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<li><a class="reference internal" href="#">Clustering text documents using k-means</a><ul>
<li><a class="reference internal" href="#loading-text-data">Loading text data</a></li>
<li><a class="reference internal" href="#quantifying-the-quality-of-clustering-results">Quantifying the quality of clustering results</a></li>
<li><a class="reference internal" href="#k-means-clustering-on-text-features">K-means clustering on text features</a><ul>
<li><a class="reference internal" href="#feature-extraction-using-tfidfvectorizer">Feature Extraction using TfidfVectorizer</a></li>
<li><a class="reference internal" href="#clustering-sparse-data-with-k-means">Clustering sparse data with k-means</a></li>
<li><a class="reference internal" href="#performing-dimensionality-reduction-using-lsa">Performing dimensionality reduction using LSA</a></li>
<li><a class="reference internal" href="#top-terms-per-cluster">Top terms per cluster</a></li>
<li><a class="reference internal" href="#hashingvectorizer">HashingVectorizer</a></li>
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<p>Click <a class="reference internal" href="#sphx-glr-download-auto-examples-text-plot-document-clustering-py"><span class="std std-ref">here</span></a>
to download the full example code or to run this example in your browser via Binder</p>
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<section class="sphx-glr-example-title" id="clustering-text-documents-using-k-means">
<span id="sphx-glr-auto-examples-text-plot-document-clustering-py"></span><h1>Clustering text documents using k-means<a class="headerlink" href="#clustering-text-documents-using-k-means" title="Permalink to this heading">¶</a></h1>
<p>This is an example showing how the scikit-learn API can be used to cluster
documents by topics using a <a class="reference external" href="https://en.wikipedia.org/wiki/Bag-of-words_model">Bag of Words approach</a>.</p>
<p>Two algorithms are demoed: <a class="reference internal" href="../../modules/generated/sklearn.cluster.KMeans.html#sklearn.cluster.KMeans" title="sklearn.cluster.KMeans"><code class="xref py py-class docutils literal notranslate"><span class="pre">KMeans</span></code></a> and its more
scalable variant, <a class="reference internal" href="../../modules/generated/sklearn.cluster.MiniBatchKMeans.html#sklearn.cluster.MiniBatchKMeans" title="sklearn.cluster.MiniBatchKMeans"><code class="xref py py-class docutils literal notranslate"><span class="pre">MiniBatchKMeans</span></code></a>. Additionally,
latent semantic analysis is used to reduce dimensionality and discover latent
patterns in the data.</p>
<p>This example uses two different text vectorizers: a
<a class="reference internal" href="../../modules/generated/sklearn.feature_extraction.text.TfidfVectorizer.html#sklearn.feature_extraction.text.TfidfVectorizer" title="sklearn.feature_extraction.text.TfidfVectorizer"><code class="xref py py-class docutils literal notranslate"><span class="pre">TfidfVectorizer</span></code></a> and a
<a class="reference internal" href="../../modules/generated/sklearn.feature_extraction.text.HashingVectorizer.html#sklearn.feature_extraction.text.HashingVectorizer" title="sklearn.feature_extraction.text.HashingVectorizer"><code class="xref py py-class docutils literal notranslate"><span class="pre">HashingVectorizer</span></code></a>. See the example
notebook <a class="reference internal" href="plot_hashing_vs_dict_vectorizer.html#sphx-glr-auto-examples-text-plot-hashing-vs-dict-vectorizer-py"><span class="std std-ref">FeatureHasher and DictVectorizer Comparison</span></a>
for more information on vectorizers and a comparison of their processing times.</p>
<p>For document analysis via a supervised learning approach, see the example script
<a class="reference internal" href="plot_document_classification_20newsgroups.html#sphx-glr-auto-examples-text-plot-document-classification-20newsgroups-py"><span class="std std-ref">Classification of text documents using sparse features</span></a>.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="c1"># Author: Peter Prettenhofer <[email protected]></span>
<span class="c1"># Lars Buitinck</span>
<span class="c1"># Olivier Grisel <[email protected]></span>
<span class="c1"># Arturo Amor <[email protected]></span>
<span class="c1"># License: BSD 3 clause</span>
</pre></div>
</div>
<section id="loading-text-data">
<h2>Loading text data<a class="headerlink" href="#loading-text-data" title="Permalink to this heading">¶</a></h2>
<p>We load data from <a class="reference internal" href="../../datasets/real_world.html#newsgroups-dataset"><span class="std std-ref">The 20 newsgroups text dataset</span></a>, 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
<a class="reference internal" href="plot_document_classification_20newsgroups.html#sphx-glr-auto-examples-text-plot-document-classification-20newsgroups-py"><span class="std std-ref">Classification of text documents using sparse features</span></a>
to gain intuition on the overlap of such topics.</p>
<p>Notice that, by default, the text samples contain some message metadata such
as <code class="docutils literal notranslate"><span class="pre">"headers"</span></code>, <code class="docutils literal notranslate"><span class="pre">"footers"</span></code> (signatures) and <code class="docutils literal notranslate"><span class="pre">"quotes"</span></code> to other posts. We use
the <code class="docutils literal notranslate"><span class="pre">remove</span></code> parameter from <a class="reference internal" href="../../modules/generated/sklearn.datasets.fetch_20newsgroups.html#sklearn.datasets.fetch_20newsgroups" title="sklearn.datasets.fetch_20newsgroups"><code class="xref py py-func docutils literal notranslate"><span class="pre">fetch_20newsgroups</span></code></a> to
strip those features and have a more sensible clustering problem.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="kn">from</span> <span class="nn">sklearn.datasets</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.datasets.fetch_20newsgroups.html#sklearn.datasets.fetch_20newsgroups" title="sklearn.datasets.fetch_20newsgroups" class="sphx-glr-backref-module-sklearn-datasets sphx-glr-backref-type-py-function"><span class="n">fetch_20newsgroups</span></a>
<span class="n">categories</span> <span class="o">=</span> <span class="p">[</span>
<span class="s2">"alt.atheism"</span><span class="p">,</span>
<span class="s2">"talk.religion.misc"</span><span class="p">,</span>
<span class="s2">"comp.graphics"</span><span class="p">,</span>
<span class="s2">"sci.space"</span><span class="p">,</span>
<span class="p">]</span>
<span class="n">dataset</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.datasets.fetch_20newsgroups.html#sklearn.datasets.fetch_20newsgroups" title="sklearn.datasets.fetch_20newsgroups" class="sphx-glr-backref-module-sklearn-datasets sphx-glr-backref-type-py-function"><span class="n">fetch_20newsgroups</span></a><span class="p">(</span>
<span class="n">remove</span><span class="o">=</span><span class="p">(</span><span class="s2">"headers"</span><span class="p">,</span> <span class="s2">"footers"</span><span class="p">,</span> <span class="s2">"quotes"</span><span class="p">),</span>
<span class="n">subset</span><span class="o">=</span><span class="s2">"all"</span><span class="p">,</span>
