Coupled Cross-correlation Neural Network Algorithm for Principal Singular Triplet Extraction of a Cross-covariance Matrix |
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| Xiaowei Feng, Xiangyu Kong and Hongguang Ma, "Coupled Cross-correlation Neural Network Algorithm for Principal Singular Triplet Extraction of a Cross-covariance Matrix," IEEE/CAA J. of Autom. Sinica, vol. 3, no. 2, pp. 147-156, 2016. |
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| Authors: | Xiaowei Feng Xiangyu Kong Hongguang Ma |
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| Affiliation: | 1. Xi'an Research Institute of High Technology, Xi'an 710025, China;;2. Hongguang Ma is with Beijing Institute of Technology, Zhuhai 519088, China |
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| Abstract: | This paper proposes a novel coupled neural network learning algorithm to extract the principal singular triplet (PST) of a cross-correlation matrix between two high-dimensional data streams. We firstly introduce a novel information criterion (NIC), in which the stationary points are singular triplet of the crosscorrelation matrix. Then, based on Newton's method, we obtain a coupled system of ordinary differential equations (ODEs) from the NIC. The ODEs have the same equilibria as the gradient of NIC, however, only the first PST of the system is stable (which is also the desired solution), and all others are (unstable) saddle points. Based on the system, we finally obtain a fast and stable algorithm for PST extraction. The proposed algorithm can solve the speed-stability problem that plagues most noncoupled learning rules. Moreover, the proposed algorithm can also be used to extract multiple PSTs effectively by using sequential method. |
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| Keywords: | Singular value decomposition (SVD) coupled algorithm cross-correlation neural network (CNN) speed-stability problem principal singular subspace (PSS) principal singular triplet (PST) |
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