Time efficient variants of Twin Extreme Learning Machine

Twin Extreme Learning Machine models can obtain better generalization ability than the standard Extreme Learning Machine model. But, they require to solve a pair of quadratic programming problems for this. It makes them more complex and computationally expensive than the standard Extreme Learning Machine model. In this paper, we propose two novel time-efficient formulations of the Twin Extreme Learning Machine, which only require the solution of systems of linear equations for obtaining the final classifier. In this sense, they can combine the benefits of the Twin Support Vector Machine and standard Extreme Learning Machine in the true sense. We term our first formulation as 'Least Squared Twin Extreme Learning Machine'. It minimizes the L 2-norm of error variables in its optimization problem. Our second formulation 'Weighted Linear loss Twin Extreme Learning Machine' uses the weighted linear loss function for calculating the empirical error, which makes it insensitive towards outliers. Numerical results obtained with multiple benchmark datasets show that proposed formulations are time efficient with better generalization ability. Further, we have used the proposed formulations in the detection of phishing websites and shown that they are much more effective in the detection of phishing websites than other Extreme Learning Machine models.