The Optimal Design of Weighted Order Statistics Filters by Using Support Vector Machines
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The Optimal Design of Weighted Order Statistics Filters by Using Support Vector Machines Chih-Chia Yao and Pao-Ta Yu Department of Computer Science and Information Engineering, College of Engineering, National Chung Cheng University, Chia-yi 62107, Taiwan Received 10 January 2005; Revised 13 September 2005; Accepted 7 November 2005 Recommended for Publication by Moon Gi Kang Support vector machines (SVMs), a classification algorithm for the machine learning community, have been shown to provide higher performance than traditional learning machines. In this paper, the technique of SVMs is introduced into the design of weighted order statistics (WOS) filters. WOS filters are highly effective, in processing digital signals, because they have a simple window structure. However, due to threshold decomposition and stacking property, the development of WOS filters cannot significantly improve both the design complexity and estimation error. This paper proposes a new designing technique which can improve the learning speed and reduce the complexity of designing WOS filters. This technique uses a dichotomous approach to reduce the Boolean functions from 255 levels to two levels, which are separated by an optimal hyperplane. Furthermore, the optimal hyperplane is gotten by using the technique of SVMs. Our proposed method approximates the optimal weighted order statistics filters more rapidly than the adaptive neural filters. Copyright © 2006 Hindawi Publishing Corporation. All rights reserved.
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INTRODUCTION
Support vector machines (SVMs), a classification algorithm for the machine learning community, have attracted much attention in recent years [1–5]. In many applications, SVMs have been shown to provide higher performance than traditional learning machines [6–8]. The principle of SVMs is based on approximating structural risk minimization. It shows that the generalization error is bounded by the sum of the training set error and a term dependent on the Vapnik-Chervonenkis dimension of the learning machines [2]. The idea of SVMs originates from finding an optimal separating hyperplane which separates the largest possible fraction of training set of each class of data while maximizing the distance from either class to the separating hyperplane. According to Vapnik [9], this hyperplane minimizes the risk of misclassifying not only the examples in the training set, but also the unseen examples of the test set. SVMs performance versus traditional learning machines suggested that a redesign approach could overcome significant problems under study [10–15]. In this paper, a new dichotomous technique for designing WOS filter by SVMs is proposed. WOS filters are a special subset of stack filters, and
are used in a lot of applications including noise cancellation, image restoration, and texture analysis [16–21]. Each stack filter based on a positive Boolean function can be characterized by two properties—threshold decomposition and stacking property [11, 22]. The Boolean function on which each WOS filter is based is a threshold lo
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