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word-movers-distance-in-python.html
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word-movers-distance-in-python.html
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<title>Word Mover’s Distance in Python</title>
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<h1 class="entry-title">
<a href="//vene.ro/blog/word-movers-distance-in-python.html" rel="bookmark"
title="Permalink to Word Mover’s Distance in Python">Word Mover’s Distance in Python</a></h1>
<p class="subtitle"><time datetime="2015-11-07T12:00:00+01:00">Sat, 07 Nov 2015</time><label for="word-movers-distance-in-python" class="margin-toggle"> ⊕</label><input type="checkbox" id="word-movers-distance-in-python" class="margin-toggle" /><span class="marginnote">Category: <a href="//vene.ro/category/python.html">python</a><br />
#<a href="//vene.ro/tag/word-embeddings.html">word embeddings</a> #<a href="//vene.ro/tag/text-classification.html">text classification</a> #<a href="//vene.ro/tag/earth-movers-distance.html">earth mover's distance</a></span></p> </header>
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<p>*A guide to scikit-learn compatible nearest neighbors classification using the recently introduced word mover’s distance (<span class="caps">WMD</span>). *
Joint post with the awesome <a href="http://matthewkusner.com">Matt Kusner</a>!</p>
<p><a href="http://nbviewer.jupyter.org/github/vene/vene.github.io/blob/pelican/content/blog/word-movers-distance-in-python.ipynb">Source of this Jupyter notebook.</a></p>
<p>In document classification and other natural language processing applications, having a good measure of the similarity of two texts can be a valuable building block. Ideally, such a measure would capture semantic information. Cosine similarity on bag-of-words vectors is known to do well in practice, but it inherently cannot capture when documents say the same thing in completely different words.</p>
<p>Take, for example, two headlines:</p>
<ul>
<li><em>Obama speaks to the media in Illinois</em></li>
<li><em>The President greets the press in Chicago</em></li>
</ul>
<p>These have no content words in common, so according to most bag of words—based metrics, their distance would be maximal. (For such applications, you probably don’t want to count stopwords such as <em>the</em> and <em>in</em>, which don’t truly signal semantic similarity.)</p>
<p>One way out of this conundrum is the word mover’s distance (<span class="caps">WMD</span>), introduced in
<a href="http://mkusner.github.io/publications/WMD.pdf"><em>From Word Embeddings To Document Distances</em></a>,
(Matt J. Kusner, Yu Sun, Nicholas I. Kolkin, Kilian Q. Weinberger, <span class="caps">ICML</span> 2015).
<span class="caps">WMD</span> adapts the <a href="https://en.wikipedia.org/wiki/Earth_mover%27s_distance">earth mover’s distance</a> to the space of documents: the distance between two texts is given by the total amount of “mass” needed to move the words from one side into the other, multiplied by the distance the words need to move. So, starting from a measure of the distance between different words, we can get a principled document-level distance. Here is a visualisation of the idea, from the <span class="caps">ICML</span> slides:</p>
<p><img alt="WMD example from Matt's slides" src="https://vene.ro/images/wmd-obama.png"/></p>
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<h2 id="Prepare-some-word-embeddings">Prepare some word embeddings<a class="anchor-link" href="#Prepare-some-word-embeddings">¶</a></h2><p>The key ingredient in <span class="caps">WMD</span> is a good distance measure between words. Dense representations of words, also known by the trendier name “word embeddings” (because “distributed word representations” didn’t stick), do the trick here. We could train the embeddings ourselves, but for meaningful results we would need tons of documents, and that might take a while. So let’s just use the ones from the <a href="https://code.google.com/p/word2vec/"><code>word2vec</code></a> team. <a href="https://drive.google.com/file/d/0B7XkCwpI5KDYNlNUTTlSS21pQmM/edit?usp=sharing">(download link)</a></p>
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<div class="highlight hl-ipython3"><pre><span></span><span class="kn">import</span> <span class="nn">os</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> <span class="n">fetch_20newsgroups</span>
<span class="kn">from</span> <span class="nn">sklearn.feature_extraction.text</span> <span class="kn">import</span> <span class="n">CountVectorizer</span>
<span class="kn">from</span> <span class="nn">sklearn.cross_validation</span> <span class="kn">import</span> <span class="n">train_test_split</span>
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<div class="highlight hl-ipython3"><pre><span></span><span class="k">if</span> <span class="ow">not</span> <span class="n">os</span><span class="o">.</span><span class="n">path</span><span class="o">.</span><span class="n">exists</span><span class="p">(</span><span class="s2">"data/embed.dat"</span><span class="p">):</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">"Caching word embeddings in memmapped format..."</span><span class="p">)</span>
