Support Vector Machine with Heavy-tailed Distribution Data

As an implementation of the supervised machine learning, a Support Vector Machine (SVM) has been widely used as a powerful data discriminative classifier. It is defined by a separating hyperplane, which is obtained given labeled training data, and this hyperplane categorizes new examples. Among the parameters to compute the optimal hyperplane, the kernel plays a role to transform the problem into separable states. As a kernel trick for radial basis functions, Gaussian function is mostly used. While its popularity and analytical conciseness, it is not able to capture the heavy-tailed behavior. We apply Gram-Charlier A series to describe the heavy-tailed distribution of the given dataset. As an example, we perform simulations to classify various options with the stock underlying, which are characterized by the strike price and maturity, in Korean option market according to their underlying industries such as manufacturing business and finance industry, demonstrating the versatile applicability of our scheme.