{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,11]],"date-time":"2026-05-11T11:59:18Z","timestamp":1778500758129,"version":"3.51.4"},"reference-count":38,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2022,10,31]],"date-time":"2022-10-31T00:00:00Z","timestamp":1667174400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["U20A20158"],"award-info":[{"award-number":["U20A20158"]}]},{"name":"National Natural Science Foundation of China","award":["2021B0101410004"],"award-info":[{"award-number":["2021B0101410004"]}]},{"name":"Key-Area Research and Development Program of Guangdong Province","award":["U20A20158"],"award-info":[{"award-number":["U20A20158"]}]},{"name":"Key-Area Research and Development Program of Guangdong Province","award":["2021B0101410004"],"award-info":[{"award-number":["2021B0101410004"]}]},{"name":"National Program for Special Support of Eminent Professionals","award":["U20A20158"],"award-info":[{"award-number":["U20A20158"]}]},{"name":"National Program for Special Support of Eminent Professionals","award":["2021B0101410004"],"award-info":[{"award-number":["2021B0101410004"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Ordinal regression methods are widely used to predict the ordered labels of data, among which support vector ordinal regression (SVOR) methods are popular because of their good generalization. In many realistic circumstances, data are collected by a distributed network. In order to protect privacy or due to some practical constraints, data cannot be transmitted to a center for processing. However, as far as we know, existing SVOR methods are all centralized. In the above situations, centralized methods are inapplicable, and distributed methods are more suitable choices. In this paper, we propose a distributed SVOR (dSVOR) algorithm. First, we formulate a constrained optimization problem for SVOR in distributed circumstances. Since there are some difficulties in solving the problem with classical methods, we used the random approximation method and the hinge loss function to transform the problem into a convex optimization problem with constraints. Then, we propose subgradient-based algorithm dSVOR to solve it. To illustrate the effectiveness, we theoretically analyze the consensus and convergence of the proposed method, and conduct experiments on both synthetic data and a real-world example. The experimental results show that the proposed dSVOR could achieve close performance to that of the corresponding centralized method, which needs all the data to be collected together.<\/jats:p>","DOI":"10.3390\/e24111567","type":"journal-article","created":{"date-parts":[[2022,10,31]],"date-time":"2022-10-31T23:26:32Z","timestamp":1667258792000},"page":"1567","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Distributed Support Vector Ordinal Regression over Networks"],"prefix":"10.3390","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5035-0330","authenticated-orcid":false,"given":"Huan","family":"Liu","sequence":"first","affiliation":[{"name":"College of Information Science and Electronic Engineering, Zhejiang University, Hangzhou 310027, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5082-7300","authenticated-orcid":false,"given":"Jiankai","family":"Tu","sequence":"additional","affiliation":[{"name":"College of Information Science and Electronic Engineering, Zhejiang University, Hangzhou 310027, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3147-1553","authenticated-orcid":false,"given":"Chunguang","family":"Li","sequence":"additional","affiliation":[{"name":"College of Information Science and Electronic Engineering, Zhejiang University, Hangzhou 310027, China"}]}],"member":"1968","published-online":{"date-parts":[[2022,10,31]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Doyle, O.M., Westman, E., Marqu, A.F., Mecocci, P., Vellas, B., Tsolaki, M., K\u0142oszewska, I., Soininen, H., Lovestone, S., and Williams, S.C. 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