<span class="n">categories</span><span class="o">=</span><span class="n">categories</span><span class="p">,</span>
<span class="n">shuffle</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span>
<span class="n">random_state</span><span class="o">=</span><span class="mi">42</span><span class="p">,</span>
<span class="p">)</span>
<span class="n">labels</span> <span class="o">=</span> <span class="n">dataset</span><span class="o">.</span><span class="n">target</span>
<span class="n">unique_labels</span><span class="p">,</span> <span class="n">category_sizes</span> <span class="o">=</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.unique.html#numpy.unique" title="numpy.unique" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">unique</span></a><span class="p">(</span><span class="n">labels</span><span class="p">,</span> <span class="n">return_counts</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="n">true_k</span> <span class="o">=</span> <span class="n">unique_labels</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
<span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"</span><span class="si">{</span><span class="nb">len</span><span class="p">(</span><span class="n">dataset</span><span class="o">.</span><span class="n">data</span><span class="p">)</span><span class="si">}</span><span class="s2"> documents - </span><span class="si">{</span><span class="n">true_k</span><span class="si">}</span><span class="s2"> categories"</span><span class="p">)</span>
</pre></div>
</div>
<div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>3387 documents - 4 categories
</pre></div>
</div>
</section>
<section id="quantifying-the-quality-of-clustering-results">
<h2>Quantifying the quality of clustering results<a class="headerlink" href="#quantifying-the-quality-of-clustering-results" title="Permalink to this heading">¶</a></h2>
<p>In this section we define a function to score different clustering pipelines
using several metrics.</p>
<p>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:</p>
<ul class="simple">
<li><p>homogeneity, which quantifies how much clusters contain only members of a
single class;</p></li>
<li><p>completeness, which quantifies how much members of a given class are
assigned to the same clusters;</p></li>
<li><p>V-measure, the harmonic mean of completeness and homogeneity;</p></li>
<li><p>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;</p></li>
<li><p>Adjusted Rand-Index, a chance-adjusted Rand-Index such that random cluster
assignment have an ARI of 0.0 in expectation.</p></li>
</ul>
<p>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.</p>
<p>For more reference, see <a class="reference internal" href="../../modules/clustering.html#clustering-evaluation"><span class="std std-ref">Clustering performance evaluation</span></a>.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">collections</span> <span class="kn">import</span> <a href="https://docs.python.org/3/library/collections.html#collections.defaultdict" title="collections.defaultdict" class="sphx-glr-backref-module-collections sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">defaultdict</span></a>
<span class="kn">from</span> <span class="nn">sklearn</span> <span class="kn">import</span> <span class="n">metrics</span>
<span class="kn">from</span> <span class="nn">time</span> <span class="kn">import</span> <a href="https://docs.python.org/3/library/time.html#time.time" title="time.time" class="sphx-glr-backref-module-time sphx-glr-backref-type-py-function"><span class="n">time</span></a>
<span class="n">evaluations</span> <span class="o">=</span> <span class="p">[]</span>
<span class="n">evaluations_std</span> <span class="o">=</span> <span class="p">[]</span>
<span class="k">def</span> <span class="nf">fit_and_evaluate</span><span class="p">(</span><span class="n">km</span><span class="p">,</span> <span class="n">X</span><span class="p">,</span> <span class="n">name</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">n_runs</span><span class="o">=</span><span class="mi">5</span><span class="p">):</span>
<span class="n">name</span> <span class="o">=</span> <span class="n">km</span><span class="o">.</span><span class="vm">__class__</span><span class="o">.</span><span class="vm">__name__</span> <span class="k">if</span> <span class="n">name</span> <span class="ow">is</span> <span class="kc">None</span> <span class="k">else</span> <span class="n">name</span>
<span class="n">train_times</span> <span class="o">=</span> <span class="p">[]</span>
<span class="n">scores</span> <span class="o">=</span> <a href="https://docs.python.org/3/library/collections.html#collections.defaultdict" title="collections.defaultdict" class="sphx-glr-backref-module-collections sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">defaultdict</span></a><span class="p">(</span><span class="nb">list</span><span class="p">)</span>
<span class="k">for</span> <span class="n">seed</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n_runs</span><span class="p">):</span>
<span class="n">km</span><span class="o">.</span><span class="n">set_params</span><span class="p">(</span><span class="n">random_state</span><span class="o">=</span><span class="n">seed</span><span class="p">)</span>
<span class="n">t0</span> <span class="o">=</span> <a href="https://docs.python.org/3/library/time.html#time.time" title="time.time" class="sphx-glr-backref-module-time sphx-glr-backref-type-py-function"><span class="n">time</span></a><span class="p">()</span>
<span class="n">km</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X</span><span class="p">)</span>
<span class="n">train_times</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><a href="https://docs.python.org/3/library/time.html#time.time" title="time.time" class="sphx-glr-backref-module-time sphx-glr-backref-type-py-function"><span class="n">time</span></a><span class="p">()</span> <span class="o">-</span> <span class="n">t0</span><span class="p">)</span>
<span class="n">scores</span><span class="p">[</span><span class="s2">"Homogeneity"</span><span class="p">]</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><a href="../../modules/generated/sklearn.metrics.homogeneity_score.html#sklearn.metrics.homogeneity_score" title="sklearn.metrics.homogeneity_score" class="sphx-glr-backref-module-sklearn-metrics sphx-glr-backref-type-py-function"><span class="n">metrics</span><span class="o">.</span><span class="n">homogeneity_score</span></a><span class="p">(</span><span class="n">labels</span><span class="p">,</span> <span class="n">km</span><span class="o">.</span><span class="n">labels_</span><span class="p">))</span>
<span class="n">scores</span><span class="p">[</span><span class="s2">"Completeness"</span><span class="p">]</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><a href="../../modules/generated/sklearn.metrics.completeness_score.html#sklearn.metrics.completeness_score" title="sklearn.metrics.completeness_score" class="sphx-glr-backref-module-sklearn-metrics sphx-glr-backref-type-py-function"><span class="n">metrics</span><span class="o">.</span><span class="n">completeness_score</span></a><span class="p">(</span><span class="n">labels</span><span class="p">,</span> <span class="n">km</span><span class="o">.</span><span class="n">labels_</span><span class="p">))</span>
