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Plot Document Clustering

======================================= Clustering text documents using k-means

This is an example showing how the scikit-learn API can be used to cluster documents by topics using a Bag of Words approach <https://en.wikipedia.org/wiki/Bag-of-words_model>_.

Two algorithms are demonstrated, namely :class:~sklearn.cluster.KMeans and its more scalable variant, :class:~sklearn.cluster.MiniBatchKMeans. Additionally, latent semantic analysis is used to reduce dimensionality and discover latent patterns in the data.

This example uses two different text vectorizers: a

class:

~sklearn.feature_extraction.text.TfidfVectorizer and a

class:

~sklearn.feature_extraction.text.HashingVectorizer. See the example notebook :ref:sphx_glr_auto_examples_text_plot_hashing_vs_dict_vectorizer.py for more information on vectorizers and a comparison of their processing times.

For document analysis via a supervised learning approach, see the example script

ref:

sphx_glr_auto_examples_text_plot_document_classification_20newsgroups.py.

Imports for Text Document Clustering with K-Means, TF-IDF, and Latent Semantic Analysis

KMeans and MiniBatchKMeans partition TF-IDF document vectors into k clusters by iteratively assigning documents to the nearest centroid and recomputing centroids, but their effectiveness on raw high-dimensional text features is limited by the curse of dimensionality: In sparse TF-IDF spaces with thousands of features, distance metrics become less discriminative because all pairwise distances converge to similar values. TruncatedSVD (Latent Semantic Analysis) addresses this by projecting the sparse document-term matrix into a dense 100-dimensional space that captures the dominant semantic axes of variation, followed by Normalizer to project vectors onto the unit sphere where cosine similarity governs cluster assignments.

The evaluation framework uses both supervised metrics (homogeneity, completeness, V-measure, Adjusted Rand Index) that compare cluster labels against known newsgroup categories, and an unsupervised metric (Silhouette Coefficient) that measures intra-cluster cohesion versus inter-cluster separation: HashingVectorizer provides a memory-efficient alternative to TfidfVectorizer by mapping tokens to feature indices via a hash function without storing any vocabulary dictionary, at the cost of hash collisions and lost interpretability. The TfidfTransformer can be chained after HashingVectorizer to recover IDF weighting. Running each clustering configuration over 5 random seeds captures the variance due to k-means initialization sensitivity, which is especially pronounced in high-dimensional sparse spaces where initial centroids can land on outlier documents.

# Authors: The scikit-learn developers
# SPDX-License-Identifier: BSD-3-Clause

# %%
# Loading text data
# =================
#
# We load data from :ref:`20newsgroups_dataset`, which comprises around 18,000
# newsgroups posts on 20 topics. For illustrative purposes and to reduce the
# computational cost, we select a subset of 4 topics only accounting for around
# 3,400 documents. See the example
# :ref:`sphx_glr_auto_examples_text_plot_document_classification_20newsgroups.py`
# to gain intuition on the overlap of such topics.
#
# Notice that, by default, the text samples contain some message metadata such
# as `"headers"`, `"footers"` (signatures) and `"quotes"` to other posts. We use
# the `remove` parameter from :func:`~sklearn.datasets.fetch_20newsgroups` to
# strip those features and have a more sensible clustering problem.

import numpy as np

from sklearn.datasets import fetch_20newsgroups

categories = [
    "alt.atheism",
    "talk.religion.misc",
    "comp.graphics",
    "sci.space",
]

dataset = fetch_20newsgroups(
    remove=("headers", "footers", "quotes"),
    subset="all",
    categories=categories,
    shuffle=True,
    random_state=42,
)

labels = dataset.target
unique_labels, category_sizes = np.unique(labels, return_counts=True)
true_k = unique_labels.shape[0]

print(f"{len(dataset.data)} documents - {true_k} categories")

# %%
# Quantifying the quality of clustering results
# =============================================
#
# In this section we define a function to score different clustering pipelines
# using several metrics.
#
# Clustering algorithms are fundamentally unsupervised learning methods.
# However, since we happen to have class labels for this specific dataset, it is
# possible to use evaluation metrics that leverage this "supervised" ground
# truth information to quantify the quality of the resulting clusters. Examples
# of such metrics are the following:
#
# - homogeneity, which quantifies how much clusters contain only members of a
#   single class;
#
# - completeness, which quantifies how much members of a given class are
#   assigned to the same clusters;
#
# - V-measure, the harmonic mean of completeness and homogeneity;
#
# - Rand-Index, which measures how frequently pairs of data points are grouped
#   consistently according to the result of the clustering algorithm and the
#   ground truth class assignment;
#
# - Adjusted Rand-Index, a chance-adjusted Rand-Index such that random cluster
#   assignment have an ARI of 0.0 in expectation.
#
# If the ground truth labels are not known, evaluation can only be performed
# using the model results itself. In that case, the Silhouette Coefficient comes in
# handy. See :ref:`sphx_glr_auto_examples_cluster_plot_kmeans_silhouette_analysis.py`
# for an example on how to do it.
#
# For more reference, see :ref:`clustering_evaluation`.

