Hierarchical Clustering with cosine similarity metric in fcluster package - linux

Question

I use scipy.cluster.hierarchy to do a hierarchical clustering on a set of points using "cosine" similarity metric. As an example, I have:
import scipy.cluster.hierarchy as hac
import matplotlib.pyplot as plt
Points =
np.array([[ 0. , 0.23508573],
[ 0.00754775 , 0.26717266],
[ 0.00595464 , 0.27775905],
[ 0.01220563 , 0.23622067],
[ 0.00542628 , 0.14185873],
[ 0.03078922 , 0.11273108],
[ 0.06707743 ,-0.1061131 ],
[ 0.04411757 ,-0.10775407],
[ 0.01349434 , 0.00112159],
[ 0.04066034 , 0.11639591],
[ 0. , 0.29046682],
[ 0.07338036 , 0.00609912],
[ 0.01864988 , 0.0316196 ],
[ 0. , 0.07270636],
[ 0. , 0. ]])
z = hac.linkage(Points, metric='cosine', method='complete')
labels = hac.fcluster(z, 0.1, criterion="distance")
plt.scatter(Points[:, 0], Points[:, 1], c=labels.astype(np.float))
plt.show()
Since I use cosine metric, in some cases the dot product of two vectors can be negative or norm of some vectors can be zero. It means z output will have some negative or infinite elements which is not valid for fcluster (as below):
z =
[[ 0.00000000e+00 1.00000000e+01 0.00000000e+00 2.00000000e+00]
[ 1.30000000e+01 1.50000000e+01 0.00000000e+00 3.00000000e+00]
[ 8.00000000e+00 1.10000000e+01 4.26658708e-13 2.00000000e+00]
[ 1.00000000e+00 2.00000000e+00 2.31748880e-05 2.00000000e+00]
[ 3.00000000e+00 4.00000000e+00 8.96700489e-05 2.00000000e+00]
[ 1.60000000e+01 1.80000000e+01 3.98805492e-04 5.00000000e+00]
[ 1.90000000e+01 2.00000000e+01 1.33225099e-03 7.00000000e+00]
[ 5.00000000e+00 9.00000000e+00 2.41120340e-03 2.00000000e+00]
[ 6.00000000e+00 7.00000000e+00 1.52914684e-02 2.00000000e+00]
[ 1.20000000e+01 2.20000000e+01 3.52441432e-02 3.00000000e+00]
[ 2.10000000e+01 2.40000000e+01 1.38662986e-01 1.00000000e+01]
[ 1.70000000e+01 2.30000000e+01 6.99056531e-01 4.00000000e+00]
[ 2.50000000e+01 2.60000000e+01 1.92543748e+00 1.40000000e+01]
[ -1.00000000e+00 2.70000000e+01 inf 1.50000000e+01]]
To solve this problem, I checked linkage() function and inside it I needed to check _hierarchy.linkage() method. I use pycharm text editor and when I asked for "linkage" source code, it opened up a python file namely "_hierarchy.py" inside the directory like the following:
.PyCharm40/system/python_stubs/-1247972723/scipy/cluster/_hierarchy.py
This python file doesn't have any definition for all included functions.
I am wondering what is the correct source of this function to revise it or is there another way to solve this problem.
I would be appreciated for your helps and hints.

Answer 1

You have a zero vector 0 0 in your data set. For such data, cosine distance is undefined, so you are using an inappropriate distance function!
This is a definition gap that cannot be trivially closed. inf is as incorrect as 0. The distance to 0 0 with cosine cannot be defined without contraditions. You must not use cosine on such data.
Back to your actual question: _hierarchy is a Cython module. It is not pure python, but it is compiled to native code. You can easily see the source code on Github:
https://github.com/scipy/scipy/blob/master/scipy/cluster/_hierarchy.pyx