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Training and Testing Low-degree Polynomial Data Mappings via Linear SVM

Yin-Wen Chang
Cho-Jui Hsieh
Kai-Wei Chang
Michael Ringgaard
Chih-Jen Lin
Journal of Machine Learning Research, vol. 11(Apr) (2010), 1471−1490


Kernel techniques have long been used in SVM to handle linearly inseparable problems by transforming data to a high dimensional space, but training and testing large data sets is often time consuming. In contrast, we can efficiently train and test much larger data sets using linear SVM without kernels. In this work, we apply fast linear-SVM methods to the explicit form of polynomially mapped data and investigate implementation issues. The approach enjoys fast training and testing, but may sometimes achieve 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 apply the proposed method to a natural language processing (NLP) application by improving the testing accuracy under some training/testing speed requirements.

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