ADMM-Based Algorithm for Training Fault Tolerant RBF Networks and Selecting Centers

In the training stage of radial basis function (RBF) networks, we need to select some suitable RBF centers first. However, many existing center selection algorithms were designed for the fault-free situation. This brief develops a fault tolerant algorithm that trains an RBF network and selects the R...

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Bibliographic Details
Published in:IEEE transaction on neural networks and learning systems 2018-08, Vol.29 (8), p.3870-3878
Main Authors: Wang, Hao, Feng, Ruibin, Han, Zi-Fa, Leung, Chi-Sing
Format: Article
Language:English
Subjects:
Algorithms
Alternating direction method of multipliers (ADMM)
Basis functions
centers selection
Circuit faults
Computer simulation
Fault tolerance
Fault tolerant systems
Linear programming
Objective function
Optimization
Radial basis function
radial basis function (RBF)
Radial basis function networks
Training
Weights & measures
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Summary:In the training stage of radial basis function (RBF) networks, we need to select some suitable RBF centers first. However, many existing center selection algorithms were designed for the fault-free situation. This brief develops a fault tolerant algorithm that trains an RBF network and selects the RBF centers simultaneously. We first select all the input vectors from the training set as the RBF centers. Afterward, we define the corresponding fault tolerant objective function. We then add an \ell _{1} -norm term into the objective function. As the \ell _{1} -norm term is able to force some unimportant weights to zero, center selection can be achieved at the training stage. Since the \ell _{1} -norm term is nondifferentiable, we formulate the original problem as a constrained optimization problem. Based on the alternating direction method of multipliers framework, we then develop an algorithm to solve the constrained optimization problem. The convergence proof of the proposed algorithm is provided. Simulation results show that the proposed algorithm is superior to many existing center selection algorithms.
ISSN:2162-237X
2162-2388
DOI:10.1109/TNNLS.2017.2731319