Robust regression and outlier detection
Robust regression and outlier detection
Fast polar decomposition of an arbitrary matrix
SIAM Journal on Scientific and Statistical Computing
Complete Orthogonal Decomposition for Weighted Least Squares
SIAM Journal on Matrix Analysis and Applications
The multivariate least-trimmed squares estimator
Journal of Multivariate Analysis
Sales forecasting using extreme learning machine with applications in fashion retailing
Decision Support Systems
Meta-metric Evaluation of E-Commerce-related Metrics
Electronic Notes in Theoretical Computer Science (ENTCS)
Modeling Permeability Prediction Using Extreme Learning Machines
AMS '10 Proceedings of the 2010 Fourth Asia International Conference on Mathematical/Analytical Modelling and Computer Simulation
Universal approximation using incremental constructive feedforward networks with random hidden nodes
IEEE Transactions on Neural Networks
IWANN'13 Proceedings of the 12th international conference on Artificial Neural Networks: advances in computational intelligence - Volume Part I
Engineering Applications of Artificial Intelligence
Applications of Hybrid Extreme Rotation Forests for image segmentation
International Journal of Hybrid Intelligent Systems
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The output weights computing of extreme learning machine (ELM) encounters two problems, the computational and outlier robustness problems. The computational problem occurs when the hidden layer output matrix is a not full column rank matrix or an ill-conditioned matrix because of randomly generated input weights and biases. An existing solution to this problem is Singular Value Decomposition (SVD) method. However, the training speed is still affected by the large complexity of SVD when computing the Moore-Penrose (MP) pseudo inverse. The outlier robustness problem may occur when the training data set contaminated with outliers then the accuracy rate of ELM is extremely affected. This paper proposes the Extended Complete Orthogonal Decomposition (ECOD) method to solve the computational problem in ELM weights computing via ECODLS algorithm. And the paper also proposes the other three algorithms, i.e. the iteratively reweighted least squares (IRWLS-ELM), ELM based on the multivariate least-trimmed squares (MLTS-ELM), and ELM based on the one-step reweighted MLTS (RMLTS-ELM) to solve the outlier robustness problem. However, they also encounter the computational problem. Therefore, the ECOD via ECODLS algorithm is also used successfully in the three proposed algorithms. The experiments of regression problems were conducted on both toy and real-world data sets. The outlier types are one-sided and two-sided outliers. Each experiment was randomly contaminated with outliers, of one type only, with 10%, 20%, 30%, 40%, and 50% of the total training data size. Meta-metrics evaluation was used to measure the outlier robustness of the proposed algorithms compared to the existing algorithms, i.e. the minimax probability machine regression (MPMR) and the ordinary ELM. The experimental results showed that ECOD can effectively replace SVD. The ECOD is robust to the not full column rank or the ill-conditional problem. The speed of the ELM training using ECOD is also faster than the ordinary training algorithm. Moreover, the meta-metrics measure showed that the proposed algorithms are less affected by the increasing number of outliers than the existing algorithms.