Low-degree Polynomial Mapping of Data for SVM

Non-linear mapping functions have long been used in SVM to transform data into a higher dimensional space, allowing the classifier to separate linearly inseparable data. Kernel tricks are used to handle the huge number of features of the mapped data point. However, the training/testing for large data is often time consuming. Following the recent advances in training large linear SVM (i.e., SVM without using nonlinear kernels), this work discusses a method that strikes a balance between the training/testing speed and the testing accuracy. We apply the fast training method for linear SVM to the expanded form of data under low-degree polynomial mappings. The method enjoys fast training/testing, but may achieve testing accuracy close to that of using highly nonlinear kernels. Empirical experiments show that the proposed method is useful for certain large-scale data sets. We successfully demonstrate an NLP application by improving the testing accuracy under some training/testing speed requirements.