# Kernels (ML) Mercers theorem gives us equality between the **kernel function** and the **inner product** of some feature mapped observations. See this video [here](https://www.youtube.com/watch?v=v7uWNN8S7LY&list=PLAJOFd5cEXsrNcvSgEDgRSZ0G6mQOtCIT&index=4). For a visualization of this, see [this part](https://youtu.be/v7uWNN8S7LY?list=PLAJOFd5cEXsrNcvSgEDgRSZ0G6mQOtCIT&t=788) of the video. And [here](https://www.youtube.com/watch?v=v7uWNN8S7LY&list=PLAJOFd5cEXsrNcvSgEDgRSZ0G6mQOtCIT&index=4&t=880s) is a good example. ### Kernel Trick The kernel trick is effectively a way to compute similarities (dot products) between our points in the high dimensional space, without ever needing to transform all of our points to the high dimensional space. --- Date: 20211222 Links to: [Basis Functions](Basis%20Functions.md) Tags: References: * [Kernels (youtube, ritvikmath)](https://www.youtube.com/watch?v=OKFMZQyDROI&t=397s) * [04 - THE KERNEL TRICK - INTRODUCTION TO REGRESSION AND KERNEL METHODS - YouTube](https://www.youtube.com/watch?v=v7uWNN8S7LY&list=PLAJOFd5cEXsrNcvSgEDgRSZ0G6mQOtCIT&index=4) * [Kernels! - YouTube](https://www.youtube.com/watch?v=y_RjsDHl5Y4&t=4238s) * [Gaussian Processes - YouTube](https://www.youtube.com/watch?v=UBDgSHPxVME) * [Kernel Cookbook](https://www.cs.toronto.edu/~duvenaud/cookbook/) * [Kernel Functions for Machine Learning Applications – César Souza](http://crsouza.com/2010/03/17/kernel-functions-for-machine-learning-applications/)