Quaternion neural network with geometrical operators
Quaternion neural network with geometrical operators
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发表时间：
2004-12
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通讯作者：
N. Matsui;T. Isokawa;Hiromi Kusamichi;F. Peper;H. Nishimura
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作者：
N. Matsui;T. Isokawa;Hiromi Kusamichi;F. Peper;H. Nishimura
四元数神经网络是其中神经元的计算基于四元数的模型，四元数是虚数的四维等价物。本文通过实验表明，四元数版本的反向传播（BP）算法实现正确的几何变换在三维空间中，以及在颜色空间的图像压缩问题，而实值BP算法失败。四元数神经网络在3位奇偶校验问题上的收敛速度也上级实值神经网络，如模拟所示。
Quaternion neural networks are models in which computations of the neurons are based on quaternions, the four-dimensional equivalents of imaginary numbers. This paper shows by experiments that the quaternion-version of the Back Propagation (BP) algorithm achieves correct geometrical transformations in three-dimensional space, as well as in color space for an image compression problem, whereas real-valued BP algorithms fail. The quaternion neural network also performs superior in terms of convergence speed to a real-valued neural network with respect to the 3-bit parity check problem, as simulations show.