from collections import defaultdict
from time import time

from sklearn import metrics

evaluations = []
evaluations_std = []

def fit_and_evaluate(km, X, name=None, n_runs=5):
    name = km.__class__.__name__ if name is None else name

    train_times = []
    scores = defaultdict(list)
    for seed in range(n_runs):
        km.set_params(random_state=seed)
        t0 = time()
        km.fit(X)
        train_times.append(time() - t0)
        scores["Homogeneity"].append(metrics.homogeneity_score(labels, km.labels_))
        scores["Completeness"].append(metrics.completeness_score(labels, km.labels_))
        scores["V-measure"].append(metrics.v_measure_score(labels, km.labels_))
        scores["Adjusted Rand-Index"].append(
            metrics.adjusted_rand_score(labels, km.labels_)
        )
        scores["Silhouette Coefficient"].append(
            metrics.silhouette_score(X, km.labels_, sample_size=2000)
        )
    train_times = np.asarray(train_times)

    print(f"clustering done in {train_times.mean():.2f} ± {train_times.std():.2f} s ")
    evaluation = {
        "estimator": name,
        "train_time": train_times.mean(),
    }
    evaluation_std = {
        "estimator": name,
        "train_time": train_times.std(),
    }
    for score_name, score_values in scores.items():
        mean_score, std_score = np.mean(score_values), np.std(score_values)
        print(f"{score_name}: {mean_score:.3f} ± {std_score:.3f}")
        evaluation[score_name] = mean_score
        evaluation_std[score_name] = std_score
    evaluations.append(evaluation)
    evaluations_std.append(evaluation_std)


# %%
# K-means clustering on text features
# ===================================
#
# Two feature extraction methods are used in this example:
#
# - :class:`~sklearn.feature_extraction.text.TfidfVectorizer` uses an in-memory
#   vocabulary (a Python dict) to map the most frequent words to features
#   indices and hence compute a word occurrence frequency (sparse) matrix. The
#   word frequencies are then reweighted using the Inverse Document Frequency
#   (IDF) vector collected feature-wise over the corpus.
#
# - :class:`~sklearn.feature_extraction.text.HashingVectorizer` hashes word
#   occurrences to a fixed dimensional space, possibly with collisions. The word
#   count vectors are then normalized to each have l2-norm equal to one
#   (projected to the euclidean unit-sphere) which seems to be important for
#   k-means to work in high dimensional space.
#
# Furthermore it is possible to post-process those extracted features using
# dimensionality reduction. We will explore the impact of those choices on the
# clustering quality in the following.
#
# Feature Extraction using TfidfVectorizer
# ----------------------------------------
#
# We first benchmark the estimators using a dictionary vectorizer along with an
# IDF normalization as provided by
# :class:`~sklearn.feature_extraction.text.TfidfVectorizer`.

from sklearn.feature_extraction.text import TfidfVectorizer

vectorizer = TfidfVectorizer(
    max_df=0.5,
    min_df=5,
    stop_words="english",
)
t0 = time()
X_tfidf = vectorizer.fit_transform(dataset.data)

print(f"vectorization done in {time() - t0:.3f} s")
print(f"n_samples: {X_tfidf.shape[0]}, n_features: {X_tfidf.shape[1]}")

# %%
# After ignoring terms that appear in more than 50% of the documents (as set by
# `max_df=0.5`) and terms that are not present in at least 5 documents (set by
# `min_df=5`), the resulting number of unique terms `n_features` is around
# 8,000. We can additionally quantify the sparsity of the `X_tfidf` matrix as
# the fraction of non-zero entries divided by the total number of elements.

print(f"{X_tfidf.nnz / np.prod(X_tfidf.shape):.3f}")

