{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,27]],"date-time":"2025-10-27T16:16:47Z","timestamp":1761581807367,"version":"build-2065373602"},"reference-count":43,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2019,3,7]],"date-time":"2019-03-07T00:00:00Z","timestamp":1551916800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>In semi-supervised label propagation (LP), the data manifold is approximated by a graph, which is considered as a similarity metric. Graph estimation is a crucial task, as it affects the further processes applied on the graph (e.g., LP, classification). As our knowledge of data is limited, a single approximation cannot easily find the appropriate graph, so in line with this, multiple graphs are constructed. Recently, multi-metric fusion techniques have been used to construct more accurate graphs which better represent the data manifold and, hence, improve the performance of LP. However, most of these algorithms disregard use of the information of label space in the LP process. In this article, we propose a new multi-metric graph-fusion method, based on the Flexible Manifold Embedding algorithm. Our proposed method represents a unified framework that merges two phases: graph fusion and LP. Based on one available view, different simple graphs were efficiently generated and used as input to our proposed fusion approach. Moreover, our method incorporated the label space information as a new form of graph, namely the Correlation Graph, with other similarity graphs. Furthermore, it updated the correlation graph to find a better representation of the data manifold. Our experimental results on four face datasets in face recognition demonstrated the superiority of the proposed method compared to other state-of-the-art algorithms.<\/jats:p>","DOI":"10.3390\/computation7010015","type":"journal-article","created":{"date-parts":[[2019,3,8]],"date-time":"2019-03-08T04:58:35Z","timestamp":1552021115000},"page":"15","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Multi Similarity Metric Fusion in Graph-Based Semi-Supervised Learning"],"prefix":"10.3390","volume":"7","author":[{"given":"Saeedeh","family":"Bahrami","sequence":"first","affiliation":[{"name":"Department of Artificial Intelligence, Faculty of Computer Engineering, Shahid Rajaee Teacher Training University (SRTTU), Tehran 16788-15811, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0372-6144","authenticated-orcid":false,"given":"Alireza","family":"Bosaghzadeh","sequence":"additional","affiliation":[{"name":"Department of Artificial Intelligence, Faculty of Computer Engineering, Shahid Rajaee Teacher Training University (SRTTU), Tehran 16788-15811, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fadi","family":"Dornaika","sequence":"additional","affiliation":[{"name":"Faculty of Computer Engineering, University of the Basque Country, 20018 San Sebastian, Spain"},{"name":"Ikerbasque, Foundation for science, 48013 Bilbao, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,3,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Bashir, Y., Aslam, A., Kamran, M., Qureshi, M., Jahangir, A., Rafiq, M., Bibi, N., and Muhammad, N. (2017). On forgotten topological indices of some dendrimers structure. Molecules, 22.","DOI":"10.3390\/molecules22060867"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"4269","DOI":"10.1109\/TIP.2017.2717505","article-title":"Discriminative deep metric learning for face and kinship verification","volume":"26","author":"Lu","year":"2017","journal-title":"IEEE Trans. Image Process."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"667","DOI":"10.1016\/j.neucom.2017.09.019","article-title":"Person re-identification by order-induced metric fusion","volume":"275","author":"Mirmahboub","year":"2018","journal-title":"Neurocomputing"},{"key":"ref_4","unstructured":"Zhang, H., Huang, T.S., Nasrabadi, N.M., and Zhang, Y. (2011, January 5\u20138). Heterogeneous Multi-Metric Learning for Multi-Sensor Fusion. Proceedings of the 14th International Conference on Informatio Fusion (FUSION), Chicago, IL, USA."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"80","DOI":"10.1016\/j.inffus.2015.12.004","article-title":"Metricfusion: Generalized metric swarm learning for similarity measure","volume":"30","author":"Zhang","year":"2016","journal-title":"Inf. Fusion"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"803","DOI":"10.1109\/TGRS.2012.2205002","article-title":"A graph-based classification method for hyperspectral images","volume":"51","author":"Bai","year":"2013","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Boiman, O., Shechtman, E., and Irani, M. (2008, January 23\u201328). In defense of nearest-neighbor based image classification. Proceedings of the Conference on Computer Vision and Pattern Recognition (CVPR), Anchorage, AK, USA.","DOI":"10.1109\/CVPR.2008.4587598"},{"key":"ref_8","first-page":"100","article-title":"Algorithm as 136: A k-means clustering algorithm","volume":"28","author":"Hartigan","year":"1979","journal-title":"J. R. Stat. Soc."