{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,24]],"date-time":"2026-02-24T21:05:28Z","timestamp":1771967128914,"version":"3.50.1"},"reference-count":57,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2019,7,17]],"date-time":"2019-07-17T00:00:00Z","timestamp":1563321600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001691","name":"Japan Society for the Promotion of Science","doi-asserted-by":"publisher","award":["KAKENHI 15H01678, 15H03636, 16K00044, and 19H04071"],"award-info":[{"award-number":["KAKENHI 15H01678, 15H03636, 16K00044, and 19H04071"]}],"id":[{"id":"10.13039\/501100001691","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The quality of online services highly depends on the accuracy of the recommendations they can provide to users. Researchers have proposed various similarity measures based on the assumption that similar people like or dislike similar items or people, in order to improve the accuracy of their services. Additionally, statistical models, such as the stochastic block models, have been used to understand network structures. In this paper, we discuss the relationship between similarity-based methods and statistical models using the Bernoulli mixture models and the expectation-maximization (EM) algorithm. The Bernoulli mixture model naturally leads to a completely positive matrix as the similarity matrix. We prove that most of the commonly used similarity measures yield completely positive matrices as the similarity matrix. Based on this relationship, we propose an algorithm to transform the similarity matrix to the Bernoulli mixture model. Such a correspondence provides a statistical interpretation to similarity-based methods. Using this algorithm, we conduct numerical experiments using synthetic data and real-world data provided from an online dating site, and report the efficiency of the recommendation system based on the Bernoulli mixture models.<\/jats:p>","DOI":"10.3390\/e21070702","type":"journal-article","created":{"date-parts":[[2019,7,17]],"date-time":"2019-07-17T11:25:12Z","timestamp":1563362712000},"page":"702","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Model Description of Similarity-Based Recommendation Systems"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6878-5850","authenticated-orcid":false,"given":"Takafumi","family":"Kanamori","sequence":"first","affiliation":[{"name":"Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8552, Japan"},{"name":"RIKEN AIP, Nihonbashi 1-chome Mitsui Building, 15th floor, 1-4-1 Nihonbashi, Chuo-ku, Tokyo 103-0027, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Naoya","family":"Osugi","sequence":"additional","affiliation":[{"name":"Recruit Technologies Co., Ltd., GranTokyo South Tower, 1-9-2 Marunouchi, Chiyoda-ku, Tokyo 100-6640, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,7,17]]},"reference":[{"key":"ref_1","first-page":"1","article-title":"Link prediction in social networks: The state-of-the-art","volume":"58","author":"Wang","year":"2015","journal-title":"Sci. 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