Relaxed constraints support vector machines for noisy data

Real-world data collected for computer-based applications are frequently impure. Differentiation of outliers and noisy data from normal ones is a major task in data mining applications. On the other hand, elimination of noisy and outlier data from training samples of a dataset may lead to over-fitting or information loss. A fuzzy support vector machine (FSVM) provides an effective means to deal with this problem. It reduces the effect of the noisy data and outliers by using a fuzzy membership functions. In this paper, a new formation for SVMs is introduced that considers importance degrees for training samples. The constraints of the SVM are converted to fuzzy inequalities. The proposed method, RSVM, shows better efficiency in the classification of data in different domains. Especially, using the proposed RSVM for multi-class classification of arrhythmia disease is presented at the end of this paper as a practical case study to show the effectiveness of the proposed system.