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"586","DOI":"10.1109\/72.846731","article-title":"Clustering of the self-organizing map","volume":"11","author":"Vesanto","year":"2000","journal-title":"IEEE Trans. Neural Netw."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"395","DOI":"10.1007\/s11222-007-9033-z","article-title":"A tutorial on spectral clustering","volume":"17","year":"2007","journal-title":"Stat. Comput."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1993","DOI":"10.1016\/j.patcog.2009.12.022","article-title":"Graph-optimized locality preserving projections","volume":"43","author":"Zhang","year":"2010","journal-title":"Pattern Recognit."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"441","DOI":"10.1016\/j.neucom.2013.03.045","article-title":"L1-graph construction using structured sparsity","volume":"120","author":"Zhou","year":"2013","journal-title":"Neurocomputing"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"14:1","DOI":"10.1145\/1899412.1899418","article-title":"Image annotation by k nn-sparse graph-based label propagation over noisily tagged web images","volume":"2","author":"Tang","year":"2011","journal-title":"ACM Trans. Intell. Syst. Technol."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1109\/TKDE.2007.190672","article-title":"Label propagation through linear neighborhoods","volume":"20","author":"Wang","year":"2008","journal-title":"IEEE Trans. Knowl. Data Eng."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"3249","DOI":"10.1109\/TIP.2016.2563981","article-title":"Multi-modal curriculum learning for semi-supervised image classification","volume":"25","author":"Gong","year":"2016","journal-title":"IEEE Trans. Image Process."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"2691","DOI":"10.1016\/j.physleta.2017.06.018","article-title":"Label propagation algorithm for community detection based on node importance and label influence","volume":"381","author":"Zhang","year":"2017","journal-title":"Phys. Lett. A"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"18","DOI":"10.1016\/j.eswa.2019.01.031","article-title":"Interactive image segmentation using label propagation through complex networks","volume":"123","author":"Breve","year":"2019","journal-title":"Expert Syst. Appl."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"314","DOI":"10.1016\/j.eswa.2018.07.075","article-title":"Dynamic graph-based label propagation for density peaks clustering","volume":"115","author":"Seyedi","year":"2019","journal-title":"Expert Syst. Appl."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"515","DOI":"10.3390\/rs10040515","article-title":"Semi-supervised classification of hyperspectral images based on extended label propagation and rolling guidance filtering","volume":"10","author":"Cui","year":"2018","journal-title":"Remote Sens."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Chapelle, O., Sch\u00f6lkopf, B., and Zien, A. (2006). Semi-Supervised Learning, MIT Press. Chapter 11.","DOI":"10.7551\/mitpress\/9780262033589.001.0001"},{"key":"ref_21","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_22","unstructured":"Zhou, D., Bousquet, O., Lal, T.N., Weston, J., and Sch\u00f6lkopf, B. (2004, January 13\u201316). Learning with local and global consistency. Proceedings of the 18th Conference on Advances in Neural Information Processing Systems (NIPS), Vancouver, BC, Canada."},{"key":"ref_23","unstructured":"Zhu, X., Ghahramani, Z., and Lafferty, J.D. (2003, January 21\u201324). Semi-supervised learning using gaussian fields and harmonic functions. Proceedings of the 20th International Conference on Machine Learning (ICML-03), Washington, DC, USA."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1999","DOI":"10.1109\/TNNLS.2013.2271327","article-title":"Multiple graph label propagation by sparse integration","volume":"24","author":"Karasuyama","year":"2013","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"14","DOI":"10.1016\/j.patcog.2017.03.014","article-title":"Dynamic graph fusion label propagation for semi-supervised multi-modality classification","volume":"68","author":"Lin","year":"2017","journal-title":"Pattern Recognit."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1016\/j.patcog.2016.10.009","article-title":"Alzheimer\u2019s Disease Neuroimaging, I. Multi-modal classification of alzheimer\u2019s disease using nonlinear graph fusion","volume":"63","author":"Tong","year":"2017","journal-title":"Pattern Recognit."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"333:1","DOI":"10.1038\/nmeth.2810","article-title":"Similarity network fusion for aggregating data types on a genomic scale","volume":"11","author":"Wang","year":"2014","journal-title":"Nat. Methods"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1016\/j.patcog.2015.10.006","article-title":"Dynamic label propagation for semi-supervised multi-class multi-label classification","volume":"52","author":"Wang","year":"2016","journal-title":"Pattern Recognit."