# %%
# We find that around 0.7% of the entries of the `X_tfidf` matrix are non-zero.
#
# .. _kmeans_sparse_high_dim:
#
# Clustering sparse data with k-means
# -----------------------------------
#
# As both :class:`~sklearn.cluster.KMeans` and
# :class:`~sklearn.cluster.MiniBatchKMeans` optimize a non-convex objective
# function, their clustering is not guaranteed to be optimal for a given random
# init. Even further, on sparse high-dimensional data such as text vectorized
# using the Bag of Words approach, k-means can initialize centroids on extremely
# isolated data points. Those data points can stay their own centroids all
# along.
#
# The following code illustrates how the previous phenomenon can sometimes lead
# to highly imbalanced clusters, depending on the random initialization:

from sklearn.cluster import KMeans

for seed in range(5):
    kmeans = KMeans(
        n_clusters=true_k,
        max_iter=100,
        n_init=1,
        random_state=seed,
    ).fit(X_tfidf)
    cluster_ids, cluster_sizes = np.unique(kmeans.labels_, return_counts=True)
    print(f"Number of elements assigned to each cluster: {cluster_sizes}")
print()
print(
    "True number of documents in each category according to the class labels: "
    f"{category_sizes}"
)

# %%
# To avoid this problem, one possibility is to increase the number of runs with
# independent random initiations `n_init`. In such case the clustering with the
# best inertia (objective function of k-means) is chosen.

kmeans = KMeans(
    n_clusters=true_k,
    max_iter=100,
    n_init=5,
)

fit_and_evaluate(kmeans, X_tfidf, name="KMeans\non tf-idf vectors")

# %%
# All those clustering evaluation metrics have a maximum value of 1.0 (for a
# perfect clustering result). Higher values are better. Values of the Adjusted
# Rand-Index close to 0.0 correspond to a random labeling. Notice from the
# scores above that the cluster assignment is indeed well above chance level,
# but the overall quality can certainly improve.
#
# Keep in mind that the class labels may not reflect accurately the document
# topics and therefore metrics that use labels are not necessarily the best to
# evaluate the quality of our clustering pipeline.
#
# Performing dimensionality reduction using LSA
# ---------------------------------------------
#
# A `n_init=1` can still be used as long as the dimension of the vectorized
# space is reduced first to make k-means more stable. For such purpose we use
# :class:`~sklearn.decomposition.TruncatedSVD`, which works on term count/tf-idf
# matrices. Since SVD results are not normalized, we redo the normalization to
# improve the :class:`~sklearn.cluster.KMeans` result. Using SVD to reduce the
# dimensionality of TF-IDF document vectors is often known as `latent semantic
# analysis <https://en.wikipedia.org/wiki/Latent_semantic_analysis>`_ (LSA) in
# the information retrieval and text mining literature.

from sklearn.decomposition import TruncatedSVD
from sklearn.pipeline import make_pipeline
from sklearn.preprocessing import Normalizer

lsa = make_pipeline(TruncatedSVD(n_components=100), Normalizer(copy=False))
t0 = time()
X_lsa = lsa.fit_transform(X_tfidf)
explained_variance = lsa[0].explained_variance_ratio_.sum()

print(f"LSA done in {time() - t0:.3f} s")
print(f"Explained variance of the SVD step: {explained_variance * 100:.1f}%")

# %%
# Using a single initialization means the processing time will be reduced for
# both :class:`~sklearn.cluster.KMeans` and
# :class:`~sklearn.cluster.MiniBatchKMeans`.

kmeans = KMeans(
    n_clusters=true_k,
    max_iter=100,
    n_init=1,
)

fit_and_evaluate(kmeans, X_lsa, name="KMeans\nwith LSA on tf-idf vectors")

# %%
# We can observe that clustering on the LSA representation of the document is
# significantly faster (both because of `n_init=1` and because the
# dimensionality of the LSA feature space is much smaller). Furthermore, all the
# clustering evaluation metrics have improved. We repeat the experiment with
# :class:`~sklearn.cluster.MiniBatchKMeans`.

from sklearn.cluster import MiniBatchKMeans

minibatch_kmeans = MiniBatchKMeans(
    n_clusters=true_k,
    n_init=1,
    init_size=1000,
    batch_size=1000,
)

fit_and_evaluate(
    minibatch_kmeans,
    X_lsa,
    name="MiniBatchKMeans\nwith LSA on tf-idf vectors",
)

# %%
# Top terms per cluster
# ---------------------
#
# Since :class:`~sklearn.feature_extraction.text.TfidfVectorizer` can be
# inverted we can identify the cluster centers, which provide an intuition of
# the most influential words **for each cluster**. See the example script
# :ref:`sphx_glr_auto_examples_text_plot_document_classification_20newsgroups.py`
# for a comparison with the most predictive words **for each target class**.

original_space_centroids = lsa[0].inverse_transform(kmeans.cluster_centers_)
order_centroids = original_space_centroids.argsort()[:, ::-1]
terms = vectorizer.get_feature_names_out()

for i in range(true_k):
    print(f"Cluster {i}: ", end="")
    for ind in order_centroids[i, :10]:
        print(f"{terms[ind]} ", end="")
    print()

