{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,29]],"date-time":"2022-03-29T03:23:07Z","timestamp":1648524187565},"reference-count":10,"publisher":"MIT Press - Journals","issue":"11","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Neural Computation"],"published-print":{"date-parts":[[2001,11,1]]},"abstract":"<jats:p> Real classification problems involve structured data that can be essentially grouped into a relatively small number of clusters. It is shown that, under a local clustering condition, a set of points of a given class, embedded in binary space by a set of randomly parameterized surfaces, is linearly separable from other classes, with arbitrarily high probability. We call such a data set a local relative cluster. The size of the embedding set is shown to be inversely proportional to the squared local clustering degree. A simple parameterization by embedding hyperplanes, implementing a voting system, results in a random reduction of the nearest-neighbor method and leads to the separation of multicluster data by a network with two internal layers. This represents a considerable reduction of the learning problem with respect to known techniques, resolving a long-standing question on the complexity of random embedding. Numerical tests show that the proposed method performs as well as state-of the-art methods and in a small fraction of the time. <\/jats:p>","DOI":"10.1162\/089976601753196012","type":"journal-article","created":{"date-parts":[[2002,7,27]],"date-time":"2002-07-27T11:56:30Z","timestamp":1027770990000},"page":"2533-2548","source":"Crossref","is-referenced-by-count":0,"title":["Random Embedding Machines for Pattern Recognition"],"prefix":"10.1162","volume":"13","author":[{"given":"Yoram","family":"Baram","sequence":"first","affiliation":[{"name":"Department of Computer Science, Technion, Israel Institute of Technology, Haifa 32000, Israel"}]}],"member":"281","reference":[{"key":"p_1","doi-asserted-by":"publisher","DOI":"10.1109\/34.709564"},{"key":"p_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0031-3203(99)00050-3"},{"key":"p_4","doi-asserted-by":"publisher","DOI":"10.1162\/neco.1989.1.1.151"},{"key":"p_5","doi-asserted-by":"publisher","DOI":"10.1162\/neco.1990.2.2.198"},{"key":"p_8","doi-asserted-by":"publisher","DOI":"10.1109\/34.730549"},{"key":"p_11","doi-asserted-by":"publisher","DOI":"10.1126\/science.220.4598.671"},{"key":"p_12","doi-asserted-by":"publisher","DOI":"10.1209\/0295-5075\/11\/6\/001"},{"key":"p_16","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0000(90)90028-J"},{"key":"p_17","doi-asserted-by":"publisher","DOI":"10.1037\/h0042519"},{"key":"p_19","doi-asserted-by":"publisher","DOI":"10.1137\/1116025"}],"container-title":["Neural Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mitpressjournals.org\/doi\/pdf\/10.1162\/089976601753196012","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,3,12]],"date-time":"2021-03-12T21:49:08Z","timestamp":1615585748000},"score":1,"resource":{"primary":{"URL":"https:\/\/direct.mit.edu\/neco\/article\/13\/11\/2533-2548\/6471"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2001,11,1]]},"references-count":10,"journal-issue":{"issue":"11","published-print":{"date-parts":[[2001,11,1]]}},"alternative-id":["10.1162\/089976601753196012"],"URL":"https:\/\/doi.org\/10.1162\/089976601753196012","relation":{},"ISSN":["0899-7667","1530-888X"],"issn-type":[{"value":"0899-7667","type":"print"},{"value":"1530-888X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2001,11,1]]}}}