L2 Support Vector Machine Research Articles

A New Fault Diagnosis Method for Unbalanced Data Based on 1DCNN and L2-SVM

In general, the measured health condition data from rolling bearings usually exhibit imbalanced distribution. However, traditional intelligent fault diagnosis methods usually assume that the data categories are balanced. To improve the diagnosis accuracy of unbalanced datasets, a new fault diagnosis method for unbalanced data based on 1DCNN and L2-SVM is proposed in this paper. Firstly, to prevent the minority class samples from being heavily suppressed by the rectified linear unit (ReLU) activation function in the traditional convolutional neural network (CNN), ReLU is improved by linear and scaled exponential linear units (SELUs). Secondly, to solve the problem where the cross-entropy loss treats all input samples equally, it is replaced by the L2-support vector machine (L2-SVM) loss. Furthermore, a dynamic adjustment parameter is introduced to assign less misclassification cost to the majority of class samples. Finally, we add a new modulation factor that reduces the weight of more distinguishable samples to generate more focus on training indiscernible samples. The proposed method is carried out on two kinds of bearing datasets. The experimental results illustrate a significant improvement in recognition accuracy and the higher diagnosis performance of the model when dealing with unbalanced data compared with other intelligent methods.

Modified Frank–Wolfe algorithm for enhanced sparsity in support vector machine classifiers

Abstract This work proposes a new algorithm for training a re-weighted l2 Support Vector Machine (SVM), inspired on the re-weighted Lasso algorithm of Candes et al. and on the equivalence between Lasso and SVM shown recently by Jaggi. In particular, the margin required for each training vector is set independently, defining a new weighted SVM model. These weights are selected to be binary, and they are automatically adapted during the training of the model, resulting in a variation of the Frank–Wolfe optimization algorithm with essentially the same computational complexity as the original algorithm. As shown experimentally, this algorithm is computationally cheaper to apply since it requires less iterations to converge, and it produces models with a sparser representation in terms of support vectors and which are more stable with respect to the selection of the regularization hyper-parameter.

Opinion mining on book review using CNN-L2-SVM algorithm

Review of a product can represent quality of a product itself. An extraction to that review can be used to know sentiment of that opinion. Process to extract useful information of user review is called Opinion Mining. Review extraction model that is enhancing nowadays is Deep Learning model. This Model has been used by many researchers to obtain excellent performance on Natural Language Processing. In this research, one of deep learning model, Convolutional Neural Network (CNN) is used for feature extraction and L2 Support Vector Machine (SVM) as classifier. These methods are implemented to know the sentiment of book review data. The result of this method shows state-of-the art performance in 83.23% for training phase and 64.6% for testing phase.

Landslide susceptibility mapping & prediction using Support Vector Machine for Mandakini River Basin, Garhwal Himalaya, India

In recent years, various machine learning techniques have been applied for landslide susceptibility mapping. In this study, three different variants of support vector machine viz., SVM, Proximal Support Vector Machine (PSVM) and L2-Support Vector Machine - Modified Finite Newton (L2-SVM-MFN) have been applied on the Mandakini River Basin in Uttarakhand, India to carry out the landslide susceptibility mapping. Eight thematic layers such as elevation, slope, aspect, drainages, geology/lithology, buffer of thrusts/faults, buffer of streams and soil along with the past landslide data were mapped in GIS environment and used for landslide susceptibility mapping in MATLAB. The study area covering 1625km2 has merely 0.11% of area under landslides. There are 2009 pixels for past landslides out of which 50% (1000) landslides were considered as training set while remaining 50% as testing set. The performance of these techniques has been evaluated and the computational results show that L2-SVM-MFN obtains higher prediction values (0.829) of receiver operating characteristic curve (AUC-area under the curve) as compared to 0.807 for PSVM model and 0.79 for SVM. The results obtained from L2-SVM-MFN model are found to be superior than other SVM prediction models and suggest the usefulness of this technique to problem of landslide susceptibility mapping where training data is very less. However, these techniques can be used for satisfactory determination of susceptible zones with these inputs.

Properties of the solution of L2-Support Vector Machine as a function of regularization parameter

The goal of this paper is to study some mathematical properties of so-called L2 Soft Margin Support Vector Machines (L2-SVMs) for data classification. Their dual formulations build a family of quadratic programming problems depending on one regularization parameter. The dependence of the solution on this parameter is examined. Such properties as continuity, differentiability, monotony, convexity and structure of the solution are investigated. It is shown that the solution and the objective value of the Hard Margin SVM allow estimating the slack variables of the L2-SVMs. Most results deal with the dual problem, but some statements about the primal problem are also formulated (e.g., the behavior and differentiability of slack variables). An ancillary dual problem is used as investigation tool. It is shown that it is in reality a dual formulation of a quasi identical L2-SVM primal.

Constructing L2-SVM-Based Fuzzy Classifiers in High-Dimensional Space With Automatic Model Selection and Fuzzy Rule Ranking

In this paper, a new scheme for constructing parsimonious fuzzy classifiers is proposed based on the L2-support vector machine (L2-SVM) technique with model selection and feature ranking performed simultaneously in an integrated manner, in which fuzzy rules are optimally generated from data by L2-SVM learning. In order to identify the most influential fuzzy rules induced from the SVM learning, two novel indexes for fuzzy rule ranking are proposed and named as alpha-values and omega-values of fuzzy rules in this paper. The alpha-values are defined as the Lagrangian multipliers of the L2-SVM and adopted to evaluate the output contribution of fuzzy rules, while the omega-values are developed by considering both the rule base structure and the output contribution of fuzzy rules. As a prototype-based classifier, the L2-SVM-based fuzzy classifier evades the curse of dimensionality in high-dimensional space in the sense that the number of support vectors, which equals the number of induced fuzzy rules, is not related to the dimensionality. Experimental results on high-dimensional benchmark problems have shown that by using the proposed scheme the most influential fuzzy rules can be effectively induced and selected, and at the same time feature ranking results can also be obtained to construct parsimonious fuzzy classifiers with better generalization performance than the well-known algorithms in literature.