Noisy or uncertain data are common in machine learning and data mining applications. Noisy data can significantly affect the behavior of data mining and machine learning algorithms. Robust optimization and sensitivity analysis techniques are applied to the support vector machine (SVM) learning problems to develop a noise-immune solution, and suggest new approaches for dealing with noisy data. Perturbations of model parameters are considered as well as perturbation of input data. This approach determines how the levels of noise of data and model parameters influence the SVM solution, both in linear and nonlinear problems. Probability and scenario constrained approaches are also examined as alternatives to the robust optimization approach. Several examples illustrate the proposed methods. An application to real time traffic data for the prediction of the speed of a vehicle is also discussed. Tornado data analysis is illustrated in a probability constrained approach as well.