Random Fourier Kernel Features
Approximate an RBF kernel with fixed random sinusoidal features and inspect finite-sample error.
Free theory articleApproximate an RBF kernel with fixed random sinusoidal features and inspect finite-sample error.
Concept & interpretation
Random Fourier Features provide a scalable way to approximate the Radial Basis Function (RBF) kernel for support vector machines and other kernel methods. Rather than computing the exact kernel matrix which scales quadratically with dataset size, we project inputs into a low-dimensional random feature space where the standard inner product approximates the kernel.
Experiment
Explore how the number of frequencies affects the approximation quality in the interactive module:
Random Fourier Kernel Features
- Set the Length scale to 1 and compare the exact and approximate curves.
- Increase the Frequency count to observe the approximate kernel converging toward the exact Gaussian shape.
- Observe that at x = y, the approximated kernel is always exactly 1, preserving the self-similarity property.