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In particular, our proposed weight adaptive Laplacian (WAL) method learns a new data similarity matrix that can adaptively adjust the initial graph according to the similarity weight in the input data graph. We develop three versions of these methods based on the L2-norm, fuzzy entropy regularizer, and another exponential-based weight strategy, that yield three new graph-based clustering objectives. We derive optimization algorithms to solve these objectives. Experimental results on synthetic data sets and real-world benchmark data sets exhibit the effectiveness of these new graph-based clustering methods.<\/jats:p>","DOI":"10.1162\/neco_a_00973","type":"journal-article","created":{"date-parts":[[2017,5,31]],"date-time":"2017-05-31T18:01:02Z","timestamp":1496253662000},"page":"1902-1918","source":"Crossref","is-referenced-by-count":14,"title":["A Weight-Adaptive Laplacian Embedding for Graph-Based Clustering"],"prefix":"10.1162","volume":"29","author":[{"given":"De","family":"Cheng","sequence":"first","affiliation":[{"name":"Institute of Artificial Intelligence and Robotic, Xi'an Jiaotong University, Xi'an 710049, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Feiping","family":"Nie","sequence":"additional","affiliation":[{"name":"Center for Optical Imagery Analysis and Learning, Northwestern Polytechnical University, Xi'an 710072, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jiande","family":"Sun","sequence":"additional","affiliation":[{"name":"School of Information Science and Engineering and Institute of Data Science and Technology, Shandong Normal University, Jinan 250358, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yihong","family":"Gong","sequence":"additional","affiliation":[{"name":"Institute of Artificial Intelligence and Robotic, Xi'an Jiaotong University, Xi'an 710049, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"281","reference":[{"key":"B1","author":"Asuncion A.","year":"2007","journal-title":"UCI machine learning repository"},{"key":"B2","first-page":"368","author":"Brun A.","year":"2004","journal-title":"Proceedings of the Seventh International Conference of the MICCAI"},{"key":"B3","first-page":"1737","author":"Cai X.","year":"2013","journal-title":"Proceedings of the IEEE International Conference on Computer Vision"},{"key":"B4","author":"Cai X.","year":"2013","journal-title":"Proceedings of the International Joint Conference on Artificial Intelligence"},{"key":"B5","doi-asserted-by":"publisher","DOI":"10.1109\/43.310898"},{"key":"B6","doi-asserted-by":"publisher","DOI":"10.1109\/TNNLS.2015.2441735"},{"key":"B7","first-page":"1171","author":"Chang X.","year":"2014","journal-title":"Proceedings of the 28th AAAI Conference on Artificial Intelligence"},{"key":"B8","first-page":"3464","author":"Chang X.","year":"2016","journal-title":"Proceedings of the Thirtieth AAAI Conference on Artificial Intelligence"},{"key":"B9","first-page":"551","author":"Dhillon I. 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