Analytical Calculation of Hidden Layer Biases in Extreme Learning Machines with Sinusoidal Activation Function

Abstract

ELM (Extreme Learning Machine) networks have been gaining attention due to high speed, ease of implementation and minimal human intervention compared to classical feedforward neural networks with iterative training algorithms. Part of the studies that seek improvements in ELM involves the specification of input weights and hidden layer biases, traditionally randomized. In this paper is proposed a variant of ELM network in which the hidden layer biases are analytically calculated simultaneously to the output weights in the solution of the least squares problem. The method is valid for SLFNs (single-hidden layer feedforward neural networks) with sinusoidal activation functions. Experiments have shown that calculating biases with the proposed method may reduce the amount of hidden nodes required to solve a given problem. The proposed variant received the designation CBTELM—Calculated (Hidden Layer) Biases Trigonometric ELM. In addition to standard applications of neural networks, CBTELM may be successfully used for amplitude and phase detection of noisy signals composed by sinusoids with known frequencies, as was verified in experiments.