<span class="n">scores</span><span class="p">[</span><span class="s2">"V-measure"</span><span class="p">]</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><a href="../../modules/generated/sklearn.metrics.v_measure_score.html#sklearn.metrics.v_measure_score" title="sklearn.metrics.v_measure_score" class="sphx-glr-backref-module-sklearn-metrics sphx-glr-backref-type-py-function"><span class="n">metrics</span><span class="o">.</span><span class="n">v_measure_score</span></a><span class="p">(</span><span class="n">labels</span><span class="p">,</span> <span class="n">km</span><span class="o">.</span><span class="n">labels_</span><span class="p">))</span>
<span class="n">scores</span><span class="p">[</span><span class="s2">"Adjusted Rand-Index"</span><span class="p">]</span><span class="o">.</span><span class="n">append</span><span class="p">(</span>
<a href="../../modules/generated/sklearn.metrics.adjusted_rand_score.html#sklearn.metrics.adjusted_rand_score" title="sklearn.metrics.adjusted_rand_score" class="sphx-glr-backref-module-sklearn-metrics sphx-glr-backref-type-py-function"><span class="n">metrics</span><span class="o">.</span><span class="n">adjusted_rand_score</span></a><span class="p">(</span><span class="n">labels</span><span class="p">,</span> <span class="n">km</span><span class="o">.</span><span class="n">labels_</span><span class="p">)</span>
<span class="p">)</span>
<span class="n">scores</span><span class="p">[</span><span class="s2">"Silhouette Coefficient"</span><span class="p">]</span><span class="o">.</span><span class="n">append</span><span class="p">(</span>
<a href="../../modules/generated/sklearn.metrics.silhouette_score.html#sklearn.metrics.silhouette_score" title="sklearn.metrics.silhouette_score" class="sphx-glr-backref-module-sklearn-metrics sphx-glr-backref-type-py-function"><span class="n">metrics</span><span class="o">.</span><span class="n">silhouette_score</span></a><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">km</span><span class="o">.</span><span class="n">labels_</span><span class="p">,</span> <span class="n">sample_size</span><span class="o">=</span><span class="mi">2000</span><span class="p">)</span>
<span class="p">)</span>
<span class="n">train_times</span> <span class="o">=</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.asarray.html#numpy.asarray" title="numpy.asarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">asarray</span></a><span class="p">(</span><span class="n">train_times</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"clustering done in </span><span class="si">{</span><span class="n">train_times</span><span class="o">.</span><span class="n">mean</span><span class="p">()</span><span class="si">:</span><span class="s2">.2f</span><span class="si">}</span><span class="s2"> ± </span><span class="si">{</span><span class="n">train_times</span><span class="o">.</span><span class="n">std</span><span class="p">()</span><span class="si">:</span><span class="s2">.2f</span><span class="si">}</span><span class="s2"> s "</span><span class="p">)</span>
<span class="n">evaluation</span> <span class="o">=</span> <span class="p">{</span>
<span class="s2">"estimator"</span><span class="p">:</span> <span class="n">name</span><span class="p">,</span>
<span class="s2">"train_time"</span><span class="p">:</span> <span class="n">train_times</span><span class="o">.</span><span class="n">mean</span><span class="p">(),</span>
<span class="p">}</span>
<span class="n">evaluation_std</span> <span class="o">=</span> <span class="p">{</span>
<span class="s2">"estimator"</span><span class="p">:</span> <span class="n">name</span><span class="p">,</span>
<span class="s2">"train_time"</span><span class="p">:</span> <span class="n">train_times</span><span class="o">.</span><span class="n">std</span><span class="p">(),</span>
<span class="p">}</span>
<span class="k">for</span> <span class="n">score_name</span><span class="p">,</span> <span class="n">score_values</span> <span class="ow">in</span> <span class="n">scores</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
<span class="n">mean_score</span><span class="p">,</span> <span class="n">std_score</span> <span class="o">=</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.mean.html#numpy.mean" title="numpy.mean" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">mean</span></a><span class="p">(</span><span class="n">score_values</span><span class="p">),</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.std.html#numpy.std" title="numpy.std" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">std</span></a><span class="p">(</span><span class="n">score_values</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"</span><span class="si">{</span><span class="n">score_name</span><span class="si">}</span><span class="s2">: </span><span class="si">{</span><span class="n">mean_score</span><span class="si">:</span><span class="s2">.3f</span><span class="si">}</span><span class="s2"> ± </span><span class="si">{</span><span class="n">std_score</span><span class="si">:</span><span class="s2">.3f</span><span class="si">}</span><span class="s2">"</span><span class="p">)</span>
<span class="n">evaluation</span><span class="p">[</span><span class="n">score_name</span><span class="p">]</span> <span class="o">=</span> <span class="n">mean_score</span>
<span class="n">evaluation_std</span><span class="p">[</span><span class="n">score_name</span><span class="p">]</span> <span class="o">=</span> <span class="n">std_score</span>
<span class="n">evaluations</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">evaluation</span><span class="p">)</span>
<span class="n">evaluations_std</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">evaluation_std</span><span class="p">)</span>
</pre></div>
</div>
</section>
<section id="k-means-clustering-on-text-features">
<h2>K-means clustering on text features<a class="headerlink" href="#k-means-clustering-on-text-features" title="Permalink to this heading">¶</a></h2>
<p>Two feature extraction methods are used in this example:</p>
<ul class="simple">
<li><p><a class="reference internal" href="../../modules/generated/sklearn.feature_extraction.text.TfidfVectorizer.html#sklearn.feature_extraction.text.TfidfVectorizer" title="sklearn.feature_extraction.text.TfidfVectorizer"><code class="xref py py-class docutils literal notranslate"><span class="pre">TfidfVectorizer</span></code></a> 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.</p></li>
<li><p><a class="reference internal" href="../../modules/generated/sklearn.feature_extraction.text.HashingVectorizer.html#sklearn.feature_extraction.text.HashingVectorizer" title="sklearn.feature_extraction.text.HashingVectorizer"><code class="xref py py-class docutils literal notranslate"><span class="pre">HashingVectorizer</span></code></a> 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.</p></li>
</ul>
<p>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.</p>
<section id="feature-extraction-using-tfidfvectorizer">
<h3>Feature Extraction using TfidfVectorizer<a class="headerlink" href="#feature-extraction-using-tfidfvectorizer" title="Permalink to this heading">¶</a></h3>
<p>We first benchmark the estimators using a dictionary vectorizer along with an
IDF normalization as provided by
