  Large scale nonlinear classification is a challenging task in the field of
support vector machine. Online random Fourier feature map algorithms are very
important methods for dealing with large scale nonlinear classification
problems. The main shortcomings of these methods are as follows: (1) Since only
the hyperplane vector is updated during learning while the random directions
are fixed, there is no guarantee that these online methods can adapt to the
change of data distribution when the data is coming one by one. (2) The
dimension of the random direction is often higher for obtaining better
classification accuracy, which results in longer test time. In order to
overcome these shortcomings, a multi-parameter updating Fourier online gradient
descent algorithm (MPU-FOGD) is proposed for large-scale nonlinear
classification problems based on a novel random feature map. In the proposed
method, the suggested random feature map has lower dimension while the
multi-parameter updating strategy can guarantee the learning model can better
adapt to the change of data distribution when the data is coming one by one.
Theoretically, it is proved that compared with the existing random Fourier
feature maps, the proposed random feature map can give a tighter error bound.
Empirical studies on several benchmark data sets demonstrate that compared with
the state-of-the-art online random Fourier feature map methods, the proposed
MPU-FOGD can obtain better test accuracy.
