RBF networks under the concurrent fault situation

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 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 -norm term into the objective function. As the -norm term is able to force some unimportant weights to zero, center selection can be achieved at the training stage. Since the -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.

A Preference-Based Multiobjective Evolutionary Approach for Sparse Optimization

Iterative thresholding is a dominating strategy for sparse optimization problems. The main goal of iterative thresholding methods is to find a so-called -sparse solution. However, the setting of regularization parameters or the estimation of the true sparsity are nontrivial in iterative thresholding methods. To overcome this shortcoming, we propose a preference-based multiobjective evolutionary approach to solve sparse optimization problems in compressive sensing. Our basic strategy is to search the knee part of weakly Pareto front with preference on the true -sparse solution. In the noiseless case, it is easy to locate the exact position of the -sparse solution from the distribution of the solutions found by our proposed method. Therefore, our method has the ability to detect the true sparsity. Moreover, any iterative thresholding methods can be used as a local optimizer in our proposed method, and no prior estimation of sparsity is required. The proposed method can also be extended to solve sparse optimization problems with noise. Extensive experiments have been conducted to study its performance on artificial signals and magnetic resonance imaging signals. Our experimental results have shown that our proposed method is very effective for detecting sparsity and can improve the reconstruction ability of existing iterative thresholding methods.

A Regularizer Approach for RBF Networks Under the Concurrent Weight Failure Situation

Many existing results on fault-tolerant algorithms focus on the single fault source situation, where a trained network is affected by one kind of weight failure. In fact, a trained network may be affected by multiple kinds of weight failure. This paper first studies how the open weight fault and the multiplicative weight noise degrade the performance of radial basis function (RBF) networks. Afterward, we define the objective function for training fault-tolerant RBF networks. Based on the objective function, we then develop two learning algorithms, one batch mode and one online mode. Besides, the convergent conditions of our online algorithm are investigated. Finally, we develop a formula to estimate the test set error of faulty networks trained from our approach. This formula helps us to optimize some tuning parameters, such as RBF width.

Objective Function and Learning Algorithm for the General Node Fault Situation

Fault tolerance is one interesting property of artificial neural networks. However, the existing fault models are able to describe limited node fault situations only, such as stuck-at-zero and stuck-at-one. There is no general model that is able to describe a large class of node fault situations. This paper studies the performance of faulty radial basis function (RBF) networks for the general node fault situation. We first propose a general node fault model that is able to describe a large class of node fault situations, such as stuck-at-zero, stuck-at-one, and the stuck-at level being with arbitrary distribution. Afterward, we derive an expression to describe the performance of faulty RBF networks. An objective function is then identified from the formula. With the objective function, a training algorithm for the general node situation is developed. Finally, a mean prediction error (MPE) formula that is able to estimate the test set error of faulty networks is derived. The application of the MPE formula in the selection of basis width is elucidated. Simulation experiments are then performed to demonstrate the effectiveness of the proposed method.