scipy.cluster.hierarchy.from_mlab_linkage

scipy.cluster.hierarchy.from_mlab_linkage(Z)

Convert a linkage matrix generated by MATLAB(TM) to a new linkage matrix compatible with this module.

The conversion does two things:

• the indices are converted from 1..N to 0..(N-1) form, and
• a fourth column Z[:,3] is added where Z[i,3] represents the number of original observations (leaves) in the non-singleton cluster i.

This function is useful when loading in linkages from legacy data files generated by MATLAB.

Parameters:

Z : ndarray

A linkage matrix generated by MATLAB(TM).

Returns:

ZS : ndarray

A linkage matrix compatible with scipy.cluster.hierarchy.

See also

linkage

for a description of what a linkage matrix is.

to_mlab_linkage

transform from Scipy to MATLAB format.

Examples

>>> import numpy as np
>>> from scipy.cluster.hierarchy import ward, from_mlab_linkage

Given a linkage matrix in MATLAB format mZ, we can use scipy.cluster.hierarchy.from_mlab_linkage to import it into Scipy format:

>>> mZ = np.array([[1, 2, 1], [4, 5, 1], [7, 8, 1],
...                [10, 11, 1], [3, 13, 1.29099445],
...                [6, 14, 1.29099445],
...                [9, 15, 1.29099445],
...                [12, 16, 1.29099445],
...                [17, 18, 5.77350269],
...                [19, 20, 5.77350269],
...                [21, 22,  8.16496581]])

>>> Z = from_mlab_linkage(mZ)
>>> Z
array([[  0.        ,   1.        ,   1.        ,   2.        ],
       [  3.        ,   4.        ,   1.        ,   2.        ],
       [  6.        ,   7.        ,   1.        ,   2.        ],
       [  9.        ,  10.        ,   1.        ,   2.        ],
       [  2.        ,  12.        ,   1.29099445,   3.        ],
       [  5.        ,  13.        ,   1.29099445,   3.        ],
       [  8.        ,  14.        ,   1.29099445,   3.        ],
       [ 11.        ,  15.        ,   1.29099445,   3.        ],
       [ 16.        ,  17.        ,   5.77350269,   6.        ],
       [ 18.        ,  19.        ,   5.77350269,   6.        ],
       [ 20.        ,  21.        ,   8.16496581,  12.        ]])

As expected, the linkage matrix Z returned includes an additional column counting the number of original samples in each cluster. Also, all cluster indexes are reduced by 1 (MATLAB format uses 1-indexing, whereas Scipy uses 0-indexing).