# Cluster documents and identify the prominent document in the cluster?

I have a set of documents as given in the example below.

doc1 = {'Science': 0.7, 'History': 0.05, 'Politics': 0.15, 'Sports': 0.1}
doc2 = {'Science': 0.3, 'History': 0.5, 'Politics': 0.1, 'Sports': 0.1}


I want to cluster the documents and identify the most prominent document within the cluster.

e.g, cluster 1 includes = {doc1, doc4, doc5. doc8} and I want to get the most prominent document that represents this cluster (e.g., doc8). (or to identify the main theme of the cluster)

Please let me know a suitable approach to achieve this :)

• How do you want to define prominence? How about proximity to the cluster centroid? It sounds like you want a graph theoretic definition, but you don't seem to have social data. – Emre Jul 6 '17 at 4:17
• I have a cosine similarity matrix and used DBSCAN for it to cluster the documents. Now I want to know what is the most representative document in a given cluster in order to identify the main theme of the cluster :) – Smith Jul 6 '17 at 6:12

A very simple approach would be to find some kind of centroid for each cluster (e.g. averaging the distributions of the documents belonging to each cluster respectively) and then calculating the cosine distance of each document within the cluster from the corresponding centroid. The document with the shorter distance will be the closest to the centroid, hence the most "representative".

Continuing from the previous example:

import pandas as pd
import numpy as np
from sklearn.metrics import pairwise_distances
from scipy.spatial.distance import cosine
from sklearn.cluster import DBSCAN
from sklearn.preprocessing import StandardScaler

# Initialize some documents
doc1 = {'Science':0.8, 'History':0.05, 'Politics':0.15, 'Sports':0.1}
doc2 = {'News':0.2, 'Art':0.8, 'Politics':0.1, 'Sports':0.1}
doc3 = {'Science':0.8, 'History':0.1, 'Politics':0.05, 'News':0.1}
doc4 = {'Science':0.1, 'Weather':0.2, 'Art':0.7, 'Sports':0.1}
collection = [doc1, doc2, doc3, doc4]
df = pd.DataFrame(collection)
# Fill missing values with zeros
df.fillna(0, inplace=True)
# Get Feature Vectors
feature_matrix = df.as_matrix()

# Fit DBSCAN
db = DBSCAN(min_samples=1, metric='precomputed').fit(pairwise_distances(feature_matrix, metric='cosine'))
labels = db.labels_
n_clusters_ = len(set(labels)) - (1 if -1 in labels else 0)
print('Estimated number of clusters: %d' % n_clusters_)

# Find the representatives
representatives = {}
for label in set(labels):
# Find indices of documents belonging to the same cluster
ind = np.argwhere(labels==label).reshape(-1,)
# Select these specific documetns
cluster_samples = feature_matrix[ind,:]
# Calculate their centroid as an average
centroid = np.average(cluster_samples, axis=0)
# Find the distance of each document from the centroid
distances = [cosine(sample_doc, centroid) for sample_doc in cluster_samples]
# Keep the document closest to the centroid as the representative
representatives[label] = cluster_samples[np.argsort(distances),:][0]

for label, doc in representatives.iteritems():
print("Label : %d -- Representative : %s" % (label, str(doc)))

• However, while running the code I get an error saying "AttributeError: 'dict' object has no attribute 'iteritems'". Do you know how to fix it? :) – Smith Jul 7 '17 at 0:26
• Use items instead. – Emre Jul 7 '17 at 1:28
• Please let me know if I should use cosine distance or 1 - cosine distance (in other words cosine similarity) in the fit parameter of DBSCAN? DBSCAN(min_samples=1, metric='precomputed').fit(pairwise_distances(feature_matrix, metric='cosine')) – Smith Jul 7 '17 at 3:45
• @Smith, according to the sklearn.DBSCAN fit documentation you should use a distance matrix as input, not a similarity matrix.. You will need to play around with the min_samples, eps parameters according to your data.. – Bogas Jul 7 '17 at 7:56
• Please let me know if you know an answer for this datascience.stackexchange.com/questions/20255/… – Smith Jul 9 '17 at 3:49