/machine-learning-tutorials

Machine Learning Tutorials

Primary LanguagePythonMIT LicenseMIT

machine-learning-tutorials

Tutorials that provide intuition about the separating planes and surfaces of linear and non-linear classifiers.

hyperplanes

Requirements

  • Python
  • Numpy
  • SageMath

Space Transformation

Let us explore the following example, having parabolic data points separated in two classes. A neural network can trivially solve this problem even with a small depth. The example data points and the separating planes look like the following:

parabolic_points_

The separating hyperplane can be illustrated better in 3D space:

parabolic_hyperplane_

Accordingly, if we picture the data-generating functions as continuous functions in a continuous space, we get the following:

parabolic_continuous

Finally, the applied neural network transformation to the data can be seen as a transformation to the data space followed be a linear separating hyperplane:

parabolic_transformation

Thanks

Inspired by Christopher Olah's post on Neural Networks, Manifolds and Topology