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Biclustering documents with the Spectral Co-clustering algorithmΒΆ

This example demonstrates the Spectral Co-clustering algorithm on the twenty newsgroups dataset. The ‘’ category is excluded because it contains many posts containing nothing but data.

The TF-IDF vectorized posts form a word frequency matrix, which is then biclustered using Dhillon’s Spectral Co-Clustering algorithm. The resulting document-word biclusters indicate subsets words used more often in those subsets documents.

For a few of the best biclusters, its most common document categories and its ten most important words get printed. The best biclusters are determined by their normalized cut. The best words are determined by comparing their sums inside and outside the bicluster.

For comparison, the documents are also clustered using MiniBatchKMeans. The document clusters derived from the biclusters achieve a better V-measure than clusters found by MiniBatchKMeans.


Done in 9.53s. V-measure: 0.4455
Done in 12.00s. V-measure: 0.3309

Best biclusters:
bicluster 0 : 1951 documents, 4373 words
categories   : 23% talk.politics.guns, 19% talk.politics.misc, 14%
words        : gun, guns, geb, banks, firearms, drugs, gordon, clinton, cdt, amendment

bicluster 1 : 1165 documents, 3304 words
categories   : 29% talk.politics.mideast, 26% soc.religion.christian, 25% alt.atheism
words        : god, jesus, christians, atheists, kent, sin, morality, belief, resurrection, marriage

bicluster 2 : 2219 documents, 2830 words
categories   : 18% comp.sys.mac.hardware, 16%, 16%
words        : voltage, dsp, board, receiver, circuit, shipping, packages, stereo, compression, package

bicluster 3 : 1860 documents, 2745 words
categories   : 26%, 23%, 13%
words        : bike, car, dod, engine, motorcycle, ride, honda, cars, bmw, bikes

bicluster 4 : 12 documents, 155 words
categories   : 100%
words        : scorer, unassisted, reichel, semak, sweeney, kovalenko, ricci, audette, momesso, nedved

Python source code:

from __future__ import print_function


from collections import defaultdict
import operator
import re
from time import time

import numpy as np

from sklearn.cluster.bicluster import SpectralCoclustering
from sklearn.cluster import MiniBatchKMeans
from sklearn.externals import six
from sklearn.datasets.twenty_newsgroups import fetch_20newsgroups
from sklearn.feature_extraction.text import TfidfVectorizer
from sklearn.metrics.cluster import v_measure_score

def number_aware_tokenizer(doc):
    """ Tokenizer that maps all numeric tokens to a placeholder.

    For many applications, tokens that begin with a number are not directly
    useful, but the fact that such a token exists can be relevant.  By applying
    this form of dimensionality reduction, some methods may perform better.
    token_pattern = re.compile(u'(?u)\\b\\w\\w+\\b')
    tokens = token_pattern.findall(doc)
    tokens = ["#NUMBER" if token[0] in "0123456789_" else token
              for token in tokens]
    return tokens

# exclude ''
categories = ['alt.atheism', '',
              '', 'comp.sys.mac.hardware',
              '', '', '',
              '', '',
              '', 'sci.crypt', 'sci.electronics',
              '', '', 'soc.religion.christian',
              'talk.politics.guns', 'talk.politics.mideast',
              'talk.politics.misc', 'talk.religion.misc']
newsgroups = fetch_20newsgroups(categories=categories)
y_true =

vectorizer = TfidfVectorizer(stop_words='english', min_df=5,
cocluster = SpectralCoclustering(n_clusters=len(categories),
                                 svd_method='arpack', random_state=0)
kmeans = MiniBatchKMeans(n_clusters=len(categories), batch_size=20000,

X = vectorizer.fit_transform(

start_time = time()
y_cocluster = cocluster.row_labels_
print("Done in {:.2f}s. V-measure: {:.4f}".format(
    time() - start_time,
    v_measure_score(y_cocluster, y_true)))

start_time = time()
y_kmeans = kmeans.fit_predict(X)
print("Done in {:.2f}s. V-measure: {:.4f}".format(
    time() - start_time,
    v_measure_score(y_kmeans, y_true)))

feature_names = vectorizer.get_feature_names()
document_names = list(newsgroups.target_names[i] for i in

def bicluster_ncut(i):
    rows, cols = cocluster.get_indices(i)
    if not (np.any(rows) and np.any(cols)):
        import sys
        return sys.float_info.max
    row_complement = np.nonzero(np.logical_not(cocluster.rows_[i]))[0]
    col_complement = np.nonzero(np.logical_not(cocluster.columns_[i]))[0]
    weight = X[rows[:, np.newaxis], cols].sum()
    cut = (X[row_complement[:, np.newaxis], cols].sum() +
           X[rows[:, np.newaxis], col_complement].sum())
    return cut / weight

def most_common(d):
    """Items of a defaultdict(int) with the highest values.

    Like Counter.most_common in Python >=2.7.
    return sorted(six.iteritems(d), key=operator.itemgetter(1), reverse=True)

bicluster_ncuts = list(bicluster_ncut(i)
                       for i in xrange(len(newsgroups.target_names)))
best_idx = np.argsort(bicluster_ncuts)[:5]

print("Best biclusters:")
for idx, cluster in enumerate(best_idx):
    n_rows, n_cols = cocluster.get_shape(cluster)
    cluster_docs, cluster_words = cocluster.get_indices(cluster)
    if not len(cluster_docs) or not len(cluster_words):

    # categories
    counter = defaultdict(int)
    for i in cluster_docs:
        counter[document_names[i]] += 1
    cat_string = ", ".join("{:.0f}% {}".format(float(c) / n_rows * 100, name)
                           for name, c in most_common(counter)[:3])

    # words
    out_of_cluster_docs = cocluster.row_labels_ != cluster
    out_of_cluster_docs = np.where(out_of_cluster_docs)[0]
    word_col = X[:, cluster_words]
    word_scores = np.array(word_col[cluster_docs, :].sum(axis=0) -
                           word_col[out_of_cluster_docs, :].sum(axis=0))
    word_scores = word_scores.ravel()
    important_words = list(feature_names[cluster_words[i]]
                           for i in word_scores.argsort()[:-11:-1])

    print("bicluster {} : {} documents, {} words".format(
        idx, n_rows, n_cols))
    print("categories   : {}".format(cat_string))
    print("words        : {}\n".format(', '.join(important_words)))