{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,10]],"date-time":"2026-03-10T17:02:06Z","timestamp":1773162126015,"version":"3.50.1"},"reference-count":38,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2012,11,28]],"date-time":"2012-11-28T00:00:00Z","timestamp":1354060800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Information"],"abstract":"<jats:p>A multi-layered perceptron type neural network is presented and analyzed in this paper. All neuronal parameters such as input, output, action potential and connection weight are encoded by quaternions, which are a class of hypercomplex number system. Local analytic condition is imposed on the activation function in updating neurons\u2019 states in order to construct learning algorithm for this network. An error back-propagation algorithm is introduced for modifying the connection weights of the network.<\/jats:p>","DOI":"10.3390\/info3040756","type":"journal-article","created":{"date-parts":[[2012,11,28]],"date-time":"2012-11-28T11:03:39Z","timestamp":1354100619000},"page":"756-770","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":37,"title":["Quaternionic Multilayer Perceptron with Local Analyticity"],"prefix":"10.3390","volume":"3","author":[{"given":"Teijiro","family":"Isokawa","sequence":"first","affiliation":[{"name":"Graduate School of Engineering, University of Hyogo, 2167 Shosha, Himeji, Hyogo 671-2280, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Haruhiko","family":"Nishimura","sequence":"additional","affiliation":[{"name":"Graduate School of Applied Informatics, University of Hyogo, 7-1-28 Minatojima-minamimachi, Chuo-ku, Kobe, Hyogo 650-0047, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nobuyuki","family":"Matsui","sequence":"additional","affiliation":[{"name":"Graduate School of Engineering, University of Hyogo, 2167 Shosha, Himeji, Hyogo 671-2280, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2012,11,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Hirose, A. 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