Biclustering documents with the Spectral Co-clustering algorithm

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 1.62s. V-measure: 0.4385
Done in 4.87s. V-measure: 0.3344

Best biclusters:
bicluster 0 : 1830 documents, 2522 words
categories   : 22%, 19% comp.sys.mac.hardware, 18%
words        : card, pc, ram, drive, bus, mac, motherboard, port, windows, floppy

bicluster 1 : 2385 documents, 3272 words
categories   : 18%, 18%, 15% sci.electronics
words        : bike, engine, car, dod, bmw, honda, oil, motorcycle, behanna, ysu

bicluster 2 : 1886 documents, 4236 words
categories   : 23% talk.politics.guns, 19% talk.politics.misc, 13%
words        : gun, guns, firearms, geb, drugs, banks, dyer, amendment, clinton, cdt

bicluster 3 : 1146 documents, 3261 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 4 : 1736 documents, 3959 words
categories   : 26% sci.crypt, 23%, 17%
words        : clipper, encryption, key, escrow, nsa, crypto, keys, intercon, secure, wiretap

from collections import defaultdict
import operator
from time import time

import numpy as np

from sklearn.cluster import SpectralCoclustering
from sklearn.cluster import MiniBatchKMeans
from sklearn.datasets import fetch_20newsgroups
from sklearn.feature_extraction.text import TfidfVectorizer
from sklearn.metrics.cluster import v_measure_score


def number_normalizer(tokens):
    """ Map 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.
    return ("#NUMBER" if token[0].isdigit() else token for token in tokens)

class NumberNormalizingVectorizer(TfidfVectorizer):
    def build_tokenizer(self):
        tokenize = super().build_tokenizer()
        return lambda doc: list(number_normalizer(tokenize(doc)))

# 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 = NumberNormalizingVectorizer(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]
    # Note: the following is identical to X[rows[:, np.newaxis],
    # cols].sum() but much faster in scipy <= 0.16
    weight = X[rows][:, cols].sum()
    cut = (X[row_complement][:, cols].sum() +
           X[rows][:, 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(d.items(), key=operator.itemgetter(1), reverse=True)

bicluster_ncuts = list(bicluster_ncut(i)
                       for i in range(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)))

Total running time of the script: ( 0 minutes 9.376 seconds)

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