<a class="reference internal" href="../../modules/generated/sklearn.feature_extraction.text.TfidfVectorizer.html#sklearn.feature_extraction.text.TfidfVectorizer" title="sklearn.feature_extraction.text.TfidfVectorizer"><code class="xref py py-class docutils literal notranslate"><span class="pre">TfidfVectorizer</span></code></a>.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">sklearn.feature_extraction.text</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.feature_extraction.text.TfidfVectorizer.html#sklearn.feature_extraction.text.TfidfVectorizer" title="sklearn.feature_extraction.text.TfidfVectorizer" class="sphx-glr-backref-module-sklearn-feature_extraction-text sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">TfidfVectorizer</span></a>
<span class="n">vectorizer</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.feature_extraction.text.TfidfVectorizer.html#sklearn.feature_extraction.text.TfidfVectorizer" title="sklearn.feature_extraction.text.TfidfVectorizer" class="sphx-glr-backref-module-sklearn-feature_extraction-text sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">TfidfVectorizer</span></a><span class="p">(</span>
<span class="n">max_df</span><span class="o">=</span><span class="mf">0.5</span><span class="p">,</span>
<span class="n">min_df</span><span class="o">=</span><span class="mi">5</span><span class="p">,</span>
<span class="n">stop_words</span><span class="o">=</span><span class="s2">"english"</span><span class="p">,</span>
<span class="p">)</span>
<span class="n">t0</span> <span class="o">=</span> <a href="https://docs.python.org/3/library/time.html#time.time" title="time.time" class="sphx-glr-backref-module-time sphx-glr-backref-type-py-function"><span class="n">time</span></a><span class="p">()</span>
<span class="n">X_tfidf</span> <span class="o">=</span> <span class="n">vectorizer</span><span class="o">.</span><span class="n">fit_transform</span><span class="p">(</span><span class="n">dataset</span><span class="o">.</span><span class="n">data</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"vectorization done in </span><span class="si">{</span><a href="https://docs.python.org/3/library/time.html#time.time" title="time.time" class="sphx-glr-backref-module-time sphx-glr-backref-type-py-function"><span class="n">time</span></a><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">t0</span><span class="si">:</span><span class="s2">.3f</span><span class="si">}</span><span class="s2"> s"</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"n_samples: </span><span class="si">{</span><span class="n">X_tfidf</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="si">}</span><span class="s2">, n_features: </span><span class="si">{</span><span class="n">X_tfidf</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="si">}</span><span class="s2">"</span><span class="p">)</span>
</pre></div>
</div>
<div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>vectorization done in 0.476 s
n_samples: 3387, n_features: 7929
</pre></div>
</div>
<p>After ignoring terms that appear in more than 50% of the documents (as set by
<code class="docutils literal notranslate"><span class="pre">max_df=0.5</span></code>) and terms that are not present in at least 5 documents (set by
<code class="docutils literal notranslate"><span class="pre">min_df=5</span></code>), the resulting number of unique terms <code class="docutils literal notranslate"><span class="pre">n_features</span></code> is around
8,000. We can additionally quantify the sparsity of the <code class="docutils literal notranslate"><span class="pre">X_tfidf</span></code> matrix as
the fraction of non-zero entries devided by the total number of elements.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"</span><span class="si">{</span><span class="n">X_tfidf</span><span class="o">.</span><span class="n">nnz</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><a href="https://numpy.org/doc/stable/reference/generated/numpy.prod.html#numpy.prod" title="numpy.prod" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">prod</span></a><span class="p">(</span><span class="n">X_tfidf</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span><span class="si">:</span><span class="s2">.3f</span><span class="si">}</span><span class="s2">"</span><span class="p">)</span>
</pre></div>
</div>
<div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>0.007
</pre></div>
</div>
<p>We find that around 0.7% of the entries of the <code class="docutils literal notranslate"><span class="pre">X_tfidf</span></code> matrix are non-zero.</p>
</section>
<section id="clustering-sparse-data-with-k-means">
<span id="kmeans-sparse-high-dim"></span><h3>Clustering sparse data with k-means<a class="headerlink" href="#clustering-sparse-data-with-k-means" title="Permalink to this heading">¶</a></h3>
<p>As both <a class="reference internal" href="../../modules/generated/sklearn.cluster.KMeans.html#sklearn.cluster.KMeans" title="sklearn.cluster.KMeans"><code class="xref py py-class docutils literal notranslate"><span class="pre">KMeans</span></code></a> and
<a class="reference internal" href="../../modules/generated/sklearn.cluster.MiniBatchKMeans.html#sklearn.cluster.MiniBatchKMeans" title="sklearn.cluster.MiniBatchKMeans"><code class="xref py py-class docutils literal notranslate"><span class="pre">MiniBatchKMeans</span></code></a> 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.</p>
<p>The following code illustrates how the previous phenomenon can sometimes lead
to highly imbalanced clusters, depending on the random initialization:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">sklearn.cluster</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.cluster.KMeans.html#sklearn.cluster.KMeans" title="sklearn.cluster.KMeans" class="sphx-glr-backref-module-sklearn-cluster sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">KMeans</span></a>
<span class="k">for</span> <span class="n">seed</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">5</span><span class="p">):</span>
<span class="n">kmeans</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.cluster.KMeans.html#sklearn.cluster.KMeans" title="sklearn.cluster.KMeans" class="sphx-glr-backref-module-sklearn-cluster sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">KMeans</span></a><span class="p">(</span>
<span class="n">n_clusters</span><span class="o">=</span><span class="n">true_k</span><span class="p">,</span>
<span class="n">max_iter</span><span class="o">=</span><span class="mi">100</span><span class="p">,</span>
<span class="n">n_init</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span>
<span class="n">random_state</span><span class="o">=</span><span class="n">seed</span><span class="p">,</span>
<span class="p">)</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_tfidf</span><span class="p">)</span>
<span class="n">cluster_ids</span><span class="p">,</span> <span class="n">cluster_sizes</span> <span class="o">=</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.unique.html#numpy.unique" title="numpy.unique" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">unique</span></a><span class="p">(</span><span class="n">kmeans</span><span class="o">.</span><span class="n">labels_</span><span class="p">,</span> <span class="n">return_counts</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"Number of elements asigned to each cluster: </span><span class="si">{</span><span class="n">cluster_sizes</span><span class="si">}</span><span class="s2">"</span><span class="p">)</span>
<span class="nb">print</span><span class="p">()</span>
<span class="nb">print</span><span class="p">(</span>