# %%
# HashingVectorizer
# -----------------
# An alternative vectorization can be done using a
# :class:`~sklearn.feature_extraction.text.HashingVectorizer` instance, which
# does not provide IDF weighting as this is a stateless model (the fit method
# does nothing). When IDF weighting is needed it can be added by pipelining the
# :class:`~sklearn.feature_extraction.text.HashingVectorizer` output to a
# :class:`~sklearn.feature_extraction.text.TfidfTransformer` instance. In this
# case we also add LSA to the pipeline to reduce the dimension and sparcity of
# the hashed vector space.

from sklearn.feature_extraction.text import HashingVectorizer, TfidfTransformer

lsa_vectorizer = make_pipeline(
    HashingVectorizer(stop_words="english", n_features=50_000),
    TfidfTransformer(),
    TruncatedSVD(n_components=100, random_state=0),
    Normalizer(copy=False),
)

t0 = time()
X_hashed_lsa = lsa_vectorizer.fit_transform(dataset.data)
print(f"vectorization done in {time() - t0:.3f} s")

# %%
# One can observe that the LSA step takes a relatively long time to fit,
# especially with hashed vectors. The reason is that a hashed space is typically
# large (set to `n_features=50_000` in this example). One can try lowering the
# number of features at the expense of having a larger fraction of features with
# hash collisions as shown in the example notebook
# :ref:`sphx_glr_auto_examples_text_plot_hashing_vs_dict_vectorizer.py`.
#
# We now fit and evaluate the `kmeans` and `minibatch_kmeans` instances on this
# hashed-lsa-reduced data:

fit_and_evaluate(kmeans, X_hashed_lsa, name="KMeans\nwith LSA on hashed vectors")

# %%
fit_and_evaluate(
    minibatch_kmeans,
    X_hashed_lsa,
    name="MiniBatchKMeans\nwith LSA on hashed vectors",
)

# %%
# Both methods lead to good results that are similar to running the same models
# on the traditional LSA vectors (without hashing).
#
# Clustering evaluation summary
# ==============================

import matplotlib.pyplot as plt
import pandas as pd

fig, (ax0, ax1) = plt.subplots(ncols=2, figsize=(16, 6), sharey=True)

df = pd.DataFrame(evaluations[::-1]).set_index("estimator")
df_std = pd.DataFrame(evaluations_std[::-1]).set_index("estimator")

df.drop(
    ["train_time"],
    axis="columns",
).plot.barh(ax=ax0, xerr=df_std)
ax0.set_xlabel("Clustering scores")
ax0.set_ylabel("")

df["train_time"].plot.barh(ax=ax1, xerr=df_std["train_time"])
ax1.set_xlabel("Clustering time (s)")
plt.tight_layout()

# %%
# :class:`~sklearn.cluster.KMeans` and :class:`~sklearn.cluster.MiniBatchKMeans`
# suffer from the phenomenon called the `Curse of Dimensionality
# <https://en.wikipedia.org/wiki/Curse_of_dimensionality>`_ for high dimensional
# datasets such as text data. That is the reason why the overall scores improve
# when using LSA. Using LSA reduced data also improves the stability and
# requires lower clustering time, though keep in mind that the LSA step itself
# takes a long time, especially with hashed vectors.
#
# The Silhouette Coefficient is defined between 0 and 1. In all cases we obtain
# values close to 0 (even if they improve a bit after using LSA) because its
# definition requires measuring distances, in contrast with other evaluation
# metrics such as the V-measure and the Adjusted Rand Index which are only based
# on cluster assignments rather than distances. Notice that strictly speaking,
# one should not compare the Silhouette Coefficient between spaces of different
# dimension, due to the different notions of distance they imply.
#
# The homogeneity, completeness and hence v-measure metrics do not yield a
# baseline with regards to random labeling: this means that depending on the
# number of samples, clusters and ground truth classes, a completely random
# labeling will not always yield the same values. In particular random labeling
# won't yield zero scores, especially when the number of clusters is large. This
# problem can safely be ignored when the number of samples is more than a
# thousand and the number of clusters is less than 10, which is the case of the
# present example. For smaller sample sizes or larger number of clusters it is
# safer to use an adjusted index such as the Adjusted Rand Index (ARI). See the
# example
# :ref:`sphx_glr_auto_examples_cluster_plot_adjusted_for_chance_measures.py` for
# a demo on the effect of random labeling.
#
# The size of the error bars show that :class:`~sklearn.cluster.MiniBatchKMeans`
# is less stable than :class:`~sklearn.cluster.KMeans` for this relatively small
# dataset. It is more interesting to use when the number of samples is much
# bigger, but it can come at the expense of a small degradation in clustering
# quality compared to the traditional k-means algorithm.