Small Number of Hidden Units for ELM with Two-Stage Linear Model

Abstract

The single-hidden-layer feedforward neural networks (SLFNs) are frequently used in machine learning due to their ability which can form boundaries with arbitrary shapes if the activation function of hidden units is chosen properly. Most learning algorithms for the neural networks based on gradient descent are still slow because of the many learning steps. Recently, a learning algorithm called extreme learning machine (ELM) has been proposed for training SLFNs to overcome this problem. It randomly chooses the input weights and hidden-layer biases, and analytically determines the output weights by the matrix inverse operation. This algorithm can achieve good generalization performance with high learning speed in many applications. However, this algorithm often requires a large number of hidden units and takes long time for classification of new observations. In this paper, a new approach for training SLFNs called least-squares extreme learning machine (LS-ELM) is proposed. Unlike the gradient descent-based algorithms and the ELM, our approach analytically determines the input weights, hidden-layer biases and output weights based on linear models. For training with a large number of input patterns, an online training scheme with sub-blocks of the training set is also introduced. Experimental results for real applications show that our proposed algorithm offers high classification accuracy with a smaller number of hidden units and extremely high speed in both learning and testing.