<span class="kn">from</span> <span class="nn">gensim.models.word2vec</span> <span class="kn">import</span> <span class="n">Word2Vec</span>
<span class="n">wv</span> <span class="o">=</span> <span class="n">Word2Vec</span><span class="o">.</span><span class="n">load_word2vec_format</span><span class="p">(</span>
<span class="s2">"data/GoogleNews-vectors-negative300.bin.gz"</span><span class="p">,</span>
<span class="n">binary</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="n">fp</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">memmap</span><span class="p">(</span><span class="s2">"data/embed.dat"</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">double</span><span class="p">,</span> <span class="n">mode</span><span class="o">=</span><span class="s1">'w+'</span><span class="p">,</span> <span class="n">shape</span><span class="o">=</span><span class="n">wv</span><span class="o">.</span><span class="n">syn0norm</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span>
<span class="n">fp</span><span class="p">[:]</span> <span class="o">=</span> <span class="n">wv</span><span class="o">.</span><span class="n">syn0norm</span><span class="p">[:]</span>
<span class="k">with</span> <span class="nb">open</span><span class="p">(</span><span class="s2">"data/embed.vocab"</span><span class="p">,</span> <span class="s2">"w"</span><span class="p">)</span> <span class="k">as</span> <span class="n">f</span><span class="p">:</span>
<span class="k">for</span> <span class="n">_</span><span class="p">,</span> <span class="n">w</span> <span class="ow">in</span> <span class="nb">sorted</span><span class="p">((</span><span class="n">voc</span><span class="o">.</span><span class="n">index</span><span class="p">,</span> <span class="n">word</span><span class="p">)</span> <span class="k">for</span> <span class="n">word</span><span class="p">,</span> <span class="n">voc</span> <span class="ow">in</span> <span class="n">wv</span><span class="o">.</span><span class="n">vocab</span><span class="o">.</span><span class="n">items</span><span class="p">()):</span>
<span class="nb">print</span><span class="p">(</span><span class="n">w</span><span class="p">,</span> <span class="n">file</span><span class="o">=</span><span class="n">f</span><span class="p">)</span>
<span class="k">del</span> <span class="n">fp</span><span class="p">,</span> <span class="n">wv</span>
<span class="n">W</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">memmap</span><span class="p">(</span><span class="s2">"data/embed.dat"</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">double</span><span class="p">,</span> <span class="n">mode</span><span class="o">=</span><span class="s2">"r"</span><span class="p">,</span> <span class="n">shape</span><span class="o">=</span><span class="p">(</span><span class="mi">3000000</span><span class="p">,</span> <span class="mi">300</span><span class="p">))</span>
<span class="k">with</span> <span class="nb">open</span><span class="p">(</span><span class="s2">"data/embed.vocab"</span><span class="p">)</span> <span class="k">as</span> <span class="n">f</span><span class="p">:</span>
<span class="n">vocab_list</span> <span class="o">=</span> <span class="nb">map</span><span class="p">(</span><span class="nb">str</span><span class="o">.</span><span class="n">strip</span><span class="p">,</span> <span class="n">f</span><span class="o">.</span><span class="n">readlines</span><span class="p">())</span>
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<div class="highlight hl-ipython3"><pre><span></span><span class="n">vocab_dict</span> <span class="o">=</span> <span class="p">{</span><span class="n">w</span><span class="p">:</span> <span class="n">k</span> <span class="k">for</span> <span class="n">k</span><span class="p">,</span> <span class="n">w</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">vocab_list</span><span class="p">)}</span>
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<h2 id="Reproducing-the-demo-above">Reproducing the demo above<a class="anchor-link" href="#Reproducing-the-demo-above">¶</a></h2>
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<div class="highlight hl-ipython3"><pre><span></span><span class="n">d1</span> <span class="o">=</span> <span class="s2">"Obama speaks to the media in Illinois"</span>
<span class="n">d2</span> <span class="o">=</span> <span class="s2">"The President addresses the press in Chicago"</span>
<span class="n">vect</span> <span class="o">=</span> <span class="n">CountVectorizer</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="o">.</span><span class="n">fit</span><span class="p">([</span><span class="n">d1</span><span class="p">,</span> <span class="n">d2</span><span class="p">])</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">"Features:"</span><span class="p">,</span> <span class="s2">", "</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="n">vect</span><span class="o">.</span><span class="n">get_feature_names</span><span class="p">()))</span>
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<pre>Features: addresses, chicago, illinois, media, obama, president, press, speaks