<span class="s2">"True number of documents in each category according to the class labels: "</span>
<span class="sa">f</span><span class="s2">"</span><span class="si">{</span><span class="n">category_sizes</span><span class="si">}</span><span class="s2">"</span>
<span class="p">)</span>
</pre></div>
</div>
<div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>Number of elements asigned to each cluster: [ 1 1 3384 1]
Number of elements asigned to each cluster: [1733 717 238 699]
Number of elements asigned to each cluster: [1115 256 1417 599]
Number of elements asigned to each cluster: [1695 649 446 597]
Number of elements asigned to each cluster: [ 254 2117 459 557]
True number of documents in each category according to the class labels: [799 973 987 628]
</pre></div>
</div>
<p>To avoid this problem, one possibility is to increase the number of runs with
independent random initiations <code class="docutils literal notranslate"><span class="pre">n_init</span></code>. In such case the clustering with the
best inertia (objective function of k-means) is chosen.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">kmeans</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.cluster.KMeans.html#sklearn.cluster.KMeans" title="sklearn.cluster.KMeans" class="sphx-glr-backref-module-sklearn-cluster sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">KMeans</span></a><span class="p">(</span>
<span class="n">n_clusters</span><span class="o">=</span><span class="n">true_k</span><span class="p">,</span>
<span class="n">max_iter</span><span class="o">=</span><span class="mi">100</span><span class="p">,</span>
<span class="n">n_init</span><span class="o">=</span><span class="mi">5</span><span class="p">,</span>
<span class="p">)</span>
<span class="n">fit_and_evaluate</span><span class="p">(</span><span class="n">kmeans</span><span class="p">,</span> <span class="n">X_tfidf</span><span class="p">,</span> <span class="n">name</span><span class="o">=</span><span class="s2">"KMeans</span><span class="se">\n</span><span class="s2">on tf-idf vectors"</span><span class="p">)</span>
</pre></div>
</div>
<div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>clustering done in 0.20 ± 0.05 s
Homogeneity: 0.347 ± 0.009
Completeness: 0.397 ± 0.006
V-measure: 0.370 ± 0.007
Adjusted Rand-Index: 0.197 ± 0.014
Silhouette Coefficient: 0.007 ± 0.001
</pre></div>
</div>
<p>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.</p>
<p>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.</p>
</section>
<section id="performing-dimensionality-reduction-using-lsa">
<h3>Performing dimensionality reduction using LSA<a class="headerlink" href="#performing-dimensionality-reduction-using-lsa" title="Permalink to this heading">¶</a></h3>
<p>A <code class="docutils literal notranslate"><span class="pre">n_init=1</span></code> 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
<a class="reference internal" href="../../modules/generated/sklearn.decomposition.TruncatedSVD.html#sklearn.decomposition.TruncatedSVD" title="sklearn.decomposition.TruncatedSVD"><code class="xref py py-class docutils literal notranslate"><span class="pre">TruncatedSVD</span></code></a>, which works on term count/tf-idf
matrices. Since SVD results are not normalized, we redo the normalization to
improve the <a class="reference internal" href="../../modules/generated/sklearn.cluster.KMeans.html#sklearn.cluster.KMeans" title="sklearn.cluster.KMeans"><code class="xref py py-class docutils literal notranslate"><span class="pre">KMeans</span></code></a> result. Using SVD to reduce the
dimensionality of TF-IDF document vectors is often known as <a class="reference external" href="https://en.wikipedia.org/wiki/Latent_semantic_analysis">latent semantic
analysis</a> (LSA) in
the information retrieval and text mining literature.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">sklearn.decomposition</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.decomposition.TruncatedSVD.html#sklearn.decomposition.TruncatedSVD" title="sklearn.decomposition.TruncatedSVD" class="sphx-glr-backref-module-sklearn-decomposition sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">TruncatedSVD</span></a>
<span class="kn">from</span> <span class="nn">sklearn.pipeline</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.pipeline.make_pipeline.html#sklearn.pipeline.make_pipeline" title="sklearn.pipeline.make_pipeline" class="sphx-glr-backref-module-sklearn-pipeline sphx-glr-backref-type-py-function"><span class="n">make_pipeline</span></a>
<span class="kn">from</span> <span class="nn">sklearn.preprocessing</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.preprocessing.Normalizer.html#sklearn.preprocessing.Normalizer" title="sklearn.preprocessing.Normalizer" class="sphx-glr-backref-module-sklearn-preprocessing sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">Normalizer</span></a>
<span class="n">lsa</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.pipeline.make_pipeline.html#sklearn.pipeline.make_pipeline" title="sklearn.pipeline.make_pipeline" class="sphx-glr-backref-module-sklearn-pipeline sphx-glr-backref-type-py-function"><span class="n">make_pipeline</span></a><span class="p">(</span><a href="../../modules/generated/sklearn.decomposition.TruncatedSVD.html#sklearn.decomposition.TruncatedSVD" title="sklearn.decomposition.TruncatedSVD" class="sphx-glr-backref-module-sklearn-decomposition sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">TruncatedSVD</span></a><span class="p">(</span><span class="n">n_components</span><span class="o">=</span><span class="mi">100</span><span class="p">),</span> <a href="../../modules/generated/sklearn.preprocessing.Normalizer.html#sklearn.preprocessing.Normalizer" title="sklearn.preprocessing.Normalizer" class="sphx-glr-backref-module-sklearn-preprocessing sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">Normalizer</span></a><span class="p">(</span><span class="n">copy</span><span class="o">=</span><span class="kc">False</span><span class="p">))</span>
<span class="n">t0</span> <span class="o">=</span> <a href="https://docs.python.org/3/library/time.html#time.time" title="time.time" class="sphx-glr-backref-module-time sphx-glr-backref-type-py-function"><span class="n">time</span></a><span class="p">()</span>
<span class="n">X_lsa</span> <span class="o">=</span> <span class="n">lsa</span><span class="o">.</span><span class="n">fit_transform</span><span class="p">(</span><span class="n">X_tfidf</span><span class="p">)</span>
<span class="n">explained_variance</span> <span class="o">=</span> <span class="n">lsa</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">explained_variance_ratio_</span><span class="o">.</span><span class="n">sum</span><span class="p">()</span>
<span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"LSA done in </span><span class="si">{</span><a href="https://docs.python.org/3/library/time.html#time.time" title="time.time" class="sphx-glr-backref-module-time sphx-glr-backref-type-py-function"><span class="n">time</span></a><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">t0</span><span class="si">:</span><span class="s2">.3f</span><span class="si">}</span><span class="s2"> s"</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"Explained variance of the SVD step: </span><span class="si">{</span><span class="n">explained_variance</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">100</span><span class="si">:</span><span class="s2">.1f</span><span class="si">}</span><span class="s2">%"</span><span class="p">)</span>
