TY - JOUR
T1 - Best Rank-One Approximation of Fourth-Order Partially Symmetric Tensors by Neural Network
AU - Xuezhong Wang, Maolin Che & Yimin Wei
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 4
SP - 673
EP - 700
PY - 2018
DA - 2018/06
SN - 11
DO - http://doi.org/10.4208/nmtma.2018.s01
UR - https://global-sci.org/intro/article_detail/nmtma/12467.html
KW - 
AB - <p style="text-align: justify;">Our purpose is to compute the multi-partially symmetric rank-one approximations
of higher-order multi-partially symmetric tensors. A special case is the partially
symmetric rank-one approximation for the fourth-order partially symmetric tensors,
which is related to the biquadratic optimization problem. For the special case, we implement
the neural network model by the ordinary differential equations (ODEs), which
is a class of continuous-time recurrent neural network. Several properties of states for
the network are established. We prove that the solution of the ODE is locally asymptotically
stable by establishing an appropriate Lyapunov function under mild conditions.
Similarly, we consider how to compute the multi-partially symmetric rank-one approximations
of multi-partially symmetric tensors via neural networks. Finally, we define
the restricted $M$-singular values and the corresponding restricted $M$-singular vectors of
higher-order multi-partially symmetric tensors and design to compute them. Numerical
results show that the neural network models are efficient.</p>