Matrix-Valued Neural Networks

作者: Călin-Adrian Popa

DOI: 10.1007/978-3-319-19824-8_20

关键词: Artificial neural networkBackpropagationNervous system network modelsAlgorithmPhysical neural networkComputer scienceTypes of artificial neural networksGradient descentTime delay neural networkFeedforward neural network

摘要: This paper introduces matrix-valued feedforward neural networks, for which the inputs, outputs, weights and biases are all square matrices. type of networks represents a natural generalization complex-, hyperbolic-, quaternion- Clifford-valued that have been intensively studied over last few years. The full deduction gradient descent algorithm training such is presented. proposed tested on three synthetic function approximation problems, with promising results future.

参考文章(24)
T. Nitta, Generalization ability of the three-dimensional back-propagation network world congress on computational intelligence. ,vol. 5, pp. 2895- 2900 ,(1994) , 10.1109/ICNN.1994.374691
Tohru Nitta, An Analysis of the Fundamental Structure of Complex-Valued Neurons Neural Processing Letters. ,vol. 12, pp. 239- 246 ,(2000) , 10.1023/A:1026582217675
P. Arena, L. Fortuna, L. Occhipinti, M.G. Xibilia, Neural networks for quaternion-valued function approximation international symposium on circuits and systems. ,vol. 6, pp. 307- 310 ,(1994) , 10.1109/ISCAS.1994.409587
J.K. Pearson, D.L. Bisset, Neural networks in the Clifford domain world congress on computational intelligence. ,vol. 3, pp. 1465- 1469 ,(1994) , 10.1109/ICNN.1994.374502
T. Nitta, A quaternary version of the back-propagation algorithm international conference on networks. ,vol. 5, pp. 2753- 2756 ,(1995) , 10.1109/ICNN.1995.488166
Yasuaki Kuroe, Shinpei Tanigawa, Hitoshi Iima, Models of hopfield-type clifford neural networks and their energy functions - hyperbolic and dual valued networks - international conference on neural information processing. pp. 560- 569 ,(2011) , 10.1007/978-3-642-24955-6_67