</pre></div>
</div>
<div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>LSA done in 0.394 s
Explained variance of the SVD step: 18.4%
</pre></div>
</div>
<p>Using a single initialization means the processing time will be reduced for
both <a class="reference internal" href="../../modules/generated/sklearn.cluster.KMeans.html#sklearn.cluster.KMeans" title="sklearn.cluster.KMeans"><code class="xref py py-class docutils literal notranslate"><span class="pre">KMeans</span></code></a> and
<a class="reference internal" href="../../modules/generated/sklearn.cluster.MiniBatchKMeans.html#sklearn.cluster.MiniBatchKMeans" title="sklearn.cluster.MiniBatchKMeans"><code class="xref py py-class docutils literal notranslate"><span class="pre">MiniBatchKMeans</span></code></a>.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">kmeans</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.cluster.KMeans.html#sklearn.cluster.KMeans" title="sklearn.cluster.KMeans" class="sphx-glr-backref-module-sklearn-cluster sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">KMeans</span></a><span class="p">(</span>
<span class="n">n_clusters</span><span class="o">=</span><span class="n">true_k</span><span class="p">,</span>
<span class="n">max_iter</span><span class="o">=</span><span class="mi">100</span><span class="p">,</span>
<span class="n">n_init</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span>
<span class="p">)</span>
<span class="n">fit_and_evaluate</span><span class="p">(</span><span class="n">kmeans</span><span class="p">,</span> <span class="n">X_lsa</span><span class="p">,</span> <span class="n">name</span><span class="o">=</span><span class="s2">"KMeans</span><span class="se">\n</span><span class="s2">with LSA on tf-idf vectors"</span><span class="p">)</span>
</pre></div>
</div>
<div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>clustering done in 0.02 ± 0.00 s
Homogeneity: 0.396 ± 0.005
Completeness: 0.424 ± 0.024
V-measure: 0.409 ± 0.013
Adjusted Rand-Index: 0.341 ± 0.036
Silhouette Coefficient: 0.029 ± 0.001
</pre></div>
</div>
<p>We can observe that clustering on the LSA representation of the document is
significantly faster (both because of <code class="docutils literal notranslate"><span class="pre">n_init=1</span></code> 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
<a class="reference internal" href="../../modules/generated/sklearn.cluster.MiniBatchKMeans.html#sklearn.cluster.MiniBatchKMeans" title="sklearn.cluster.MiniBatchKMeans"><code class="xref py py-class docutils literal notranslate"><span class="pre">MiniBatchKMeans</span></code></a>.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">sklearn.cluster</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.cluster.MiniBatchKMeans.html#sklearn.cluster.MiniBatchKMeans" title="sklearn.cluster.MiniBatchKMeans" class="sphx-glr-backref-module-sklearn-cluster sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">MiniBatchKMeans</span></a>
<span class="n">minibatch_kmeans</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.cluster.MiniBatchKMeans.html#sklearn.cluster.MiniBatchKMeans" title="sklearn.cluster.MiniBatchKMeans" class="sphx-glr-backref-module-sklearn-cluster sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">MiniBatchKMeans</span></a><span class="p">(</span>
<span class="n">n_clusters</span><span class="o">=</span><span class="n">true_k</span><span class="p">,</span>
<span class="n">n_init</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span>
<span class="n">init_size</span><span class="o">=</span><span class="mi">1000</span><span class="p">,</span>
<span class="n">batch_size</span><span class="o">=</span><span class="mi">1000</span><span class="p">,</span>
<span class="p">)</span>
<span class="n">fit_and_evaluate</span><span class="p">(</span>
<span class="n">minibatch_kmeans</span><span class="p">,</span>
<span class="n">X_lsa</span><span class="p">,</span>
<span class="n">name</span><span class="o">=</span><span class="s2">"MiniBatchKMeans</span><span class="se">\n</span><span class="s2">with LSA on tf-idf vectors"</span><span class="p">,</span>
<span class="p">)</span>
</pre></div>
</div>
<div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>clustering done in 0.02 ± 0.00 s
Homogeneity: 0.353 ± 0.072
Completeness: 0.384 ± 0.018
V-measure: 0.365 ± 0.051
Adjusted Rand-Index: 0.316 ± 0.093
Silhouette Coefficient: 0.025 ± 0.006
</pre></div>
</div>
</section>
<section id="top-terms-per-cluster">
<h3>Top terms per cluster<a class="headerlink" href="#top-terms-per-cluster" title="Permalink to this heading">¶</a></h3>
<p>Since <a class="reference internal" href="../../modules/generated/sklearn.feature_extraction.text.TfidfVectorizer.html#sklearn.feature_extraction.text.TfidfVectorizer" title="sklearn.feature_extraction.text.TfidfVectorizer"><code class="xref py py-class docutils literal notranslate"><span class="pre">TfidfVectorizer</span></code></a> can be
inverted we can identify the cluster centers, which provide an intuition of
the most influential words <strong>for each cluster</strong>. See the example script
<a class="reference internal" href="plot_document_classification_20newsgroups.html#sphx-glr-auto-examples-text-plot-document-classification-20newsgroups-py"><span class="std std-ref">Classification of text documents using sparse features</span></a>
for a comparison with the most predictive words <strong>for each target class</strong>.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">original_space_centroids</span> <span class="o">=</span> <span class="n">lsa</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">inverse_transform</span><span class="p">(</span><span class="n">kmeans</span><span class="o">.</span><span class="n">cluster_centers_</span><span class="p">)</span>
<span class="n">order_centroids</span> <span class="o">=</span> <span class="n">original_space_centroids</span><span class="o">.</span><span class="n">argsort</span><span class="p">()[:,</span> <span class="p">::</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
<span class="n">terms</span> <span class="o">=</span> <span class="n">vectorizer</span><span class="o">.</span><span class="n">get_feature_names_out</span><span class="p">()</span>
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">true_k</span><span class="p">):</span>
<span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"Cluster </span><span class="si">{</span><span class="n">i</span><span class="si">}</span><span class="s2">: "</span><span class="p">,</span> <span class="n">end</span><span class="o">=</span><span class="s2">""</span><span class="p">)</span>
<span class="k">for</span> <span class="n">ind</span> <span class="ow">in</span> <span class="n">order_centroids</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="p">:</span><span class="mi">10</span><span class="p">]:</span>
<span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"</span><span class="si">{</span><span class="n">terms</span><span class="p">[</span><span class="n">ind</span><span class="p">]</span><span class="si">}</span><span class="s2"> "</span><span class="p">,</span> <span class="n">end</span><span class="o">=</span><span class="s2">""</span><span class="p">)</span>
<span class="nb">print</span><span class="p">()</span>
