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

• Published in: IEEE transaction on neural networks and learning systems Vol. 29; no. 8; pp. 3870 - 3878
• Main Authors: Wang, Hao, Feng, Ruibin, Han, Zi-Fa, Leung, Chi-Sing
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.08.2018; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• 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
• ISSN: 2162-237X; 2162-2388; 2162-2388
• DOI: 10.1109/TNNLS.2017.2731319

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 <inline-formula> <tex-math notation="LaTeX">\ell _{1} </tex-math></inline-formula>-norm term into the objective function. As the <inline-formula> <tex-math notation="LaTeX">\ell _{1} </tex-math></inline-formula>-norm term is able to force some unimportant weights to zero, center selection can be achieved at the training stage. Since the <inline-formula> <tex-math notation="LaTeX">\ell _{1} </tex-math></inline-formula>-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.