Fast learning complex-valued classifiers for real-valued classification problems

In this paper, we present two fast learning complex-valued, single hidden layer neural network classifiers namely, ‘bilinear branch-cut complex-valued extreme learning machine (BB-CELM)’ and ‘phase encoded complex-valued extreme learning machine (PE-CELM)’ to solve real-valued classification problems. BB-CELM and PE-CELM use the bilinear transformation with a branch-cut at 2π and the phase encoded transformation, respectively, at the input layer to transform the feature space from the real domain to complex domain (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Re \rightarrow \mathbb{C}}$$\end{document}). A complex-valued activation function of the type of hyperbolic secant employed at the hidden layer maps the complex-valued feature space to a hyper dimensional complex space (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{C}^m \rightarrow \mathbb{C}^K\quad K > m}$$\end{document}). BB-CELM and PE-CELM are trained by choosing the hidden layer parameters randomly and computing the output weights analytically. Therefore, these classifiers require minimal computational effort during the training process. The performances of these classifiers are evaluated on a set of benchmark classification problems from the UCI machine learning repository and a practical acoustic emission signal classification problem. The results of the performance study highlight the superior classification ability of BB-CELM and PE-CELM classifiers.