Spherical k-means implementation in Python
I've been using scipy's k-means for quite some time now, and I'm pretty happy about the way it works in terms of usability and efficiency. However, now I want to explore different k-means variants, more specifically, I'd like to apply spherical k-means in some of my problems.
Do you know any good Python implementation (i.e. similar to scipy's k-means) of spherical k-means? If not, how hard would it be to modify scipy's source code to adapt its k-means algorithm to be spherical?
Thank you.
Answer
In spherical k-means, you aim to guarantee that the centers are on the sphere, so you could adjust the algorithm to use the cosine distance, and should additionally normalize the centroids of the final result.
When using the Euclidean distance, I prefer to think of the algorithm as projecting the cluster centers onto the unit sphere in each iteration, i.e., the centers should be normalized after each maximization step.
Indeed, when the centers and data points are both normalized, there is a 1-to-1 relationship between the cosine distance and Euclidean distance
|a - b|_2 = 2 * (1 - cos(a,b))
The package jasonlaska/spherecluster modifies scikit-learns's k-means into spherical k-means and also provides another sphere clustering algorithm.