Colah’s Deformed Grid
Colah’s deformed grid is a popular visualization technique for illustrating the effects of non-linear transformations on data. It’s particularly useful for understanding concepts like:
- Recurrent Neural Networks (RNNs): How information is processed over time.
- Convolutional Neural Networks (CNNs): How spatial features are extracted from images.
- Autoencoders: How latent representations are learned.
In this article, we’ll learn how to plot this grid using Python’s matplotlib library.
Generating the Deformed Grid
First, we need to create a function to generate the deformed grid coordinates.
Function Definition
import numpy as np import matplotlib.pyplot as plt def generate_deformed_grid(grid_size, deformation_function): """Generates a deformed grid. Args: grid_size: The size of the grid (number of points per axis). deformation_function: A function that takes a 2D point as input and returns the deformed point. Returns: A tuple of 2 NumPy arrays containing the x and y coordinates of the grid points. """ x = np.linspace(0, 1, grid_size) y = np.linspace(0, 1, grid_size) xv, yv = np.meshgrid(x, y) # Apply the deformation function to each point in the grid deformed_x, deformed_y = deformation_function(xv, yv) return deformed_x, deformed_y Example Deformation Function
Let’s define a simple deformation function that stretches the grid along the y-axis.
def stretch_y(x, y): """Stretches the grid along the y-axis.""" return x, y * 2 Plotting the Grid
Creating and Plotting
# Generate the deformed grid deformed_x, deformed_y = generate_deformed_grid(20, stretch_y) # Plot the deformed grid plt.figure(figsize=(5, 5)) plt.plot(deformed_x, deformed_y, 'b.', markersize=1) plt.xlabel('X') plt.ylabel('Y') plt.title('Deformed Grid') plt.xlim(0, 1) plt.ylim(0, 1) plt.grid(True) plt.show() Output
This code will generate a plot similar to this:
[Output Image of the Deformed Grid] Customization
The beauty of Colah’s deformed grid lies in its ability to illustrate various transformations. You can customize the deformation function to achieve different effects.
Examples
- Rotation: Rotate the grid by a specific angle.
- Shearing: Shear the grid along one axis.
- Nonlinear Transformations: Apply more complex functions to create interesting visual effects.
Conclusion
This article has guided you through the process of plotting Colah’s deformed grid using matplotlib in Python. By creating custom deformation functions, you can visualize and understand the impact of different transformations on data. This is a powerful technique for gaining insights into various machine learning concepts.