PCA 3D Visualizations

This module produces informative visualizations of atleast 3-dimensional data, optionally using principal component analysis and automatic clustering.

Features

• Animated: high-quality videos with multi-processed video production using pympanim.
• (Pdf) snapshots that can be used in research papers or where the full video cannot be used.
• Supports automatic clustering for informative zooms
• Supports trajectories of data, for example for visualizing data through time for a recurrent network or through layers of a feedforward network.
• Supports using different markers, in any combination of style and color

Installation

This package requires ffmpeg to be installed.

pip install pca3dvis

Example Videos

examples/gaus_balls.py

https://youtu.be/n9rpWhuN6LA

examples/all_rand.py

https://www.youtube.com/watch?v=YnIRqSQ8lAU

Usage

Video introduction at https://youtu.be/JqfVY9pdxY8

Projecting to 3D from higher dimensions

There are many approaches for projecting to 3-dimensions. Once you have used any of these projections, you can use this library to visualize the resulting 3d scatter plot.

This library provides one linear projection that depends on the eigenvectors of the covariance matrix, called principal component analysis. For more information see Wold, Esbensen, and Geladi, 1987

To quickly generate a pca3dvis.trajectory.ProjectedTrajectory using this technique for an arbitrary ndarray[samples, features] where features > 3, the following snippet will work:

import numpy as np
import pca3dvis.pcs as pcs

data: np.ndarray # must have shape [samples > 3, features > 3]
lbls: np.ndarray # must have shape [samples = data.shape[0], ...]
traj = pcs.get_pc_trajectory([data], lbls)

This creates a trajectory with a single snapshot; for multiple snapshots, just have [data] instead be a list of ndarrays which each have the same number of samples but possibly different numbers of features.

Converting 3D data to trajectories

A trajectory is a sequence of one or more snapshots which have the same labels. They include the projection matrix that created them from the original data. For quickly plotting already projected data, the labels can be swapped with all zeros of the appropriate shape and the projection matrix with the identity map.

import numpy as np
import pca3dvis.snapshot
import pca3dvis.trajectory

raw_data: np.ndarray # must have shape [samples > 3, og_features]
proj_matrices: np.ndarray # must have shape [og_features, 3]
lbls: np.ndarray # must have shape [samples = data.shape[0], ...]
snap = pca3dvis.snapshot.project_with_matrix(raw_data, lbls, proj_matrices)

traj = pca3dvis.trajectory.ProjectedTrajectory([snap]) # trajectory of one snap

Plotting trajectories

Plotting trajectories, the main feature of this module, requires only that you give a name to each snapshot and give markers to each label.

Markers are described as follows: Suppose there are N samples and M distinct styles. Then for each style m, you will create a bool numpy array with shape (N,) mask where mask[i] is True if sample[i] should be rendered with style m. The style is described with a dict which are the keyword arguments to scatter. It should at least specifiy the size and color (s and c respectively), and it may use a colormap to do so, but if it does it must specify the norm exactly, i.e., with vmin and vmax not None.

For a more complete example of styling, see examples/gaus_balls.py.

import numpy as np
import pca3dvis.trajectory
import pca3dvis.worker

traj: pca3dvis.trajectory.ProjectedTrajectory
titles = [f'Snapshot {i+1}' for i in range(traj.num_snapshots)]
markers = [(
    np.ones(traj.num_samples, 'bool'),
    {'s': 20, 'c': 'tab:red'}
)]
pca3dvis.worker.generate(traj, markers, titles, 'out/my_out_folder',
                         draft=True, clusters=True)