</pre></div>
</div>
<div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>Cluster 0: think just don people like know want say good really
Cluster 1: god people jesus say religion did does christian said evidence
Cluster 2: thanks graphics image know edu does files file program mail
Cluster 3: space launch orbit earth shuttle like nasa moon mission time
</pre></div>
</div>
</section>
<section id="hashingvectorizer">
<h3>HashingVectorizer<a class="headerlink" href="#hashingvectorizer" title="Permalink to this heading">¶</a></h3>
<p>An alternative vectorization can be done using a
<a class="reference internal" href="../../modules/generated/sklearn.feature_extraction.text.HashingVectorizer.html#sklearn.feature_extraction.text.HashingVectorizer" title="sklearn.feature_extraction.text.HashingVectorizer"><code class="xref py py-class docutils literal notranslate"><span class="pre">HashingVectorizer</span></code></a> 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
<a class="reference internal" href="../../modules/generated/sklearn.feature_extraction.text.HashingVectorizer.html#sklearn.feature_extraction.text.HashingVectorizer" title="sklearn.feature_extraction.text.HashingVectorizer"><code class="xref py py-class docutils literal notranslate"><span class="pre">HashingVectorizer</span></code></a> output to a
<a class="reference internal" href="../../modules/generated/sklearn.feature_extraction.text.TfidfTransformer.html#sklearn.feature_extraction.text.TfidfTransformer" title="sklearn.feature_extraction.text.TfidfTransformer"><code class="xref py py-class docutils literal notranslate"><span class="pre">TfidfTransformer</span></code></a> instance. In this
case we also add LSA to the pipeline to reduce the dimension and sparcity of
the hashed vector space.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">sklearn.feature_extraction.text</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.feature_extraction.text.HashingVectorizer.html#sklearn.feature_extraction.text.HashingVectorizer" title="sklearn.feature_extraction.text.HashingVectorizer" class="sphx-glr-backref-module-sklearn-feature_extraction-text sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">HashingVectorizer</span></a>
<span class="kn">from</span> <span class="nn">sklearn.feature_extraction.text</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.feature_extraction.text.TfidfTransformer.html#sklearn.feature_extraction.text.TfidfTransformer" title="sklearn.feature_extraction.text.TfidfTransformer" class="sphx-glr-backref-module-sklearn-feature_extraction-text sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">TfidfTransformer</span></a>
<span class="n">lsa_vectorizer</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.pipeline.make_pipeline.html#sklearn.pipeline.make_pipeline" title="sklearn.pipeline.make_pipeline" class="sphx-glr-backref-module-sklearn-pipeline sphx-glr-backref-type-py-function"><span class="n">make_pipeline</span></a><span class="p">(</span>
<a href="../../modules/generated/sklearn.feature_extraction.text.HashingVectorizer.html#sklearn.feature_extraction.text.HashingVectorizer" title="sklearn.feature_extraction.text.HashingVectorizer" class="sphx-glr-backref-module-sklearn-feature_extraction-text sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">HashingVectorizer</span></a><span class="p">(</span><span class="n">stop_words</span><span class="o">=</span><span class="s2">"english"</span><span class="p">,</span> <span class="n">n_features</span><span class="o">=</span><span class="mi">50_000</span><span class="p">),</span>
<a href="../../modules/generated/sklearn.feature_extraction.text.TfidfTransformer.html#sklearn.feature_extraction.text.TfidfTransformer" title="sklearn.feature_extraction.text.TfidfTransformer" class="sphx-glr-backref-module-sklearn-feature_extraction-text sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">TfidfTransformer</span></a><span class="p">(),</span>
<a href="../../modules/generated/sklearn.decomposition.TruncatedSVD.html#sklearn.decomposition.TruncatedSVD" title="sklearn.decomposition.TruncatedSVD" class="sphx-glr-backref-module-sklearn-decomposition sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">TruncatedSVD</span></a><span class="p">(</span><span class="n">n_components</span><span class="o">=</span><span class="mi">100</span><span class="p">,</span> <span class="n">random_state</span><span class="o">=</span><span class="mi">0</span><span class="p">),</span>
<a href="../../modules/generated/sklearn.preprocessing.Normalizer.html#sklearn.preprocessing.Normalizer" title="sklearn.preprocessing.Normalizer" class="sphx-glr-backref-module-sklearn-preprocessing sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">Normalizer</span></a><span class="p">(</span><span class="n">copy</span><span class="o">=</span><span class="kc">False</span><span class="p">),</span>
<span class="p">)</span>
<span class="n">t0</span> <span class="o">=</span> <a href="https://docs.python.org/3/library/time.html#time.time" title="time.time" class="sphx-glr-backref-module-time sphx-glr-backref-type-py-function"><span class="n">time</span></a><span class="p">()</span>
<span class="n">X_hashed_lsa</span> <span class="o">=</span> <span class="n">lsa_vectorizer</span><span class="o">.</span><span class="n">fit_transform</span><span class="p">(</span><span class="n">dataset</span><span class="o">.</span><span class="n">data</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"vectorization done in </span><span class="si">{</span><a href="https://docs.python.org/3/library/time.html#time.time" title="time.time" class="sphx-glr-backref-module-time sphx-glr-backref-type-py-function"><span class="n">time</span></a><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">t0</span><span class="si">:</span><span class="s2">.3f</span><span class="si">}</span><span class="s2"> s"</span><span class="p">)</span>
</pre></div>
</div>
<div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>vectorization done in 2.607 s
</pre></div>
</div>
<p>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 <code class="docutils literal notranslate"><span class="pre">n_features=50_000</span></code> 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
<a class="reference internal" href="plot_hashing_vs_dict_vectorizer.html#sphx-glr-auto-examples-text-plot-hashing-vs-dict-vectorizer-py"><span class="std std-ref">FeatureHasher and DictVectorizer Comparison</span></a>.</p>
<p>We now fit and evaluate the <code class="docutils literal notranslate"><span class="pre">kmeans</span></code> and <code class="docutils literal notranslate"><span class="pre">minibatch_kmeans</span></code> instances on this
hashed-lsa-reduced data:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">fit_and_evaluate</span><span class="p">(</span><span class="n">kmeans</span><span class="p">,</span> <span class="n">X_hashed_lsa</span><span class="p">,</span> <span class="n">name</span><span class="o">=</span><span class="s2">"KMeans</span><span class="se">\n</span><span class="s2">with LSA on hashed vectors"</span><span class="p">)</span>
</pre></div>
</div>
<div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>clustering done in 0.03 ± 0.01 s
Homogeneity: 0.390 ± 0.013
Completeness: 0.439 ± 0.016
V-measure: 0.413 ± 0.014
Adjusted Rand-Index: 0.328 ± 0.013
Silhouette Coefficient: 0.030 ± 0.001
