python-cluster is a "simple" package that allows to create several groups (clusters) of objects from a list. It's meant to be flexible and able to cluster any object. To ensure this kind of flexibility, you need not only to supply the list of objects, but also a function that calculates the similarity between two of those objects. For simple datatypes, like integers, this can be as simple as a subtraction, but more complex calculations are possible. Right now, it is possible to generate the clusters using a hierarchical clustering and the popular K-Means algorithm. For the hierarchical algorithm there are different "linkage" (single, complete, average and uclus) methods available.

Algorithms are based on the document found at http://www.elet.polimi.it/upload/matteucc/Clustering/tutorial_html/

A simple python program could look like this:

>>> from cluster import HierarchicalClustering
>>> data = [12,34,23,32,46,96,13]
>>> cl = HierarchicalClustering(data, lambda x,y: abs(x-y))
>>> cl.getlevel(10)     # get clusters of items closer than 10
[96, 46, [12, 13, 23, 34, 32]]
>>> cl.getlevel(5)      # get clusters of items closer than 5
[96, 46, [12, 13], 23, [34, 32]]

Note, that when you retrieve a set of clusters, it immediately starts the clustering process, which is quite complex. If you intend to create clusters from a large dataset, consider doing that in a separate thread.

For K-Means clustering it would look like this:

>>> from cluster import KMeansClustering
>>> cl = KMeansClustering([(1,1), (2,1), (5,3), ...])
>>> clusters = cl.getclusters(2)

The parameter passed to getclusters is the count of clusters generated.

Authors of new added functionalities:

• Garcia Aranda, Jose Javier jose_javier.garcia_aranda@alcatel-lucent.com
• Ramos Diaz, Juan juanrd0088@gmail.com

Acknoledgements:

Authors want to thank the Spanish Economy & competitiveness Ministry which funds this research through "INNPACTO" innovation program IPT-2012-0839-430000.

High dimensionality (HD) problems are those which have items with high number of dimensions There are two types of HD problems:: a)set of items with large number of dimensions. b)set of items with a limited number of dimensions from a large available number of dimensions For example considering dimensions X, Y, Z, K, L, M and the items: item1=(X=2, Z=5, L=7) item2=(X=6, Y=5, M=7)

The HD problems involves a high cost computation because distance functions in this case takes more operations than Low dimensionality problems.

For case "b" (valid also for "a"), a new distance for HD problems is available: HDdistItems() ,HDequals() This distance function compares dimensions between 2 items. Each dimension of item1 is searched in item2, and if it is found, then the distance takes into account the difference (manhattan style). If the dimension does not exist in item2, a maximum value is added to the total distance between item1 and item2

There is no difference with current usage:

>>>cl = KMeansClustering(users,HDdistItems,HDequals);

Additionally, now the number of iterations can be limited in order to save time Experimentally, we have concluded that 10 iterations is enough accurate for most cases. The new HDgetClusters() function is linear. Avoid the recalculation of centroids whereas original function getClusters() is N*N complex, because recalculate the centroid when move an item from one cluster to another. This new function can be used for low and high dimensionality problems, increasing performance in both cases:

>>>solution = cl.HDgetclusters(numclusters,max_iterations)

Other new available optimization inside HDcentroid() function in is the use of mean instead median at centroid calculation. median is more accurate but involves more computations when N is huge. The function HDcentroid() is invoked internally by HDgetclusters()