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Register a new userDiversifying Support Vector Machines for Boosting using Kernel Perturbation: Applications to Class Imbalance and Small Disjuncts
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The diversification (generating slightly varying separating discriminators) of Support Vector Machines (SVMs) for boosting has proven to be a challenge due to the strong learning nature of SVMs. Based on the insight that perturbing the SVM kernel may help in diversifying SVMs, we propose two kernel perturbation based boosting schemes where the kernel is modified in each round so as to increase the resolution of the kernel-induced Reimannian metric in the vicinity of the datapoints misclassified in the previous round. We propose a method for identifying the disjuncts in a dataset, dispelling the dependence on rule-based learning methods for identifying the disjuncts. We also present a new performance measure called Geometric Small Disjunct Index (GSDI) to quantify the performance on small disjuncts for balanced as well as class imbalanced datasets. Experimental comparison with a variety of state-of-the-art algorithms is carried out using the best classifiers of each type selected by a new approach inspired by multi-criteria decision making. The proposed method is found to outperform the contending state-of-the-art methods on different datasets (ranging from mildly imbalanced to highly imbalanced and characterized by varying number of disjuncts) in terms of three different performance indices (including the proposed GSDI).
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We propose new methods for Support Vector Machines (SVMs) using tree architecture for multi-class classi- fication. In each node of the tree, we select an appropriate binary classifier using entropy and generalization error estimation, then group the examples into positive and negative classes based on the selected classi- fier and train a new classifier for use in the classification phase. The proposed methods can work in time complexity between O(log2N) to O(N) where N is the number of classes. We compared the performance of our proposed methods to the traditional techniques on the UCI machine learning repository using 10-fold cross-validation. The experimental results show that our proposed methods are very useful for the problems that need fast classification time or problems with a large number of classes as the proposed methods run much faster than the traditional techniques but still provide comparable accuracy.
Support Vector Machines (SVMs) are among the most popular and the best performing classification algorithms. Various approaches have been proposed to reduce the high computation and memory cost when training and predicting based on large-scale datasets with kernel SVMs. A popular one is the linearization framework, which successfully builds a bridge between the $L_1$-loss kernel SVM and the $L_1$-loss linear SVM. For linear SVMs, very recently, a semismooth Newtons method is proposed. It is shown to be very competitive and have low computational cost. Consequently, a natural question is whether it is possible to develop a fast semismooth Newtons algorithm for kernel SVMs. Motivated by this question and the idea in linearization framework, in this paper, we focus on the $L_2$-loss kernel SVM and propose a semismooth Newtons method based linearization and approximation approach for it. The main idea of this approach is to first set up an equivalent linear SVM, then apply the Nystrom method to approximate the kernel matrix, based on which a reduced linear SVM is obtained. Finally, the fast semismooth Newtons method is employed to solve the reduced linear SVM. We also provide some theoretical analyses on the approximation of the kernel matrix. The advantage of the proposed approach is that it maintains low computational cost and keeps a fast convergence rate. Results of extensive numerical experiments verify the efficiency of the proposed approach in terms of both predicting accuracy and speed.
A widely-used tool for binary classification is the Support Vector Machine (SVM), a supervised learning technique that finds the maximum margin linear separator between the two classes. While SVMs have been well studied in the batch (offline) setting, there is considerably less work on the streaming (online) setting, which requires only a single pass over the data using sub-linear space. Existing streaming algorithms are not yet competitive with the batch implementation. In this paper, we use the formulation of the SVM as a minimum enclosing ball (MEB) problem to provide a streaming SVM algorithm based off of the blurred ball cover originally proposed by Agarwal and Sharathkumar. Our implementation consistently outperforms existing streaming SVM approaches and provides higher accuracies than libSVM on several datasets, thus making it competitive with the standard SVM batch implementation.
The twin support vector machine and its extensions have made great achievements in dealing with binary classification problems, however, which is faced with some difficulties such as model selection and solving multi-classification problems quickly. This paper is devoted to the fast regularization parameter tuning algorithm for the twin multi-class support vector machine. A new sample dataset division method is adopted and the Lagrangian multipliers are proved to be piecewise linear with respect to the regularization parameters by combining the linear equations and block matrix theory. Eight kinds of events are defined to seek for the starting event and then the solution path algorithm is designed, which greatly reduces the computational cost. In addition, only few points are combined to complete the initialization and Lagrangian multipliers are proved to be 1 as the regularization parameter tends to infinity. Simulation results based on UCI datasets show that the proposed method can achieve good classification performance with reducing the computational cost of grid search method from exponential level to the constant level.
We propose several novel methods for enhancing the multi-class SVMs by applying the generalization performance of binary classifiers as the core idea. This concept will be applied on the existing algorithms, i.e., the Decision Directed Acyclic Graph (DDAG), the Adaptive Directed Acyclic Graphs (ADAG), and Max Wins. Although in the previous approaches there have been many attempts to use some information such as the margin size and the number of support vectors as performance estimators for binary SVMs, they may not accurately reflect the actual performance of the binary SVMs. We show that the generalization ability evaluated via a cross-validation mechanism is more suitable to directly extract the actual performance of binary SVMs. Our methods are built around this performance measure, and each of them is crafted to overcome the weakness of the previous algorithm. The proposed methods include the Reordering Adaptive Directed Acyclic Graph (RADAG), Strong Elimination of the classifiers (SE), Weak Elimination of the classifiers (WE), and Voting based Candidate Filtering (VCF). Experimental results demonstrate that our methods give significantly higher accuracy than all of the traditional ones. Especially, WE provides significantly superior results compared to Max Wins which is recognized as the state of the art algorithm in terms of both accuracy and classification speed with two times faster in average.
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