scipy.cluster.hierarchy.median

scipy.cluster.hierarchy.median(y)

Perform median/WPGMC linkage.

See linkage for more information on the return structure and algorithm.

The following are common calling conventions:

1. Z = median(y)

   Performs median/WPGMC linkage on the condensed distance matrix y. See linkage for more information on the return structure and algorithm.

2. Z = median(X)

   Performs median/WPGMC linkage on the observation matrix X using Euclidean distance as the distance metric. See linkage for more information on the return structure and algorithm.

Parameters:

y : ndarray

A condensed distance matrix. A condensed distance matrix is a flat array containing the upper triangular of the distance matrix. This is the form that pdist returns. Alternatively, a collection of m observation vectors in n dimensions may be passed as a m by n array.

Returns:

Z : ndarray

The hierarchical clustering encoded as a linkage matrix.

See also

linkage

for advanced creation of hierarchical clusterings.

scipy.spatial.distance.pdist

pairwise distance metrics

Examples

>>> from scipy.cluster.hierarchy import median, fcluster
>>> from scipy.spatial.distance import pdist

First we need a toy dataset to play with:

x x    x x
x        x

x        x
x x    x x

>>> X = [[0, 0], [0, 1], [1, 0],
...      [0, 4], [0, 3], [1, 4],
...      [4, 0], [3, 0], [4, 1],
...      [4, 4], [3, 4], [4, 3]]

Then we get a condensed distance matrix from this dataset:

>>> y = pdist(X)

Finally, we can perform the clustering:

>>> Z = median(y)
>>> Z
array([[ 0.        ,  1.        ,  1.        ,  2.        ],
       [ 3.        ,  4.        ,  1.        ,  2.        ],
       [ 9.        , 10.        ,  1.        ,  2.        ],
       [ 6.        ,  7.        ,  1.        ,  2.        ],
       [ 2.        , 12.        ,  1.11803399,  3.        ],
       [ 5.        , 13.        ,  1.11803399,  3.        ],
       [ 8.        , 15.        ,  1.11803399,  3.        ],
       [11.        , 14.        ,  1.11803399,  3.        ],
       [18.        , 19.        ,  3.        ,  6.        ],
       [16.        , 17.        ,  3.5       ,  6.        ],
       [20.        , 21.        ,  3.25      , 12.        ]])

The linkage matrix Z represents a dendrogram - see scipy.cluster.hierarchy.linkage for a detailed explanation of its contents.

We can use scipy.cluster.hierarchy.fcluster to see to which cluster each initial point would belong given a distance threshold:

>>> fcluster(Z, 0.9, criterion='distance')
array([ 7,  8,  9, 10, 11, 12,  1,  2,  3,  4,  5,  6], dtype=int32)
>>> fcluster(Z, 1.1, criterion='distance')
array([5, 5, 6, 7, 7, 8, 1, 1, 2, 3, 3, 4], dtype=int32)
>>> fcluster(Z, 2, criterion='distance')
array([3, 3, 3, 4, 4, 4, 1, 1, 1, 2, 2, 2], dtype=int32)
>>> fcluster(Z, 4, criterion='distance')
array([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], dtype=int32)

Also scipy.cluster.hierarchy.dendrogram can be used to generate a plot of the dendrogram.