upper triangular and squareform of same distance matrix yield different linkage solutions about scipy-cluster HOT 2 CLOSED

Hi again,
 after consulting the source code we found that when using a square matrix as input
to linkage, linkage assumes the input is data -- not a distance matrix -- and
calculates a new distance matrix by calling pdist.  Thus:
where 
Y = pdist(data) and Y_sq = squareform(Y),

linkage(Y_sq) is equivalent to linkage(pdist(Y_sq, metric='euclidean'))

cheers,
Andy

Hi Andy,

Thanks for your report. As you stated, the two possibilities for the first 
input to
``linkage`` is either:
   * the upper triangular of the distance matrix Y, or
   * the original matrix of observations X used to produce Y via pdist.

This is consistent with MATLAB's documentation as shown below.
"""
Z = linkage(y)
Z = linkage(y,method)
Z = linkage(X,method,metric)
Z = linkage(X,method,inputs)
"""

This is also consistent with the hcluster documentation.

"""
Z = linkage(X, method, metric='euclidean')

 Performs hierarchical clustering on the objects defined by the
 n by m observation matrix X.
"""

I hope this helps.

Thanks,

Damian