# 23. Hierarchical Clustering

An implementation of hierarchical clustering is provided in the SciPy package. Among other things, it allows to build clusters from similarity matrices and make dendrogram plots. The following example shows how to do this for an already computed similarity matrix. The similarity data are computed from events in an area with induced seismicity (using the cross-correlation routines in `obspy.signal`) and can be fetched from our examples webserver:

First, we import the necessary modules and load the data stored on our webserver:

    >>> import io, urllib
    >>> import numpy as np
    >>> import matplotlib.pyplot as plt
    >>> from scipy.cluster import hierarchy
    >>> from scipy.spatial import distance
    >>>
    >>> url = "https://examples.obspy.org/dissimilarities.npz"
    >>> with io.BytesIO(urllib.urlopen(url).read()) as fh, np.load(fh) as data:
    ...     dissimilarity = data['dissimilarity']

Now, we can start building up the plots. First, we plot the dissimilarity matrix:

    >>> plt.subplot(121)
    >>> plt.imshow(1 - dissimilarity, interpolation="nearest")

After that, we use SciPy to build up and plot the dendrogram into the right-hand subplot:

    >>> dissimilarity = distance.squareform(dissimilarity)
    >>> threshold = 0.3
    >>> linkage = hierarchy.linkage(dissimilarity, method="single")
    >>> clusters = hierarchy.fcluster(linkage, threshold, criterion="distance")
    >>>
    >>> plt.subplot(122)
    >>> hierarchy.dendrogram(linkage, color_threshold=0.3)
    >>> plt.xlabel("Event number")
    >>> plt.ylabel("Dissimilarity")
    >>> plt.show()

(Source code, png, hires.png)

### Thank you!

We would like to thank our contributors, whose efforts make this software what it is. These people have helped by writing code and documentation, and by testing. They have created and maintained this product, its associated libraries and applications, our build tools and our web sites.

#### Contributors

- Ackerley, Nick
- Allgeyer, Sebastien
- Ammon, Charles J.
- Antunes, Emanuel
- Arnarsson, Ólafur St.
- Bank, Markus
- Barsch, Robert
- Behr, Yannik
- Bernardi, Fabrizio
- Bernauer, Felix
- Bes de Berc, Maxime
- Beyreuther, Moritz
- Boltz, Shawn
- Bonaimé, Sébastien
- Carothers, Lloyd
- Chamberlain, Calum
- Chambers, Derrick
- Chen, Zhao
- Clark, Adam
- Danecek, Peter
- Egdorf, Sven
- Engels, Fabian
- Ermert, Laura
- Eulenfeld, Tom

- Fabbri, Tommaso
- Falco, Nicholas
- Fee, Jeremy
- Grellier, Clément
- Grunberg, Marc
- Hammer, Conny
- Heimann, Sebastian
- Heiniger, Lukas
- Hope, Gaute
- Igel, Heiner
- Inza, Adolfo
- Isken, Marius
- Ketchum, David
- Koymans, Mathijs
- Kremers, Simon
- Kress, Victor
- Krieger, Lars
- Krischer, Lion
- Kula, Damian
- Käufl, Paul
- Köhler, Andreas
- Lecocq, Thomas
- Leeman, John
- Legovini, Paride

- Lesage, Philippe
- Li, Yulin
- Lomax, Anthony
- Lopes, Rui L.
- MacCarthy, Jonathan
- Maggi, Alessia
- Martin, Henri
- Medlin, Andrew
- Megies, Tobias
- Meschede, Matthias
- Michelini, Alberto
- Miller, Nathaniel C.
- Morgenstern, Bernhard
- Nof, Ran Novitsky
- Panning, Mark P.
- Parker, Tom
- Pestourie, Romain
- Rapagnani, Giovanni
- Reyes, Celso
- Ringler, Adam
- Rothenhäusler, Nicolas
- Russo, Emiliano
- Sales de Andrade, Elliott

- Satriano, Claudio
- Saul, Joachim
- Scheingraber, Chris
- Schneider, Simon
- Sippl, Christian
- Snoke, Arthur
- Stange, Stefan
- Stähler, Simon C.
- Sullivan, Benjamin
- Tian, Dongdong
- Trabant, Chad
- Trani, Luca
- Uieda, Leonardo
- Walker, Andrew
- Walther, Marcus
- Wassermann, Joachim
- Williams, Mark C.
- Winkelman, Andrew
- Zaccarelli, Riccardo
- Zad, Seyed Kasra Hosseini
- Zhu, Lijun
- van Driel, Martin
- van Wijk, Kasper

#### Funds

ObsPy was partially funded by the

- German Science Foundation (DFG) via grant DFG IG 16/9-1
- German Ministry for Education and Research (BMBF), GEOTECHNOLOGIEN grant 03G0646H.
- NERA project (Network of European Research Infrastructures for Earthquake Risk Assessment and Mitigation) under the European Community's Seventh Framework Programme (FP7/2007-2013) grant agreement n° 262330
- Leibniz Institute for Applied Geophysics (LIAG)
- VERCE EU-FP7 project (no. 283543)