Data Science, Kernel Trick, Nonlinear Models, Machine Learning, Data Transformation.
Instead of this explicit mapping of samples using a function 𝜙(𝑥), kernel-based algorithms exploit the fact that certain functions 𝜅(𝑥,𝑦) can be expressed as the inner product <𝜙(𝑥),𝜙(𝑦)> in another space. Or the other way around: for certain functions 𝜙(𝑥), there is function 𝜅(𝑥,𝑦), so that