  Kernel methods are powerful and flexible approach to solve many problems in
machine learning. Due to the pairwise evaluations in kernel methods, the
complexity of kernel computation grows as the data size increases; thus the
applicability of kernel methods is limited for large scale datasets. Random
Fourier Features (RFF) has been proposed to scale the kernel method for solving
large scale datasets by approximating kernel function using randomized Fourier
features. While this method proved very popular, still it exists shortcomings
to be effectively used. As RFF samples the randomized features from a
distribution independent of training data, it requires sufficient large number
of feature expansions to have similar performances to kernelized classifiers,
and this is proportional to the number samples in the dataset. Thus, reducing
the number of feature dimensions is necessary to effectively scale to large
datasets. In this paper, we propose a kernel approximation method in a data
dependent way, coined as Pseudo Random Fourier Features (PRFF) for reducing the
number of feature dimensions and also to improve the prediction performance.
The proposed approach is evaluated on classification and regression problems
and compared with the RFF, orthogonal random features and Nystr{\"o}m approach
