Clustering cosine similarity matrix

clustering_cosine_similarity_matrix.py

"""
### Problem Statement ###
Let's say you have a square matrix which consists of cosine similarities (values between 0 and 1).
This square matrix can be of any size. 
You want to get clusters which maximize the values between elemnts in the cluster.
For example, for the following matrix:

  |  A  |  B  |  C  |  D
A | 1.0 | 0.1 | 0.6 |  0.4
B | 0.1 | 1.0 | 0.1 |  0.2
C | 0.6 | 0.1 | 1.0 |  0.7
D | 0.4 | 0.2 | 0.7 |  1.0

You should get 2 clusters:
cluster #1: B
cluster #2: A, C, D
"""

import numpy as np
from sklearn.cluster import SpectralClustering
mat = np.matrix([[1.,.1,.6,.4],[.1,1.,.1,.2],[.6,.1,1.,.7],[.4,.2,.7,1.]])
SpectralClustering(2).fit_predict(mat)
# >>> array([0, 1, 0, 0], dtype=int32)

# i.e., A, C, D belong to Cluster "0"
# whereas B belongs to Cluster "1"
# The algorithm takes the top k eigenvectors of the input matrix corresponding to the largest eigenvalues, 
# then runs the k-mean algorithm on the new matrix. Here is a simple code that does this for your matrix:

from sklearn.cluster import KMeans
eigen_values, eigen_vectors = np.linalg.eigh(mat)
KMeans(n_clusters=2, init='k-means++').fit_predict(eigen_vectors[:, 2:4])
# >>> array([0, 1, 0, 0], dtype=int32)

# For the cases you want the algorithm to figure out the number of clusters by itself, 
# you can use Density Based Clustering Algorithms like DBSCAN:

from sklearn.cluster import DBSCAN
DBSCAN(min_samples=1).fit_predict(mat)
# >>> array([0, 1, 2, 2])

Source: http://stackoverflow.com/a/30093501

(y)

Hi
When we want to predict the cluster of a new point, what should we do?
For example, A, B, C and D are vectors and the matrix based on their cosine-similarity is as input and now for the new vector E, how to predict its cluster?