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In various literatures, the conventional neural networks based only on real valued, are tried to solve the problem associated with high-dimensional parameters, but these neural network structures possess high complexity and are very time consuming and weak to noise. These networks are also not able to learn magnitude and phase values simultaneously in space. The quaternion is the number, which possesses the magnitude in all four directions and phase information is embedded within it. This paper presents a learning machine with a quaternionic domain neural network that can finely process magnitude and phase information of high dimension data without any hassle. The learning and generalization capability of the proposed learning machine is performed through chaotic time series predictions (Lorenz system and Chua\u2019s circuit), 3D linear transformations, and 3D face recognition as benchmark problems, which demonstrate the significance of the work.<\/jats:p>","DOI":"10.3233\/jifs-17461","type":"journal-article","created":{"date-parts":[[2019,5,17]],"date-time":"2019-05-17T11:33:36Z","timestamp":1558092816000},"page":"5189-5202","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":5,"title":["On the learning machine with quaternionic domain neural network and its high-dimensional applications"],"prefix":"10.1177","volume":"36","author":[{"given":"Sushil","family":"Kumar","sequence":"first","affiliation":[{"name":"Department of Information Technology, Ajay Kumar Garg Engineering College, Ghaziabad, India"}]},{"given":"Bipin Kumar","family":"Tripathi","sequence":"additional","affiliation":[{"name":"Department of Computer Science and Engineering, Harcourt Butler Technical University, Kanpur, India"}]}],"member":"179","published-online":{"date-parts":[[2019,5,10]]},"reference":[{"key":"e_1_3_1_2_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10489-017-0902-7"},{"issue":"05","key":"e_1_3_1_3_2","doi-asserted-by":"crossref","first-page":"727","DOI":"10.1109\/TNN.2011.2115251","article-title":"On efficient learning machine with root power mean neuron in complex domain","volume":"22","author":"Tripathi B.K.","year":"2011","unstructured":"B.K.Tripathi and P.K.Kalra, On efficient learning machine with root power mean neuron in complex domain, IEEE Transaction on Neural Networks 22(05) (2011), 727\u2013738.","journal-title":"IEEE Transaction on Neural Networks"},{"issue":"8","key":"e_1_3_1_4_2","doi-asserted-by":"crossref","first-page":"1391","DOI":"10.1016\/S0893-6080(97)00036-1","article-title":"An extension of the back-propagation algorithm to complex numbers","volume":"10","author":"Nitta T.","year":"1997","unstructured":"T.Nitta, An extension of the back-propagation algorithm to complex numbers, Neural Networks 10(8) (1997), 1391\u20131415.","journal-title":"Neural Networks"},{"key":"e_1_3_1_5_2","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1023\/A:1026582217675","article-title":"An analysis of the fundamental structure of complex-valued neurons","volume":"12","author":"Nitta T.","year":"2000","unstructured":"T.Nitta, An analysis of the fundamental structure of complex-valued neurons, Neural Process 12 (2000), 239\u2013246.","journal-title":"Neural Process"},{"key":"e_1_3_1_6_2","doi-asserted-by":"crossref","unstructured":"A.Hirose Complex-valued neural networks. 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