A Heterogeneous Ensemble of Extreme Learning Machines with Correntropy and Negative Correlation

The Extreme Learning Machine（ELM） is an effective learning algorithm for a Single-Layer Feedforward Network（SLFN）. It performs well in managing some problems due to its fast learning speed. However, in practical applications, its performance might be affected by the noise in the training data. To tackle the noise issue, we propose a novel heterogeneous ensemble of ELMs in this article. Specifically, the correntropy is used to achieve insensitive performance to outliers, while implementing Negative Correlation Learning（NCL） to enhance diversity among the ensemble. The proposed Heterogeneous Ensemble of ELMs（HE2 LM） for classification has different ELM algorithms including the Regularized ELM（RELM）, the Kernel ELM（KELM）, and the L2-norm-optimized ELM（ELML2）. The ensemble is constructed by training a randomly selected ELM classifier on a subset of the training data selected through random resampling. Then, the class label of unseen data is predicted using a maximum weighted sum approach. After splitting the training data into subsets, the proposed HE2 LM is tested through classification and regression tasks on real-world benchmark datasets and synthetic datasets. Hence, the simulation results show that compared with other algorithms, our proposed method can achieve higher prediction accuracy, better generalization, and less sensitivity to outliers.

EXTREMES OF RATIOS OF DETERMINANTS AND CANONICAL CORRELATION VARIABLES

This article develops some extremes of the ratios of determinants. The results are themultivariate extensions of the extremes of quadratic forms, and can be applied to finding thecanonicai correlation variables of two random vectors. Hence a group of canonical correlationvariables is a solution of the extreme of the ratio of determinants.