Two noise tolerant incremental learning algorithms for single layer feed-forward neural networks

This paper focuses on noise resistant incremental learning algorithms for single layer feed-forward neural networks (SLFNNs). In a physical implementation of a well trained neural network, faults or noise are unavoidable. As biological neural networks have ability to tolerate noise, we would like to have a trained neural network that has certain ability to tolerate noise too. This paper first develops a noise tolerant objective function that can handle multiplicative weight noise. We assume that multiplicative weight noise exist in the weights between the input layer and the hidden layer, and in the weights between the hidden layer and the output layer. Based on the developed objective function, we propose two noise tolerant incremental extreme learning machine algorithms, namely weight deviation incremental extreme learning machine (WDT-IELM) and weight deviation convex incremental extreme learning machine (WDTC-IELM). Compared to the original extreme learning machine algorithms, the two proposed algorithms have much better ability to tolerate the multiplicative weight noise. Several simulations are carried out to demonstrate the superiority of the two proposed algorithms.