Clustering in Python can be nicely done using the statistical tools provided by the ` sklearn ` library.

For example, the `DBSCAN` method easily implements a clustering algorithm that detects connected regions, given a maximum distance between two elements of a cluster.

However, natively the library does not support periodic boundaries, which can be sometimes annoying. But an easy workaround can be found precisely exploiting the power of the library: methods like `DBSCAN` can be given in input distance matrices directly, and then the clustering is computed on these.

The workaround is to compute the distance matrix with the periodic boundaries in it. The easiest way that I have found is to use the `scipy` function `pdist` on each coordinate, correct for the periodic boundaries, then combine the result in order to obtain a distance matrix (in square form) that can be digested by `DBSCAN`.

The following example may give you a better feeling of how it works.

import pylab as pl from sklearn.cluster import DBSCAN from scipy.spatial.distance import pdist,squareform # box size L=5. threshold=0.3 # create data X=pl.uniform(-1,1, size=(500,2)) # create for corners X[XL*0.5]-=L # finding clusters, no periodic boundaries db=DBSCAN(eps=threshold).fit(X) pl.scatter(X[:,0], X[:,1],c=db.labels_, s=3,edgecolors='None') pl.figure() # 1) find the correct distance matrix for d in xrange(X.shape[1]): # find all 1-d distances pd=pdist(X[:,d].reshape(X.shape[0],1)) # apply boundary conditions pd[pd>L*0.5]-=L try: # sum total+=pd**2 except Exception, e: # or define the sum if not previously defined total=pd**2 # transform the condensed distance matrix... total=pl.sqrt(total) # ...into a square distance matrix square=squareform(total) db=DBSCAN(eps=threshold, metric='precomputed').fit(square) pl.scatter(X[:,0], X[:,1],c=db.labels_,s=3, edgecolors='None') pl.show()

Before the periodic boundaries (Lx=Ly=5):

… and after (Lx=Ly=5):