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<p>The two documents are completely orthogonal in terms of bag-of-words</p>
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<div class="highlight hl-ipython3"><pre><span></span><span class="kn">from</span> <span class="nn">scipy.spatial.distance</span> <span class="kn">import</span> <span class="n">cosine</span>
<span class="n">v_1</span><span class="p">,</span> <span class="n">v_2</span> <span class="o">=</span> <span class="n">vect</span><span class="o">.</span><span class="n">transform</span><span class="p">([</span><span class="n">d1</span><span class="p">,</span> <span class="n">d2</span><span class="p">])</span>
<span class="n">v_1</span> <span class="o">=</span> <span class="n">v_1</span><span class="o">.</span><span class="n">toarray</span><span class="p">()</span><span class="o">.</span><span class="n">ravel</span><span class="p">()</span>
<span class="n">v_2</span> <span class="o">=</span> <span class="n">v_2</span><span class="o">.</span><span class="n">toarray</span><span class="p">()</span><span class="o">.</span><span class="n">ravel</span><span class="p">()</span>
<span class="nb">print</span><span class="p">(</span><span class="n">v_1</span><span class="p">,</span> <span class="n">v_2</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">"cosine(doc_1, doc_2) = </span><span class="si">{:.2f}</span><span class="s2">"</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">cosine</span><span class="p">(</span><span class="n">v_1</span><span class="p">,</span> <span class="n">v_2</span><span class="p">)))</span>
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<pre>[0 0 1 1 1 0 0 1] [1 1 0 0 0 1 1 0]
cosine(doc_1, doc_2) = 1.00
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<div class="highlight hl-ipython3"><pre><span></span><span class="kn">from</span> <span class="nn">sklearn.metrics</span> <span class="kn">import</span> <span class="n">euclidean_distances</span>
<span class="n">W_</span> <span class="o">=</span> <span class="n">W</span><span class="p">[[</span><span class="n">vocab_dict</span><span class="p">[</span><span class="n">w</span><span class="p">]</span> <span class="k">for</span> <span class="n">w</span> <span class="ow">in</span> <span class="n">vect</span><span class="o">.</span><span class="n">get_feature_names</span><span class="p">()]]</span>
<span class="n">D_</span> <span class="o">=</span> <span class="n">euclidean_distances</span><span class="p">(</span><span class="n">W_</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">"d(addresses, speaks) = </span><span class="si">{:.2f}</span><span class="s2">"</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">D_</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">7</span><span class="p">]))</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">"d(addresses, chicago) = </span><span class="si">{:.2f}</span><span class="s2">"</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">D_</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">]))</span>
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<pre>d(addresses, speaks) = 1.16
d(addresses, chicago) = 1.37
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<p>We will be using <a href="https://github.com/wmayner/pyemd"><code>pyemd</code></a>, a Python wrapper for <a href="http://www.ariel.ac.il/sites/ofirpele/fastemd/">Pele and Werman’s implementation of the earth mover’s distance</a>.</p>
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<div class="highlight hl-ipython3"><pre><span></span><span class="kn">from</span> <span class="nn">pyemd</span> <span class="kn">import</span> <span class="n">emd</span>
<span class="c1"># pyemd needs double precision input</span>
<span class="n">v_1</span> <span class="o">=</span> <span class="n">v_1</span><span class="o">.</span><span class="n">astype</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">double</span><span class="p">)</span>
<span class="n">v_2</span> <span class="o">=</span> <span class="n">v_2</span><span class="o">.</span><span class="n">astype</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">double</span><span class="p">)</span>
<span class="n">v_1</span> <span class="o">/=</span> <span class="n">v_1</span><span class="o">.</span><span class="n">sum</span><span class="p">()</span>
<span class="n">v_2</span> <span class="o">/=</span> <span class="n">v_2</span><span class="o">.</span><span class="n">sum</span><span class="p">()</span>
<span class="n">D_</span> <span class="o">=</span> <span class="n">D_</span><span class="o">.</span><span class="n">astype</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">double</span><span class="p">)</span>
<span class="n">D_</span> <span class="o">/=</span> <span class="n">D_</span><span class="o">.</span><span class="n">max</span><span class="p">()</span> <span class="c1"># just for comparison purposes</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">"d(doc_1, doc_2) = </span><span class="si">{:.2f}</span><span class="s2">"</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">emd</span><span class="p">(</span><span class="n">v_1</span><span class="p">,</span> <span class="n">v_2</span><span class="p">,</span> <span class="n">D_</span><span class="p">)))</span>
