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trthatcher authored Nov 5, 2018
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6 changes: 6 additions & 0 deletions NEWS.md
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# MLKernels 0.4.0
* Updated to support julia 0.7
* `PairwiseFunction` renamed to `BaseFunction` and no longer exported
* `HyperParameters` deprecated
* `MemoryLayout` types (`ColumnMajor` & `RowMajor`) deprecated and replaced with `Val(:row)` and `Val(:col)`

# MLKernels 0.3.0
* Updated to support julia 0.6

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20 changes: 10 additions & 10 deletions README.md
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#### Summary

**MLKernels.jl** is a Julia package for Mercer kernel functions (or the
covariance functions used in Gaussian processes) that are used in the kernel
methods of machine learning. This package provides a flexible datatype for
**MLKernels.jl** is a Julia package for Mercer kernel functions (or the
covariance functions used in Gaussian processes) that are used in the kernel
methods of machine learning. This package provides a flexible datatype for
representing and constructing machine learning kernels as well as an efficient
set of methods to compute or approximate kernel matrices. The package has no
set of methods to compute or approximate kernel matrices. The package has no
dependencies beyond base Julia.

#### Documentation

Full [documentation](http://mlkernels.readthedocs.org/en/latest/) is available
Full [documentation](http://mlkernels.readthedocs.org/en/latest/) is available
on **Read the Docs**.

#### Visualization
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Non-linearly separable data may be linearly separable in the transformed space.
For example, the following data set is not linearly separable:

<p align="center"><img alt="Feature Space" src="doc/images/kerneltrick/featurespace.png" /></p>
<p align="center"><img alt="Feature Space" src="docs/images/featurespace.png" /></p>

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:

<p align="center"><img alt="Transformed Data" src="doc/images/kerneltrick/hilbertspace.png" /></p>
<p align="center"><img alt="Transformed Data" src="docs/images/hilbertspace.png" /></p>

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:

<p align="center"><img alt="Transformed Data" src="doc/images/kerneltrick/kernelgeometry.png" /></p>
<p align="center"><img alt="Transformed Data" src="docs/images/kernelgeometry.png" /></p>

When translated back to the original feature space, the conic section
corresponds to a circle which can be used to perfectly separate the data:

<p align="center"><img alt="Separating Hyperplane" src="doc/images/kerneltrick/featurespaceseparated.png" /></p>
<p align="center"><img alt="Separating Hyperplane" src="docs/images/featurespaceseparated.png" /></p>

The above plots were generated using
[PyPlot.jl](https://github.com/stevengj/PyPlot.jl).
[PyPlot.jl](https://github.com/stevengj/PyPlot.jl).
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