SVM kernel approximation with Python
Introduction A high-performance SVM classifier will likely need thousands of support vectors, and the resulting high complexity of classification prevents their use in many practical applications, with large numbers of training samples or large numbers of features in the input space. To handle this, several approximations to the RBF kernel (and similar kernels) have been devised. Typically, these take the form of a function z that maps a single vector to a vector of higher dimensionality, approximating the kernel. where Phi is the implicit mapping embedded in the RBF kernel. Implementation Scikit-learn has already implemented Fourier transform and Nystroem approximation techniques using RBFSampler and Nystroem classes accordingly. import matplotlib.pyplot as plt import numpy as np from sklearn import datasets, svm, pipeline from sklearn.kernel_approximation import (RBFSampler, Nystroem) # The digits dataset digits = datasets.load_digits(n_class=9) # To apply an clas...