{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,2,1]],"date-time":"2024-02-01T11:56:33Z","timestamp":1706788593971},"reference-count":25,"publisher":"MIT Press - Journals","issue":"5","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Neural Computation"],"published-print":{"date-parts":[[2015,5]]},"abstract":" This letter investigates the characteristics of the complex-valued neuron model with parameters represented by polar coordinates (called polar variable complex-valued neuron). The parameters of the polar variable complex-valued neuron are unidentifiable. The plateau phenomenon can occur during learning of the polar variable complex-valued neuron. Furthermore, computer simulations suggest that a single polar variable complex-valued neuron has the following characteristics in the case of using the steepest gradient-descent method with square error: (1) unidentifiable parameters (singular points) degrade the learning speed and (2) a plateau can occur during learning. When the weight is attracted to the singular point, the learning tends to become stuck. However, computer simulations also show that the steepest gradient-descent method with amplitude-phase error and the complex-valued natural gradient method could reduce the effects of the singular points. The learning dynamics near singular points depends on the error functions and the training algorithms used. <\/jats:p>","DOI":"10.1162\/neco_a_00729","type":"journal-article","created":{"date-parts":[[2015,3,16]],"date-time":"2015-03-16T16:23:58Z","timestamp":1426523038000},"page":"1120-1141","source":"Crossref","is-referenced-by-count":6,"title":["Learning Dynamics of a Single Polar Variable Complex-Valued Neuron"],"prefix":"10.1162","volume":"27","author":[{"given":"Tohru","family":"Nitta","sequence":"first","affiliation":[{"name":"National Institute of Advanced Industrial Science and Technology, Tsukuba, Ibaraki, 305-8568 Japan"}]}],"member":"281","reference":[{"key":"B1","volume-title":"Advances in neural processing systems","volume":"9","author":"Amari S.","year":"1996"},{"key":"B2","doi-asserted-by":"publisher","DOI":"10.1162\/089976698300017746"},{"key":"B3","doi-asserted-by":"publisher","DOI":"10.1162\/neco.2006.18.5.1007"},{"key":"B4","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0047683"},{"key":"B5","doi-asserted-by":"publisher","DOI":"10.1109\/TNN.2008.2000391"},{"key":"B6","first-page":"221","author":"Fukumizu K.","year":"1999","journal-title":"Proceedings of the 1999 Workshop on Information-Based Induction Sciences"},{"key":"B7","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-33457-6"},{"key":"B8","doi-asserted-by":"publisher","DOI":"10.1002\/9781118590072"},{"key":"B10","first-page":"576","volume-title":"Knowledge-based intelligent information engineering systems and allied technologies","author":"Hirose A.","year":"2001"},{"key":"B11","doi-asserted-by":"publisher","DOI":"10.1364\/OL.28.002524"},{"key":"B12","first-page":"2895","volume":"5","author":"Nitta T.","year":"1994","journal-title":"Proc. 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