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">fit_and_evaluate</span><span class="p">(</span>
<span class="n">minibatch_kmeans</span><span class="p">,</span>
<span class="n">X_hashed_lsa</span><span class="p">,</span>
<span class="n">name</span><span class="o">=</span><span class="s2">"MiniBatchKMeans</span><span class="se">\n</span><span class="s2">with LSA on hashed vectors"</span><span class="p">,</span>
<span class="p">)</span>
</pre></div>
</div>
<div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>clustering done in 0.02 ± 0.00 s
Homogeneity: 0.354 ± 0.052
Completeness: 0.366 ± 0.055
V-measure: 0.359 ± 0.053
Adjusted Rand-Index: 0.312 ± 0.074
Silhouette Coefficient: 0.026 ± 0.004
</pre></div>
</div>
<p>Both methods lead to good results that are similar to running the same models
on the traditional LSA vectors (without hashing).</p>
</section>
</section>
<section id="clustering-evaluation-summary">
<h2>Clustering evaluation summary<a class="headerlink" href="#clustering-evaluation-summary" title="Permalink to this heading">¶</a></h2>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">pandas</span> <span class="k">as</span> <span class="nn">pd</span>
<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
<span class="n">fig</span><span class="p">,</span> <span class="p">(</span><span class="n">ax0</span><span class="p">,</span> <span class="n">ax1</span><span class="p">)</span> <span class="o">=</span> <a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.subplots.html#matplotlib.pyplot.subplots" title="matplotlib.pyplot.subplots" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">subplots</span></a><span class="p">(</span><span class="n">ncols</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">16</span><span class="p">,</span> <span class="mi">6</span><span class="p">),</span> <span class="n">sharey</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="n">df</span> <span class="o">=</span> <a href="https://pandas.pydata.org/pandas-docs/stable/reference/api/pandas.DataFrame.html#pandas.DataFrame" title="pandas.DataFrame" class="sphx-glr-backref-module-pandas sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">pd</span><span class="o">.</span><span class="n">DataFrame</span></a><span class="p">(</span><span class="n">evaluations</span><span class="p">[::</span><span class="o">-</span><span class="mi">1</span><span class="p">])</span><span class="o">.</span><span class="n">set_index</span><span class="p">(</span><span class="s2">"estimator"</span><span class="p">)</span>
<span class="n">df_std</span> <span class="o">=</span> <a href="https://pandas.pydata.org/pandas-docs/stable/reference/api/pandas.DataFrame.html#pandas.DataFrame" title="pandas.DataFrame" class="sphx-glr-backref-module-pandas sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">pd</span><span class="o">.</span><span class="n">DataFrame</span></a><span class="p">(</span><span class="n">evaluations_std</span><span class="p">[::</span><span class="o">-</span><span class="mi">1</span><span class="p">])</span><span class="o">.</span><span class="n">set_index</span><span class="p">(</span><span class="s2">"estimator"</span><span class="p">)</span>
<span class="n">df</span><span class="o">.</span><span class="n">drop</span><span class="p">(</span>
<span class="p">[</span><span class="s2">"train_time"</span><span class="p">],</span>
<span class="n">axis</span><span class="o">=</span><span class="s2">"columns"</span><span class="p">,</span>
<span class="p">)</span><span class="o">.</span><span class="n">plot</span><span class="o">.</span><span class="n">barh</span><span class="p">(</span><span class="n">ax</span><span class="o">=</span><span class="n">ax0</span><span class="p">,</span> <span class="n">xerr</span><span class="o">=</span><span class="n">df_std</span><span class="p">)</span>
<span class="n">ax0</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="s2">"Clustering scores"</span><span class="p">)</span>
<span class="n">ax0</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="s2">""</span><span class="p">)</span>
<span class="n">df</span><span class="p">[</span><span class="s2">"train_time"</span><span class="p">]</span><span class="o">.</span><span class="n">plot</span><span class="o">.</span><span class="n">barh</span><span class="p">(</span><span class="n">ax</span><span class="o">=</span><span class="n">ax1</span><span class="p">,</span> <span class="n">xerr</span><span class="o">=</span><span class="n">df_std</span><span class="p">[</span><span class="s2">"train_time"</span><span class="p">])</span>
<span class="n">ax1</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="s2">"Clustering time (s)"</span><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.tight_layout.html#matplotlib.pyplot.tight_layout" title="matplotlib.pyplot.tight_layout" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">tight_layout</span></a><span class="p">()</span>
</pre></div>
</div>
<img src="../../_images/sphx_glr_plot_document_clustering_001.png" srcset="../../_images/sphx_glr_plot_document_clustering_001.png" alt="plot document clustering" class = "sphx-glr-single-img"/><p><a class="reference internal" href="../../modules/generated/sklearn.cluster.KMeans.html#sklearn.cluster.KMeans" title="sklearn.cluster.KMeans"><code class="xref py py-class docutils literal notranslate"><span class="pre">KMeans</span></code></a> and <a class="reference internal" href="../../modules/generated/sklearn.cluster.MiniBatchKMeans.html#sklearn.cluster.MiniBatchKMeans" title="sklearn.cluster.MiniBatchKMeans"><code class="xref py py-class docutils literal notranslate"><span class="pre">MiniBatchKMeans</span></code></a>
suffer from the phenomenon called the <a class="reference external" href="https://en.wikipedia.org/wiki/Curse_of_dimensionality">Curse of Dimensionality</a> 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.</p>
<p>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.</p>
<p>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
<a class="reference internal" href="../cluster/plot_adjusted_for_chance_measures.html#sphx-glr-auto-examples-cluster-plot-adjusted-for-chance-measures-py"><span class="std std-ref">Adjustment for chance in clustering performance evaluation</span></a> for
a demo on the effect of random labeling.</p>
<p>The size of the error bars show that <a class="reference internal" href="../../modules/generated/sklearn.cluster.MiniBatchKMeans.html#sklearn.cluster.MiniBatchKMeans" title="sklearn.cluster.MiniBatchKMeans"><code class="xref py py-class docutils literal notranslate"><span class="pre">MiniBatchKMeans</span></code></a>
is less stable than <a class="reference internal" href="../../modules/generated/sklearn.cluster.KMeans.html#sklearn.cluster.KMeans" title="sklearn.cluster.KMeans"><code class="xref py py-class docutils literal notranslate"><span class="pre">KMeans</span></code></a> 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.</p>
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<p><a class="reference download internal" download="" href="../../_downloads/ba68199eea858ec04949b2c6c65147e0/plot_document_clustering.py"><code class="xref download docutils literal notranslate"><span class="pre">Download</span> <span class="pre">Python</span> <span class="pre">source</span> <span class="pre">code:</span> <span class="pre">plot_document_clustering.py</span></code></a></p>
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