Author(s): Utkarsh Mittal

Originally published on Towards AI.

What is a Kernel

A kernel is a similarity function. That is the whole idea.

After introducing kernels as similarity functions, the article walks through a simple dataset to show why a linear classifier fails and how lifting points to a higher-dimensional space can succeed—then reframes this lifting in terms of inner products so that the learning algorithm only needs pairwise products via a kernel function. It explains how the classifier can use a kernel matrix (pairwise similarities) instead of explicitly constructing feature maps, culminating in the idea that kernels allow computations equivalent to high- (or infinite-) dimensional dot products without ever explicitly transforming the data. The example is extended to highlight how the radial basis function kernel computes similarities through distance-based exponentials, effectively encoding an infinite set of features while keeping computation finite.

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Published via Towards AI