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In this paper, a simple and linearly convergent Lagrangian support vector machine algorithm for the dual of the twin support vector regression (TSVR) is proposed. Though at the outset the algorithm requires inverse of matrices, it has been shown that they would be obtained by performing matrix subtraction of the identity matrix by a scalar multiple of inverse of a positive semi-definite matrix that arises in the original formulation of TSVR. The algorithm can be easily implemented and does not need any optimization packages. To demonstrate its effectiveness, experiments were performed on well-known synthetic and real-world datasets. Similar or better generalization performance of the proposed method in less training time in comparison with the standard and twin support vector regression methods clearly exhibits its suitability and applicability. [ABSTRACT FROM AUTHOR]

In this paper, extreme learning machine (ELM) for ε-insensitive error loss function-based regression problem formulated in 2-norm as an unconstrained optimization problem in primal variables is proposed. Since the objective function of this unconstrained optimization problem is not twice differentiable, the popular generalized Hessian matrix and smoothing approaches are considered which lead to optimization problems whose solutions are determined using fast Newton-Armijo algorithm. The main advantage of the algorithm is that at each iteration, a system of linear equations is solved. By performing numerical experiments on a number of interesting synthetic and real-world datasets, the results of the proposed method are compared with that of ELM using additive and radial basis function hidden nodes and of support vector regression (SVR) using Gaussian kernel. Similar or better generalization performance of the proposed method on the test data in comparable computational time over ELM and SVR clearly illustrates its efficiency and applicability. [ABSTRACT FROM AUTHOR]

The 'Brainstorming' approach presented in this paper is a weighted voting method that can improve the quality of predictions generated by several machine learning (ML) methods. First, an ensemble of heterogeneous ML algorithms is trained on available experimental data, then all solutions are gathered and a consensus is built between them. The final prediction is performed using a voting procedure, whereby the vote of each method is weighted according to a quality coefficient calculated using multivariable linear regression (MLR). The MLR optimization procedure is very fast, therefore no additional computational cost is introduced by using this jury approach. Here, brainstorming is applied to selecting actives from large collections of compounds relating to five diverse biological targets of medicinal interest, namely HIV-reverse transcriptase, cyclooxygenase-2, dihydrofolate reductase, estrogen receptor, and thrombin. The MDL Drug Data Report (MDDR) database was used for selecting known inhibitors for these protein targets, and experimental data was then used to train a set of machine learning methods. The benchmark dataset (available at ) can be used for further testing of various clustering and machine learning methods when predicting the biological activity of compounds. Depending on the protein target, the overall recall value is raised by at least 20% in comparison to any single machine learning method (including ensemble methods like random forest) and unweighted simple majority voting procedures. [ABSTRACT FROM AUTHOR]

Abstract  Aiming at the common support vector machine’s biased disadvantage and computational complexity, an unbiased least squares support vector machine (LSSVM) model is proposed in this paper. The model eliminates the bias item of LSSVM by improving the form of structure risk, then the unbiased least squares support vector classifier and the unbiased least squares support vector regression are deduced. Based on this model, we design a new learning algorithm using Cholesky factorization according to the characteristic of kernel function matrix, in this way the calculation of Lagrangian multipliers is greatly simplified. Several experiments on diffenert datasets are carried out, including the common datasets classification, synthetic aperture radar image automatic target recognition and chaotic time series prediction. The experimental results of correct recognition rate and the fitting precision testify that the unbiased LSSVM model has good universal ability and fitting accuracy, better generalization capability and stability, and have a great improvement in learning speed. [ABSTRACT FROM AUTHOR]

We propose a computationally efficient method for cross-validation of the Support Vector Regression (SVR) by generalizing the decremental algorithm of SVR. Incremental and decremental algorithm of Support Vector Machines (SVM)) efficiently update the trained SVM model when a single data point is added to or removed from the training set. The computational cost of leave-one-out cross-validation can be reduced using the decremental algorithm. However, when we perform leave-m-out cross-validation (m>1), we have to repeatedly apply the decremental algorithm for each data point. In this paper, we extend the decremental algorithm of SVR ) in such a way that several data points can be removed more efficiently. Experimental results indicate that the proposed approach can reduce the computational cost. In particular, we observed that the number of breakpoints, which is the main computational cost of the involved path-following, were reduced from (O(m) to O(√m). [ABSTRACT FROM AUTHOR]