Madan Gopal

Least squares twin support vector machines for pattern classification

In this paper we formulate a least squares version of the recently proposed twin support vector machine (TSVM) for binary classification. This formulation leads to extremely simple and fast algorithm for generating binary classifiers based on two non-parallel hyperplanes. Here we attempt to solve two modified primal problems of TSVM, instead of two dual problems usually solved. We show that the solution of the two modified primal problems reduces to solving just two systems of linear equations as opposed to solving two quadratic programming problems along with two systems of linear equations in TSVM. Classification using nonlinear kernel also leads to systems of linear equations. Our experiments on publicly available datasets indicate that the proposed least squares TSVM has comparable classification accuracy to that of TSVM but with considerably lesser computational time. Since linear least squares TSVM can easily handle large datasets, we further went on to investigate its efficiency for text categorization applications. Computational results demonstrate the effectiveness of the proposed method over linear proximal SVM on all the text corpuses considered.

Application of smoothing technique on twin support vector machines

This paper enhances the recently proposed twin SVM Jayadeva et al. [Jayadeva, Khemchandani, R., Chandra, S., 2007. Twin support vector machines for pattern classification. IEEE Trans. Pattern Anal. Machine Intell. 29 (5), 905-910] using smoothing techniques to smooth twin SVM for binary classification. We attempt to solve the primal quadratic programming problems of twin SVM by converting them into smooth unconstrained minimization problems. The smooth reformulations are solved using the well-known Newton-Armijo algorithm. The effectiveness of the enhanced method is demonstrated by experimental results on available benchmark datasets.

On the compact computational domain of fuzzy-rough sets

Based on some properties of fuzzy t-norm and t-conorm operators, the concept of fuzzy-rough sets on compact computational domain has been put forward. Various mathematical properties of this new definition of fuzzy-rough sets are discussed from pattern classification viewpoint. It is established that the proposed approach identifies various patterns in the sense of fuzzy-roughness, in addition to providing deeper insight into various concepts of fuzzy-rough sets.

A hybrid SVM based decision tree

We have proposed a hybrid SVM based decision tree to speedup SVMs in its testing phase for binary classification tasks. While most existing methods addressed towards this task aim at reducing the number of support vectors, we have focused on reducing the number of test datapoints that need SVMs help in getting classified. The central idea is to approximate the decision boundary of SVM using decision trees. The resulting tree is a hybrid tree in the sense that it has both univariate and multivariate (SVM) nodes. The hybrid tree takes SVMs help only in classifying crucial datapoints lying near decision boundary; remaining less crucial datapoints are classified by fast univariate nodes. The classification accuracy of the hybrid tree is guaranteed by tuning a threshold parameter. Extensive computational comparisons on 19 publicly available datasets indicate that the proposed method achieves significant speedup when compared to SVMs, without any compromise in classification accuracy.

On adaptive trajectory tracking of a robot manipulator using inversion of its neural emulator

This paper is concerned with the design of a neuro-adaptive trajectory tracking controller. The paper presents a new control scheme based on inversion of a feedforward neural model of a robot arm. The proposed control scheme requires two modules. The first module consists of an appropriate feedforward neural model of forward dynamics of the robot arm that continuously accounts for the changes in the robot dynamics. The second module implements an efficient network inversion algorithm that computes the control action by inverting the neural model. In this paper, a new extended Kalman filter (EKF) based network inversion scheme is proposed. The scheme is evaluated through comparison with two other schemes of network inversion: gradient search in input space and Lyapunov function approach. Using these three inversion schemes the proposed controller was implemented for trajectory tracking control of a two-link manipulator. Simulation results in all cases confirm the efficacy of control input prediction using network inversion. Comparison of the inversion algorithms in terms of tracking accuracy showed the superior performance of the EKF based inversion scheme over others.

NEURO-FUZZY DECISION TREES

Fuzzy decision trees are powerful, top-down, hierarchical search methodology to extract human interpretable classification rules. However, they are often criticized to result in poor learning accuracy. In this paper, we propose Neuro-Fuzzy Decision Trees (N-FDTs); a fuzzy decision tree structure with neural like parameter adaptation strategy. In the forward cycle, we construct fuzzy decision trees using any of the standard induction algorithms like fuzzy ID3. In the feedback cycle, parameters of fuzzy decision trees have been adapted using stochastic gradient descent algorithm by traversing back from leaf to root nodes. With this strategy, during the parameter adaptation stage, we keep the hierarchical structure of fuzzy decision trees intact. The proposed approach of applying backpropagation algorithm directly on the structure of fuzzy decision trees improves its learning accuracy without compromising the comprehensibility (interpretability). The proposed methodology has been validated using computational experiments on real-world datasets.

