SDRNF: generating scalable and discriminative random nonlinear features from data

Abstract

Real world data analysis problems often require nonlinear methods to get successful prediction. Kernel methods, e.g. Kernelized Principal Component Analysis, are a common way to get nonlinear properties based on linear representations in a high-dimensional feature space. Unfortunately, traditional kernel methods are unscalable for large-size or even medium-size data. On the other hand, randomized algorithms have been recently proposed to extract nonlinear features in kernel methods. Compared with exact kernel methods, this family of approaches is capable of speeding up the training process dramatically, while maintaining acceptable the classification accuracy. However, these methods fail to engage discriminative features. This significantly limits their classification accuracy. In this paper, we propose a scalable and approximate technique called SDRNF for introducing both nonlinear and discriminative features based on randomized methods. By combining randomized kernel approximation with a couple of generalized eigenvector problems, the proposed approach proves both scalable and accurate for large-scale data. A series of experiments on two benchmark data sets MNIST and CIFAR-10 reveal that our method is fast and scalable, and also generates better classification accuracy over other competitive kernel approximation methods.