Feng Da-Zheng, Zhang Xian-Da, Bao Zheng
Key Laboratory of Radar Signal Processing, Xidian University, 710071, Xi'an, PR China.
IEEE Trans Neural Netw. 2004 Nov;15(6):1541-54. doi: 10.1109/TNN.2004.838523.
This paper proposes a novel cross-correlation neural network (CNN) model for finding the principal singular subspace of a cross-correlation matrix between two high-dimensional data streams. We introduce a novel nonquadratic criterion (NQC) for searching the optimum weights of two linear neural networks (LNN). The NQC exhibits a single global minimum attained if and only if the weight matrices of the left and right neural networks span the left and right principal singular subspace of a cross-correlation matrix, respectively. The other stationary points of the NQC are (unstable) saddle points. We develop an adaptive algorithm based on the NQC for tracking the principal singular subspace of a cross-correlation matrix between two high-dimensional vector sequences. The NQC algorithm provides a fast online learning of the optimum weights for two LNN. The global asymptotic stability of the NQC algorithm is analyzed. The NQC algorithm has several key advantages such as faster convergence, which is illustrated through simulations.
本文提出了一种新颖的互相关神经网络（CNN）模型，用于寻找两个高维数据流之间互相关矩阵的主奇异子空间。我们引入了一种新颖的非二次准则（NQC）来搜索两个线性神经网络（LNN）的最优权重。当且仅当左右神经网络的权重矩阵分别跨越互相关矩阵的左右主奇异子空间时，NQC才会呈现出唯一的全局最小值。NQC的其他驻点是（不稳定的）鞍点。我们基于NQC开发了一种自适应算法，用于跟踪两个高维向量序列之间互相关矩阵的主奇异子空间。NQC算法为两个LNN提供了最优权重的快速在线学习。分析了NQC算法的全局渐近稳定性。通过仿真说明了NQC算法具有收敛速度更快等几个关键优点。