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"997","DOI":"10.1007\/s10044-017-0613-z","article-title":"Digital watermarking using hall property image decomposition method","volume":"21","author":"Muhammad","year":"2018","journal-title":"Pattern Anal. Appl."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"795","DOI":"10.1049\/iet-ipr.2014.0395","article-title":"Digital image watermarking using partial pivoting lower and upper triangular decomposition into the wavelet domain","volume":"9","author":"Muhammad","year":"2015","journal-title":"IET Image Process."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Li, S., Liu, H., Tao, Z., and Fu, Y. (2017, January 11\u201314). Multi-view graph learning with adaptive label propagation. Proceedings of the IEEE International Conference on Big Data (Big Data), Boston, MA, USA.","DOI":"10.1109\/BigData.2017.8257918"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1016\/j.neucom.2016.08.127","article-title":"Multi-graph feature level fusion for person re-identification","volume":"259","author":"An","year":"2017","journal-title":"Neurocomputing"},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Saeedeh, B., and Bosaghzadeh, A. (2017, January 22\u201323). Deep graph fusion for graph based label propagation. Proceedings of the 10th Conference on Machine Vision and Image Processing (MVIP), Isfahan, Iran.","DOI":"10.1109\/IranianMVIP.2017.8342339"},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Zhao, R., Ouyang, W., and Wang, X. (2013, January 1\u20138). Person re-identification by salience matching. Proceedings of the IEEE International Conference on Computer Vision, Sydney, Australia.","DOI":"10.1109\/ICCV.2013.314"},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Zhao, R., Ouyang, W., and Wang, X. (2013, January 23\u201328). Unsupervised salience learning for person re-identification. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Washington, DC, USA.","DOI":"10.1109\/CVPR.2013.460"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"431","DOI":"10.1016\/j.inffus.2012.05.002","article-title":"Multi-metric learning for multi-sensor fusion based classification","volume":"14","author":"Zhang","year":"2013","journal-title":"Inf. Fusion"},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Wang, B., Tu, Z., and Tsotsos, J.K. (2013, January 1\u20138). Dynamic label propagation for semi-supervised multi-class multi-label classification. Proceedings of the IEEE International Conference on Computer Vision, Sydney Conference Centre, Darling Harbour, Sydney.","DOI":"10.1109\/ICCV.2013.60"},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Cortes, C., and Mohri, M. (2007, January 3\u20138). On transductive Regression. Proceedings of the Conference on Neural Information Processing Systems (NIPS), Hyatt Regency Vancouver, Vancouver, BC, Canada.","DOI":"10.7551\/mitpress\/7503.003.0043"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"301","DOI":"10.1016\/j.neucom.2010.03.019","article-title":"Sample-dependent graph construction with application to dimensionality reduction","volume":"74","author":"Yang","year":"2010","journal-title":"Neurocomputing"},{"key":"ref_40","unstructured":"Bang, S., Kim, D., and Choi, S. (2001). Asian Face Image Database PF01, Intelligent Multimedia Lab, University of Science and Technology."},{"key":"ref_41","unstructured":"Phillips, P.J., Moon, H., Rauss, P., and Rizvi, S.A. (1997, January 17\u201319). The feret evaluation methodology for face-recognition algorithms. Proceedings of the Conference on IEEE Computer Society Conference on Computer Vision and Pattern Recognition, San Juan, Puerto Rico, USA."},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Parkhi, O.M., Vedaldi, A., and Zisserman, A. (2015, January 7\u201310). Deep face recognition. Proceedings of the BMVC, Swansea, UK.","DOI":"10.5244\/C.29.41"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"971","DOI":"10.1109\/TPAMI.2002.1017623","article-title":"Multiresolution gray-scale and rotation invariant texture classification with local binary patterns","volume":"24","author":"Ojala","year":"2002","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."}],"container-title":["Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2079-3197\/7\/1\/15\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T12:36:54Z","timestamp":1760186214000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2079-3197\/7\/1\/15"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,3,7]]},"references-count":43,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2019,3]]}},"alternative-id":["computation7010015"],"URL":"https:\/\/doi.org\/10.3390\/computation7010015","relation":{},"ISSN":["2079-3197"],"issn-type":[{"type":"electronic","value":"2079-3197"}],"subject":[],"published":{"date-parts":[[2019,3,7]]}}}