of alternating optimization","volume":"11","author":"Bezdek","year":"2003","journal-title":"Neural Parallel Sci. Comput."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1016\/j.neucom.2011.09.002","article-title":"Spectral clustering: A semi-supervised approach","volume":"77","author":"Chen","year":"2012","journal-title":"Neurocomputing"},{"unstructured":"Macqueen, J. (July, January 21). Some Methods for Classification and Analysis of MultiVariate Observations. Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, Oakland, CA, USA.","key":"ref_31"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1074","DOI":"10.1109\/43.159993","article-title":"New spectral methods for ratio cut partitioning and clustering","volume":"11","author":"Hagen","year":"1992","journal-title":"IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"888","DOI":"10.1109\/34.868688","article-title":"Normalized cuts and image segmentation","volume":"22","author":"Shi","year":"2000","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_34","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 B Cybern."},{"unstructured":"Dua, D., and Graff, C. (2018, August 01). UCI Machine Learning Repository. Available online: http:\/\/archive.ics.uci.edu\/ml.","key":"ref_35"},{"unstructured":"Zelnik-Manor, L., and Perona, P. (2005). Self-tuning spectral clustering. Advances in Neural Information Processing Systems, MIT Press.","key":"ref_36"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"1744","DOI":"10.1109\/TCYB.2014.2359984","article-title":"Similarity learning of manifold data","volume":"45","author":"Chen","year":"2015","journal-title":"IEEE Trans. Cybern."},{"unstructured":"Roweis, S. (2018, August 01). Binary Alphadigits. Available online: https:\/\/cs.nyu.edu\/~roweis\/data.html.","key":"ref_38"},{"unstructured":"Har, M.T., Conrad, S., Shirazi, S., and Lovell, B.C. (2011, January 20\u201325). Graph embedding discriminant analysis on Grassmannian manifolds for improved image set matching. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Colorado Springs, CO, USA.","key":"ref_39"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/11\/8\/1036\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T13:10:29Z","timestamp":1760188229000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/11\/8\/1036"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,8,12]]},"references-count":39,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2019,8]]}},"alternative-id":["sym11081036"],"URL":"https:\/\/doi.org\/10.3390\/sym11081036","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2019,8,12]]}}}