Pairplot: Visualizing High Dimensional Data

This example provides how to visualize high dimensional data using the pairplot.

[1]:
import graspologic

import numpy as np
%matplotlib inline
/home/runner/.cache/pypoetry/virtualenvs/graspologic-pkHfzCJ8-py3.10/lib/python3.10/site-packages/tqdm/auto.py:21: TqdmWarning: IProgress not found. Please update jupyter and ipywidgets. See https://ipywidgets.readthedocs.io/en/stable/user_install.html
  from .autonotebook import tqdm as notebook_tqdm

Simulate a binary graph using stochastic block model

The 3-block model is defined as below:

\begin{align*} n &= [50, 50, 50]\\ P &= \begin{bmatrix}0.5 & 0.1 & 0.05 \\ 0.1 & 0.4 & 0.15 \\ 0.05 & 0.15 & 0.3 \end{bmatrix} \end{align*}

Thus, the first 50 vertices belong to block 1, the second 50 vertices belong to block 2, and the last 50 vertices belong to block 3.

[2]:
from graspologic.simulations import sbm

n_communities = [50, 50, 50]
p = [[0.5, 0.1, 0.05],
     [0.1, 0.4, 0.15],
     [0.05, 0.15, 0.3],]

np.random.seed(2)
A = sbm(n_communities, p)

Embed using adjacency spectral embedding to obtain lower dimensional representation of the graph

The embedding dimension is automatically chosen. It should embed to 3 dimensions.

[3]:
from graspologic.embed import AdjacencySpectralEmbed

ase = AdjacencySpectralEmbed()
X = ase.fit_transform(A)

print(X.shape)
(150, 3)

Use pairplot to plot the embedded data

First we generate labels that correspond to blocks. We pass the labels along with the data for pair plot.

[4]:
from graspologic.plot import pairplot

labels = ['Block 1'] * 50 + ['Block 2'] * 50 + ['Block 3'] * 50

plot = pairplot(X, labels)
../../_images/tutorials_plotting_pairplot_7_0.png
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