Tutorials that provide intuition about the separating planes and surfaces of linear and non-linear classifiers.
- Python
- Numpy
- SageMath
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:
Inspired by Christopher Olah's post on Neural Networks, Manifolds and Topology