{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,19]],"date-time":"2026-03-19T14:29:22Z","timestamp":1773930562945,"version":"3.50.1"},"reference-count":20,"publisher":"Wiley","license":[{"start":{"date-parts":[[2020,2,21]],"date-time":"2020-02-21T00:00:00Z","timestamp":1582243200000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Key R&D Program of China","award":["2017YFC0822604-2"],"award-info":[{"award-number":["2017YFC0822604-2"]}]},{"name":"National Key R&D Program of China","award":["2018060"],"award-info":[{"award-number":["2018060"]}]},{"name":"National Key R&D Program of China","award":["201910590017"],"award-info":[{"award-number":["201910590017"]}]},{"DOI":"10.13039\/501100009019","name":"Shenzhen University","doi-asserted-by":"publisher","award":["2017YFC0822604-2"],"award-info":[{"award-number":["2017YFC0822604-2"]}],"id":[{"id":"10.13039\/501100009019","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100009019","name":"Shenzhen University","doi-asserted-by":"publisher","award":["2018060"],"award-info":[{"award-number":["2018060"]}],"id":[{"id":"10.13039\/501100009019","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100009019","name":"Shenzhen University","doi-asserted-by":"publisher","award":["201910590017"],"award-info":[{"award-number":["201910590017"]}],"id":[{"id":"10.13039\/501100009019","id-type":"DOI","asserted-by":"publisher"}]},{"name":"National Training Program of Innovation and Entrepreneurship","award":["2017YFC0822604-2"],"award-info":[{"award-number":["2017YFC0822604-2"]}]},{"name":"National Training Program of Innovation and Entrepreneurship","award":["2018060"],"award-info":[{"award-number":["2018060"]}]},{"name":"National Training Program of Innovation and Entrepreneurship","award":["201910590017"],"award-info":[{"award-number":["201910590017"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Complexity"],"published-print":{"date-parts":[[2020,2,21]]},"abstract":"<jats:p>Probability density function (<jats:italic>p.d.f.<\/jats:italic>) estimation plays a very important role in the field of data mining. Kernel density estimator (KDE) is the mostly used technology to estimate the unknown <jats:italic>p.d.f.<\/jats:italic> for the given dataset. The existing KDEs are usually inefficient when handling the <jats:italic>p.d.f.<\/jats:italic> estimation problem for stream data because a bran-new KDE has to be retrained based on the combination of current data and newly coming data. This process increases the training time and wastes the computation resource. This article proposes an incremental kernel density estimator (I-KDE) which deals with the <jats:italic>p.d.f.<\/jats:italic> estimation problem in the way of data stream computation. The I-KDE updates the current KDE dynamically and gradually with the newly coming data rather than retraining the bran-new KDE with the combination of current data and newly coming data. The theoretical analysis proves the convergence of the I-KDE only if the estimated <jats:italic>p.d.f.<\/jats:italic> of newly coming data is convergent to its true <jats:italic>p.d.f<\/jats:italic>. In order to guarantee the convergence of the I-KDE, a new multivariate fixed-point iteration algorithm based on the unbiased cross validation (UCV) method is developed to determine the optimal bandwidth of the KDE. The experimental results on 10 univariate and 4 multivariate probability distributions demonstrate the feasibility and effectiveness of the I-KDE.<\/jats:p>","DOI":"10.1155\/2020\/1803525","type":"journal-article","created":{"date-parts":[[2020,2,21]],"date-time":"2020-02-21T18:31:00Z","timestamp":1582309860000},"page":"1-17","source":"Crossref","is-referenced-by-count":4,"title":["An Incremental Kernel Density Estimator for Data Stream Computation"],"prefix":"10.1155","volume":"2020","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3415-0686","authenticated-orcid":true,"given":"Yulin","family":"He","sequence":"first","affiliation":[{"name":"College of Computer Science & Software Engineering, Shenzhen University, Shenzhen 518060, China"},{"name":"National Engineering Laboratory for Big Data System Computing Technology, Shenzhen University, Shenzhen 518060, China"},{"name":"Guangdong Laboratory of Artificial Intelligence and Digital Economy (SZ), Shenzhen University, Shenzhen 518060, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jie","family":"Jiang","sequence":"additional","affiliation":[{"name":"College of Computer Science & Software Engineering, Shenzhen University, Shenzhen 518060, China"},{"name":"National Engineering Laboratory for Big Data System Computing Technology, Shenzhen University, Shenzhen 518060, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dexin","family":"Dai","sequence":"additional","affiliation":[{"name":"College of Computer Science & Software Engineering, Shenzhen University, Shenzhen 518060, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Klohoun","family":"Fabrice","sequence":"additional","affiliation":[{"name":"College of Computer Science & Software Engineering, Shenzhen University, Shenzhen 518060, China"},{"name":"National Engineering Laboratory for Big Data System Computing Technology, Shenzhen University, Shenzhen 518060, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"key":"1","year":"1986"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1007\/s11222-006-9010-y"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1109\/tpami.2005.159"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijforecast.2011.02.016"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177704472"},{"key":"8","year":"1994"},{"key":"9","year":"2018"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1990.10474983"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/71.2.353"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1994.10476814"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1007\/bf02530523"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9469.2005.00445.x"},{"issue":"1","key":"16","first-page":"114","volume":"21","year":"2016","journal-title":"Journal of Harbin University of Science and Technology"},{"issue":"2","key":"17","first-page":"90","volume":"3","year":"2011","journal-title":"International Journal of Web Applications"},{"key":"18","doi-asserted-by":"publisher","DOI":"10.1109\/tnn.2011.2169087"},{"key":"19","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2019.04.010"},{"key":"21","first-page":"1","volume":"7","year":"2006","journal-title":"Journal of Machine Learning Research"},{"key":"22","doi-asserted-by":"publisher","DOI":"10.1109\/tii.2019.2912723"},{"key":"23","doi-asserted-by":"publisher","DOI":"10.1109\/access.2018.2889355"},{"key":"24","doi-asserted-by":"publisher","DOI":"10.1007\/s41019-016-0022-0"}],"container-title":["Complexity"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2020\/1803525.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2020\/1803525.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2020\/1803525.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,2,21]],"date-time":"2020-02-21T18:31:04Z","timestamp":1582309864000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.hindawi.com\/journals\/complexity\/2020\/1803525\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,2,21]]},"references-count":20,"alternative-id":["1803525","1803525"],"URL":"https:\/\/doi.org\/10.1155\/2020\/1803525","relation":{},"ISSN":["1076-2787","1099-0526"],"issn-type":[{"value":"1076-2787","type":"print"},{"value":"1099-0526","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,2,21]]}}}