Probabilistic support vector machines for classification of noise affected data

The support vector machines (SVMs) have gained visibility and been thoroughly studied in the machine learning community. However, the performance of these machines is sensitive to noisy data and the machine may not be effective when the level of noise is high. Since the noise makes the separating margin of SVM to be a stochastic variable, a probabilistic support vector machine (PSVM) is proposed to capture the probabilistic information of the separating margin and formulate the decision function within such a noisy environment. First, all data are clustered, upon which different subsets are formed by PCA-based sampling; then, a distributed SVM system is constructed to estimate the separating margin for each subset. Next, a quadratic optimization problem is being solved with the use of probabilistic information extracted from separating margins to determine the decision function. Using the weighted average of probability of cluster centers, the confidence of the decision can be estimated. An artificial dataset and four real-life datasets from a UCI machine learning database are used to demonstrate the effectiveness of the proposed probabilistic SVM.