Reduced one-against-all method for multiclass SVM classification

Abstract We present an improved version of one-against-all method for multiclass SVM classification based on subset sample selection, named reduced one-against-all, to achieve high performance in large multiclass problems. Reduced one-against-all drastically decreases the computing effort involved in training one-against-all classifiers, without any compromise in classification accuracy. Computational comparisons on publicly available datasets indicate that the proposed method has comparable accuracy to that of conventional one-against-all method, but with an order of magnitude faster. On the largest dataset considered, reduced one-against-all method achieved 50% reduction in computing time over one-against-all method for almost the same classification accuracy. We further investigated reduced one-against-all with linear kernel for multi-label text categorization applications. Computational results demonstrate the effectiveness of the proposed method on both the text corpuses considered.

Review article: Synergizing reinforcement learning and game theory-A new direction for control

Reinforcement learning (RL) has now evolved as a major technique for adaptive optimal control of nonlinear systems. However, majority of the RL algorithms proposed so far impose a strong constraint on the structure of environment dynamics by assuming that it operates as a Markov decision process (MDP). An MDP framework envisages a single agent operating in a stationary environment thereby limiting the scope of application of RL to control problems. Recently, a new direction of research has focused on proposing Markov games as an alternative system model to enhance the generality and robustness of the RL based approaches. This paper aims to present this new direction that seeks to synergize broad areas of RL and Game theory, as an interesting and challenging avenue for designing intelligent and reliable controllers. First, we briefly review some representative RL algorithms for the sake of completeness and then describe the recent direction that seeks to integrate RL and game theory. Finally, open issues are identified and future research directions outlined.

A comparison study on multiple binary-class SVM methods for unilabel text categorization

Multiclass support vector machine (SVM) methods are well studied in recent literature. Comparison studies on UCI/statlog multiclass datasets suggest using one-against-one method for multiclass SVM classification. However, in unilabel (multiclass) text categorization with SVMs, no comparison studies exist with one-against-one and other methods, e.g. one-against-all and several well-known improvements to these approaches. In this paper, we bridge this gap by performing empirical comparison of standard one-against-all and one-against-one, together with three improvements to these standard approaches for unilabel text categorization with SVM as base binary learner. We performed all our experiments on three standard text corpuses using two types of document representation. Outcome of our experiments partly support Rifkin and Klautaus (2004) statement that, for small scale unilabel text categorization tasks, if parameters of the classifiers are well tuned, one-against-all will have better performance than one-against-one and other methods.

A Markov Game-Adaptive Fuzzy Controller for Robot Manipulators

This paper develops an adaptive fuzzy controller for robot manipulators using a Markov game formulation. The Markov game framework offers a promising platform for robust control of robot manipulators in the presence of bounded external disturbances and unknown parameter variations. We propose fuzzy Markov games as an adaptation of fuzzy Q-learning (FQL) to a continuous-action variation of Markov games, wherein the reinforcement signal is used to tune online the conclusion part of a fuzzy Markov game controller. The proposed Markov game-adaptive fuzzy controller uses a simple fuzzy inference system (FIS), is computationally efficient, generates a swift control, and requires no exact dynamics of the robot system. To illustrate the superiority of Markov game-adaptive fuzzy control, we compare the performance of the controller against a) the Markov game-based robust neural controller, b) the reinforcement learning (RL)-adaptive fuzzy controller, c) the FQL controller, d) the Hinfin theory-based robust neural game controller, and e) a standard RL-based robust neural controller, on two highly nonlinear robot arm control problems of i) a standard two-link rigid robot arm and ii) a 2-DOF SCARA robot manipulator. The proposed Markov game-adaptive fuzzy controller outperformed other controllers in terms of tracking errors and control torque requirements, over different desired trajectories. The results also demonstrate the viability of FISs for accelerating learning in Markov games and extending Markov game-based control to continuous state-action space problems.