Search⌘ K
Home
Courses
Fundamentals of Machine Learning: A Pythonic Introduction

Kernel SVM and Sparsity

Explore how kernel SVMs extend linear boundaries to nonlinear ones by mapping data into high-dimensional spaces efficiently using kernels. Understand the dual formulation and sparsity concept that enables SVMs to generalize well with minimal support vectors. Learn how to implement kernel SVMs in Python using cvxpy and sklearn-style methods with visualizations.

We'll cover the following...

Kernels in SVM

The dual formulation straightforwardly offers kernelization of SVM. As we notice in the following dual optimization problem, the Gram matrix KK can be computed using any kernel function:

max⁡aaT1−12ayTKays.t.0≤a≤C\begin{aligned} \max_{\bold a} \quad & \bold a^T\bold 1 - \frac{1}{2}\bold a^T_{\bold y}K\bold a_{\bold y}\\ \textrm{s.t.} \quad & 0\le \bold a \le C \end{aligned} ...