{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,4]],"date-time":"2026-06-04T07:17:17Z","timestamp":1780557437792,"version":"3.54.1"},"reference-count":4,"publisher":"World Scientific Pub Co Pte Lt","issue":"07","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Patt. Recogn. Artif. Intell."],"published-print":{"date-parts":[[2014,11]]},"abstract":"<jats:p> A weighted na\u00efve Bayes (WNB) classifier using R\u00e9nyi entropy is discussed with its tree augmented extension. A WNB classifier is one solution for gaining efficiency against large-scale classification problems with an enormous amount of data and a lot of features. Such a WNB classifier has been studied so far, aiming at improving the prediction performance or at reducing the number of features. Among those studies, weighting with Shannon entropy has succeeded in reducing the number of features while keeping the classification performance. However, it has not been fully revealed how different weighting methods affect the performance of classification and feature selection. In this paper, it is analyzed by changing the weights using a parametric \u03b1-R\u00e9nyi entropy. As the first clue, the relationship between R\u00e9nyi entropy and the marginal Bayes error is analyzed in detail. It was revealed that the WNB classifiers becomes the regular (without weight) na\u00efve Bayes classifier in one end (\u03b1 = 0.0) and na\u00efve Bayes classifier weighted by the marginal Bayes error in the other end (\u03b1 = \u221e). In addition, an extension of WNB classifiers to incorporate tree-structured correlation between features is discussed. <\/jats:p>","DOI":"10.1142\/s0218001414600064","type":"journal-article","created":{"date-parts":[[2014,7,28]],"date-time":"2014-07-28T21:53:49Z","timestamp":1406584429000},"page":"1460006","source":"Crossref","is-referenced-by-count":3,"title":["ANALYSIS OF RELATIONSHIP BETWEEN R\u00c9NYI ENTROPY AND MARGINAL BAYES ERROR AND ITS APPLICATION TO WEIGHTED NA\u00cfVE BAYES CLASSIFIERS"],"prefix":"10.1142","volume":"28","author":[{"given":"TOMOMI","family":"ENDO","sequence":"first","affiliation":[{"name":"Graduate School of Information Science and Technology, Hokkaido University, Sapporo 060-0814, Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"KAZUHIRO","family":"OMURA","sequence":"additional","affiliation":[{"name":"Graduate School of Information Science and Technology, Hokkaido University, Sapporo 060-0814, Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"MINEICHI","family":"KUDO","sequence":"additional","affiliation":[{"name":"Graduate School of Information Science and Technology, Hokkaido University, Sapporo 060-0814, Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"219","published-online":{"date-parts":[[2014,10,14]]},"reference":[{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1109\/18.272494"},{"key":"rf5","volume-title":"The Elements of Statistical Learning","author":"Friedman J.","year":"2009"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1023\/A:1007465528199"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1016\/S0031-3203(99)00041-2"}],"container-title":["International Journal of Pattern Recognition and Artificial Intelligence"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218001414600064","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T11:43:59Z","timestamp":1565091839000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218001414600064"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,10,14]]},"references-count":4,"journal-issue":{"issue":"07","published-online":{"date-parts":[[2014,10,14]]},"published-print":{"date-parts":[[2014,11]]}},"alternative-id":["10.1142\/S0218001414600064"],"URL":"https:\/\/doi.org\/10.1142\/s0218001414600064","relation":{},"ISSN":["0218-0014","1793-6381"],"issn-type":[{"value":"0218-0014","type":"print"},{"value":"1793-6381","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,10,14]]}}}