MLKernels.jl is a Julia package that provides a collection of common machine learning kernels and a set of methods to efficiently compute kernel matrices.
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Through the use of kernel functions, kernel-based methods may operate in a high (potentially infinite) dimensional implicit feature space without explicitly mapping data from the original feature space to the new feature space. Non-linearly separable data may be linearly separable in the transformed space. For example, the following data set is not linearly separable:
Using a Polynomial Kernel of degree 2, the points are mapped to a 3-dimensional space where a plane can be used to linearly separate the data:
Explicitly, the Polynomial Kernel of degree 2 maps the data to a cone in 3-dimensional space. The intersecting hyperplane forms a conic section with the cone:
When translated back to the original feature space, the conic section corresponds to a circle which can be used to perfectly separate the data:
The above plots were generated using PyPlot.jl.
about 16 hours ago