machine-learning-tutorials

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

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:

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

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

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:

Thanks

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