Chapter 7 - Outlier-based models of the non-tuned neural network—coding and implementation

Abstract

As a type of single-layer feed-forward neural network, the extreme learning machine (ELM) has recently garnered substantial interest from academics and scholars due to its exceptional capacity for rapid training and development, as well as its respectable ability to generalize. When dealing with real-world data sets, ELM models can be unreliable and have weak predictive capacities due to the often present heteroscedasticity within the data. Numerous ELM-based techniques capable of handling such volatility in data sets are illustrated in this chapter to address this shortcoming of the ELM model. To begin the chapter, a brief review of the background of the ELM technique is presented, following this, the detailed mathematical formulations of four ELM-based models are presented, including the classical ELM, regularized ELM (RELM), weighted regularized ELM (WRELM), and outlier-robust ELM (ORELM). Although an in-depth understanding of the formulation of these methods requires basic knowledge of ELM and coding in MATLAB, beginner users can easily apply the models developed in this chapter without having to venture into the details presented in the following sections. Following the presentation of the three developed ELM-based models, a sensitivity analysis is conducted for all user-defined parameters by considering five example cases. The user-defined parameters to be investigated include the regularization parameters, the weight function in the WRELM, and the maximum number of iterations in the ORELM. In addition to presenting an in-depth mathematical development and model description for advanced users, this chapter employs a calculator for beginner users, which allows for simple application of the methodologies without deep knowledge of MATLAB and the structure of the ELM and its developments. Indeed, the information presented in the current chapter is presented for both beginners and advanced users.