## Clustergram

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, Mini Batch K-Means and Gaussian Mixture Model (scikit-learn only) clustering, plus hierarchical/agglomerative clustering using SciPy. Alternatively, you can create clustergram using from_* constructors based on alternative clustering algorithms.

## 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` and `scipy` 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))
cgram.fit(data)
cgram.plot()
``````

## Styling

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

``````seaborn.set(style='whitegrid')

cgram.plot(
ax=ax,
size=0.5,
linewidth=0.5,
cluster_style={"color": "lightblue", "edgecolor": "black"},
line_style={"color": "red", "linestyle": "-."},
figsize=(12, 8)
)
``````

## 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))
cgram.fit(data)
cgram.plot(figsize=(12, 8), pca_weighted=True)
``````

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

## Scikit-learn, SciPy and RAPIDS cuML backends

Clustergram offers three backends for the computation - `scikit-learn` and `scipy` which use CPU and RAPIDS.AI `cuML`, which uses GPU. Note that all 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')
cgram.fit(data)
cgram.plot()
``````

Using `cuML`:

``````cgram = Clustergram(range(1, 8), backend='cuML')
cgram.fit(data)
cgram.plot()
``````

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

## Supported methods

Clustergram currently supports K-Means, Mini Batch K-Means, Gaussian Mixture Model and SciPy's hierarchical clustering methods. Note tha GMM and Mini Batch K-Means are supported only for `scikit-learn` backend and hierarchical methods are supported only for `scipy` backend.

Using K-Means (default):

``````cgram = Clustergram(range(1, 8), method='kmeans')
cgram.fit(data)
cgram.plot()
``````

Using Mini Batch K-Means, which can provide significant speedup over K-Means:

``````cgram = Clustergram(range(1, 8), method='minibatchkmeans', batch_size=100)
cgram.fit(data)
cgram.plot()
``````

Using Gaussian Mixture Model:

``````cgram = Clustergram(range(1, 8), method='gmm')
cgram.fit(data)
cgram.plot()
``````

Using Ward's hierarchical clustering:

``````cgram = Clustergram(range(1, 8), method='hierarchical', linkage='ward')
cgram.fit(data)
cgram.plot()
``````

## Manual input

Alternatively, you can create clustergram using `from_data` or `from_centers` methods based on alternative clustering algorithms.

Using `Clustergram.from_data` which creates cluster centers as mean or median values:

``````data = numpy.array([[-1, -1, 0, 10], [1, 1, 10, 2], [0, 0, 20, 4]])
labels = pandas.DataFrame({1: [0, 0, 0], 2: [0, 0, 1], 3: [0, 2, 1]})

cgram = Clustergram.from_data(data, labels)
cgram.plot()
``````

Using `Clustergram.from_centers` based on explicit cluster centers.:

``````labels = pandas.DataFrame({1: [0, 0, 0], 2: [0, 0, 1], 3: [0, 2, 1]})
centers = {
1: np.array([[0, 0]]),
2: np.array([[-1, -1], [1, 1]]),
3: np.array([[-1, -1], [1, 1], [0, 0]]),
}
cgram = Clustergram.from_centers(centers, labels)
cgram.plot(pca_weighted=False)
``````

To support PCA weighted plots you also need to pass data:

``````cgram = Clustergram.from_centers(centers, labels, data=data)
cgram.plot()
``````

## 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.fit(data)
cgram.plot(figsize=(12, 8))
``````

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

## Additional clustering performance evaluation

Clustergam includes handy wrappers around a selection of clustering performance metrics offered by
`scikit-learn`. Data which were originally computed on GPU are converted to numpy on the fly.

### Silhouette score

Compute the mean Silhouette Coefficient of all samples. See `scikit-learn` documentation for details.

``````>>> cgram.silhouette_score()
2    0.531540
3    0.447219
4    0.400154
5    0.377720
6    0.372128
7    0.331575
Name: silhouette_score, dtype: float64
``````

Once computed, resulting Series is available as `cgram.silhouette`. Calling the original method will recompute the score.

### Calinski and Harabasz score

Compute the Calinski and Harabasz score, also known as the Variance Ratio Criterion. See `scikit-learn` documentation for details.

``````>>> cgram.calinski_harabasz_score()
2    482.191469
3    441.677075
4    400.392131
5    411.175066
6    382.731416
7    352.447569
Name: calinski_harabasz_score, dtype: float64
``````

Once computed, resulting Series is available as `cgram.calinski_harabasz`. Calling the original method will recompute the score.

### Davies-Bouldin score

Compute the Davies-Bouldin score. See `scikit-learn` documentation for details.

``````>>> cgram.davies_bouldin_score()
2    0.714064
3    0.943553
4    0.943320
5    0.973248
6    0.950910
7    1.074937
Name: davies_bouldin_score, dtype: float64
``````

Once computed, resulting Series is available as `cgram.davies_bouldin`. Calling the original method will recompute the score.

## Acessing labels

`Clustergram` stores resulting labels for each of the tested options, which can be accessed as:

``````>>> cgram.labels
1  2  3  4  5  6  7
0    0  0  2  2  3  2  1
1    0  0  2  2  3  2  1
2    0  0  2  2  3  2  1
3    0  0  2  2  3  2  1
4    0  0  2  2  0  0  3
..  .. .. .. .. .. .. ..
337  0  1  1  3  2  5  0
338  0  1  1  3  2  5  0
339  0  1  1  1  1  1  4
340  0  1  1  3  2  5  5
341  0  1  1  1  1  1  5
``````

## 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

cgram.plot()
plt.savefig('clustergram.svg')
``````

### 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)
``````

## References

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.

## GitHub

https://github.com/martinfleis/clustergram