Sparse support vector machine with pinball loss

Abstract

The standard support vector machine (SVM) with a hinge loss function suffers from feature noise sensitivity and instability. Employing a pinball loss function instead of a hinge loss function in SVMs provides noise insensitivity to the model as it maximizes the quantile distance. However, the pinball loss function simultaneously causes the model to lose sparsity by penalizing correctly classified samples. To overcome the aforementioned shortcomings, we propose a novel sparse SVM with pinball loss (Pin‐SSVM) for solving classification problems. The proposed Pin‐SSVM employs L1‐norm in the SVM classifier with the pinball loss (Pin‐SVM), which ensures the robustness, sparseness, and noise insensitivity of the model. The proposed Pin‐SSVM eradicates the need to solve the dual as we simply obtain its solution by solving a linear programming problem (LPP). The proposed Pin‐SSVM does not spend more computational time as that of Pin‐SVM. Hence, solving an LPP with two linear inequality constraints does not affect the computational complexity. The numerical experiments on several real‐world benchmark noise corrupted and imbalanced UCI datasets demonstrate that the proposed Pin‐SSVM is suitable for noisy and imbalanced data sets, and in most cases, outperforms the results of the baseline models.

An Optimal DF Based Method for Transient Stability Analysis

“…In the study of feature selection, there have been methods such as principal component analysis [36,37], cultural algorithm [38], support vector machine [39] for transient feature extraction, and good results have been achieved. In terms of classifier construction, the current transient stability assessment models mainly include support vector machines [33,[40][41][42][43][44], decision trees [45][46][47] and neural networks [36,48,49]. Among them, literature [40,41] propose power grid transient stability assessment methods based on integrated multiple support vector machines from the perspective of model parameters and input feature space.…”

“…When using the "combined feature quantity" method to construct the initial transient feature set, three aspects: the systematic principle, the mainstream principle and the real-time principle are usually considered [38,49,54], that is, the selected feature quantities must meet: 1) The scale of the selected feature quantity does not change with system changes, and should be the combined index of the state variables of each component in the system; 2) There is a high correlation between the selected feature quantity and the transient stable state; 3) The chosen feature quantity must be completed in a timely manner, and it must represent the state of the system before and after the fault occurs in order to fully comprehend the fault's effect on the system. According to the above three principles, on the basis of a large number of simulation experiments, and based on the study and summary of the existing literature [43][44][45]49,50,[54][55][56], the 32-dimensional transient characteristic quantities were determined.…”

Comprehensive Review On Twin Support Vector Machines

“…SVM has remarkable advantages as it utilizes the idea of structural risk minimization (SRM) principle which provides better generalization as well as reduces error in the training phase. As a result of its superior performance even in non-linear classification problems, it has been implemented in a diverse spectrum of research fields, ranging from text classification, face recognition, financial application, brain-computer interface, bio-medicine to human action recognition [1,12,54,93,99,100,148,188,193,204,205]. Although SVM has outperformed most other systems, it still has many limitations in dealing with complex data due to its high computational cost of solving QPPs and its performance highly depends upon the choice of kernel functions and its parameters.…”