Fuzzy SVM for noisy data: A robust membership calculation method

Abstract

Support vector machine (SVM) is a theoretically well motivated algorithm developed from statistical learning theory, that have shown good performance in many fields. In spite of its success, it still suffers from a noise sensitivity problem.To relax this problem, the SVM was extended by the introduction of fuzzy memberships to the fuzzy SVM (FSVM). The FSVM also has been extended further in two ways: by adopting a different objective function with the help of domain-specific knowledge and by employing a different membership calculation method. In this paper, we propose a new membership calculation method, that belongs to the second group. It is different from previous ones in that it does not assume any simple data distribution and does not need any prior knowledge. The proposed method is based on reconstruction error, which measures the agreement between the overall data structure and a data point. Thus the reconstruction error can represent the degree of outlier-ness and help in achieving noise robustness. Experimental results with synthetic and real data sets also support this.

Improvments of Payload-based Intrusion Detection Models by Using Noise Against Fuzzy SVM

“…The optimal hyper-plane problem of the SVM can be solved by the modified version of the bSVM as follows [10]:…”

“…To improve the performance of the original fSVM, two approaches can be adopted [10]: One is to formulate the objective function in a different way to incorporate domain-specific knowledge; another is to select appreciate memberships for the specific data set. In order to remove the effect of noise in the data set, a membership function based on reconstruction error is adopted in this paper.…”

Consumer Preference Elicitation of Complex Products Using Fuzzy Support Vector Machine Active Learning

“…As a weighted variant of the soft margin SVM formulation (the soft margin SVM was initially introduced by Cortes and Vapnik 1995), the fuzzy SVM method assigns different weights to different data points to enable greater flexibility of error control. In recent years, the class of fuzzy SVM methods has gained notable popularity in the SVM literature, mainly due to its effectiveness in reducing the effect of noises/errors in the data (e.g., Wang 2002, 2004;Wang, Wang, and Lai 2005;Shilton and Lai 2007;Heo and Gader 2009). …”

“…Therefore, in the machine learning literature, researchers have explored various approaches to discern noises/outliers in the data (e.g., Wang 2002, 2004;Wang, Wang, and Lai 2005;Shilton and Lai 2007;Heo and Gader 2009). We adopt a method similar to Lin and Wang (2002) to assign each labeled profile with a fuzzy membership…”

Fuzzy Support Vector Machines for Face Recognition: A Review

“…In this paper [12] This paper [13], Support vector machine (SVM) is a hypothetically all around persuaded calculation created from statistical learning theory that have indicated great performance in numerous fields. Regardless of its prosperity, despite everything it experiences a noise sensitivity issue.…”