Visualization and diagnostics for cluster analysis

Clustergram is a diagram proposed by Matthias Schonlau in his paper The clustergram: A graph for visualizing hierarchical and nonhierarchical cluster analyses.

In hierarchical cluster analysis, dendrograms are used to visualize how clusters are formed. I propose an alternative graph called a “clustergram” to examine how cluster members are assigned to clusters as the number of clusters increases. This graph is useful in exploratory analysis for nonhierarchical clustering algorithms such as k-means and for hierarchical cluster algorithms when the number of observations is large enough to make dendrograms impractical.

The clustergram was later implemented in R by Tal Galili, who also gives a thorough explanation of the concept.

This is a Python translation of Tal’s script written for scikit-learn and RAPIDS cuML implementations of K-Means and Gaussian Mixture Model (scikit-learn only) clustering.

Getting started

You can install clustergram from conda or pip:

conda install clustergram -c conda-forge
pip install clustergram

In any case, you still need to install your selected backend (scikit-learn or cuML).

The example of clustergram on Palmer penguins dataset:

import seaborn
df = seaborn.load_dataset('penguins')

First we have to select numerical data and scale them.

from sklearn.preprocessing import scale
data = scale(df.drop(columns=['species', 'island', 'sex']).dropna())

And then we can simply pass the data to clustergram.

from clustergram import Clustergram

cgram = Clustergram(range(1, 8))

Default clustergram


Clustergram.plot() returns matplotlib axis and can be fully customised as any other matplotlib plot.


    cluster_style={"color": "lightblue", "edgecolor": "black"},
    line_style={"color": "red", "linestyle": "-."},
    figsize=(12, 8)

Colored clustergram

Mean options

On the y axis, a clustergram can use mean values as in the original paper by Matthias Schonlau or PCA weighted mean values as in the implementation by Tal Galili.

cgram = Clustergram(range(1, 8), pca_weighted=True)
cgram.plot(figsize=(12, 8))

Default clustergram

cgram = Clustergram(range(1, 8), pca_weighted=False)
cgram.plot(figsize=(12, 8))

Default clustergram

Scikit-learn and RAPIDS cuML backends

Clustergram offers two backends for the computation - scikit-learn which uses CPU and RAPIDS.AI cuML, which uses GPU. Note that both are optional dependencies, but you will need at least one of them to generate clustergram.

Using scikit-learn (default):

cgram = Clustergram(range(1, 8), backend='sklearn')

Using cuML:

cgram = Clustergram(range(1, 8), backend='cuML')

data can be all data types supported by the selected backend (including cudf.DataFrame with cuML backend).

Supported methods

Clustergram currently supports K-Means and Gaussian Mixture Model clustering methods. Note tha GMM is supported only for scikit-learn backend.

Using K-Means (default):

cgram = Clustergram(range(1, 8), method='kmeans')

Using Gaussian Mixture Model:

cgram = Clustergram(range(1, 8), method='gmm')

Partial plot

Clustergram.plot() can also plot only a part of the diagram, if you want to focus on a limited range of k.

cgram = Clustergram(range(1, 20))
cgram.plot(figsize=(12, 8))

Long clustergram

cgram.plot(k_range=range(3, 10), figsize=(12, 8))

Limited clustergram

Saving clustergram

You can save both plot and clustergram.Clustergram to a disk.

Saving plot

Clustergram.plot() returns matplotlib axis object and as such can be saved as any other plot:

import matplotlib.pyplot as plt


Saving object

If you want to save your computed clustergram.Clustergram object to a disk, you can use pickle library:

import pickle

with open('clustergram.pickle','wb') as f:
    pickle.dump(cgram, f)

Then loading is equally simple:

with open('clustergram.pickle','rb') as f:
    loaded = pickle.load(f)


Schonlau M. The clustergram: a graph for visualizing hierarchical and non-hierarchical cluster analyses. The Stata Journal, 2002; 2 (4):391-402.

Schonlau M. Visualizing Hierarchical and Non-Hierarchical Cluster Analyses with Clustergrams. Computational Statistics: 2004; 19(1):95-111.