Extreme Learning Machine for Regression and Multiclass Classification

TLDR

Least‑square and proximal support vector machines are popular for binary classification but lack direct applicability to regression and multiclass tasks, prompting the development of variants and related single‑hidden‑layer networks such as polynomial and conventional feedforward nets. This work proposes a unified extreme learning machine framework that simplifies LS‑SVM and PSVM and enables direct regression and multiclass classification. ELM operates on generalized single‑hidden‑layer feedforward networks, using a fixed feature mapping that does not require tuning of the hidden layer. Simulations show that ELM scales more efficiently, achieves comparable or superior generalization, and learns up to thousands of times faster than conventional SVM and LS‑SVM.

Abstract

Due to the simplicity of their implementations, least square support vector machine (LS-SVM) and proximal support vector machine (PSVM) have been widely used in binary classification applications. The conventional LS-SVM and PSVM cannot be used in regression and multiclass classification applications directly, although variants of LS-SVM and PSVM have been proposed to handle such cases. This paper shows that both LS-SVM and PSVM can be simplified further and a unified learning framework of LS-SVM, PSVM, and other regularization algorithms referred to extreme learning machine (ELM) can be built. ELM works for the "generalized" single-hidden-layer feedforward networks (SLFNs), but the hidden layer (or called feature mapping) in ELM need not be tuned. Such SLFNs include but are not limited to SVM, polynomial network, and the conventional feedforward neural networks. This paper shows the following: 1) ELM provides a unified learning platform with a widespread type of feature mappings and can be applied in regression and multiclass classification applications directly; 2) from the optimization method point of view, ELM has milder optimization constraints compared to LS-SVM and PSVM; 3) in theory, compared to ELM, LS-SVM and PSVM achieve suboptimal solutions and require higher computational complexity; and 4) in theory, ELM can approximate any target continuous function and classify any disjoint regions. As verified by the simulation results, ELM tends to have better scalability and achieve similar (for regression and binary class cases) or much better (for multiclass cases) generalization performance at much faster learning speed (up to thousands times) than traditional SVM and LS-SVM.