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<pre>d(doc_1, doc_2) = 0.74
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<h2 id="Document-classification">Document classification<a class="anchor-link" href="#Document-classification">¶</a></h2><p>We will use the <a href="http://qwone.com/~jason/20Newsgroups/"><em>20 Newsgroups</em></a> classification task. Because <span class="caps">WMD</span> is an expensive computation, for this demo we just use a subset. To emphasize the power of the method, we use a larger test size, but train on relatively few samples.</p>
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<div class="highlight hl-ipython3"><pre><span></span><span class="n">newsgroups</span> <span class="o">=</span> <span class="n">fetch_20newsgroups</span><span class="p">()</span>
<span class="n">docs</span><span class="p">,</span> <span class="n">y</span> <span class="o">=</span> <span class="n">newsgroups</span><span class="o">.</span><span class="n">data</span><span class="p">,</span> <span class="n">newsgroups</span><span class="o">.</span><span class="n">target</span>
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<div class="highlight hl-ipython3"><pre><span></span><span class="n">docs_train</span><span class="p">,</span> <span class="n">docs_test</span><span class="p">,</span> <span class="n">y_train</span><span class="p">,</span> <span class="n">y_test</span> <span class="o">=</span> <span class="n">train_test_split</span><span class="p">(</span><span class="n">docs</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span>
<span class="n">train_size</span><span class="o">=</span><span class="mi">100</span><span class="p">,</span>
<span class="n">test_size</span><span class="o">=</span><span class="mi">300</span><span class="p">,</span>
<span class="n">random_state</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
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<p>Since the <code>W</code> embedding array is pretty huge, we might as well restrict it to just the words that actually occur in the dataset.</p>
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<div class="highlight hl-ipython3"><pre><span></span><span class="n">vect</span> <span class="o">=</span> <span class="n">CountVectorizer</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="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">docs_train</span> <span class="o">+</span> <span class="n">docs_test</span><span class="p">)</span>
<span class="n">common</span> <span class="o">=</span> <span class="p">[</span><span class="n">word</span> <span class="k">for</span> <span class="n">word</span> <span class="ow">in</span> <span class="n">vect</span><span class="o">.</span><span class="n">get_feature_names</span><span class="p">()</span> <span class="k">if</span> <span class="n">word</span> <span class="ow">in</span> <span class="n">vocab_dict</span><span class="p">]</span>
<span class="n">W_common</span> <span class="o">=</span> <span class="n">W</span><span class="p">[[</span><span class="n">vocab_dict</span><span class="p">[</span><span class="n">w</span><span class="p">]</span> <span class="k">for</span> <span class="n">w</span> <span class="ow">in</span> <span class="n">common</span><span class="p">]]</span>
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<p>We can then create a fixed-vocabulary vectorizer using only the words we have embeddings for.</p>
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<div class="highlight hl-ipython3"><pre><span></span><span class="n">vect</span> <span class="o">=</span> <span class="n">CountVectorizer</span><span class="p">(</span><span class="n">vocabulary</span><span class="o">=</span><span class="n">common</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">double</span><span class="p">)</span>
<span class="n">X_train</span> <span class="o">=</span> <span class="n">vect</span><span class="o">.</span><span class="n">fit_transform</span><span class="p">(</span><span class="n">docs_train</span><span class="p">)</span>
<span class="n">X_test</span> <span class="o">=</span> <span class="n">vect</span><span class="o">.</span><span class="n">transform</span><span class="p">(</span><span class="n">docs_test</span><span class="p">)</span>
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<p>One way to proceed is to just pre-compute the pairwise distances between all documents, and use them to search for hyperparameters and evaluate the model. However, that would incur some extra computation, and <span class="caps">WMD</span> is expensive. Also, it’s not the most pleasant user interface. So we define some scikit-learn compatible estimators for computing the <span class="caps">WMD</span>.</p>
<p><strong><code>WordMoversKNN</code></strong> subclasses from <code>KNeighborsClassifier</code> and overrides the <code>predict</code> function to compute the <span class="caps">WMD</span> between all training and test samples.</p>
<p>In practice, however, we often don’t know what is the best <code>n_neighbors</code> to use. Simply wrapping <code>WordMoversKNN</code> in a <code>GridSearchCV</code> would be rather expensive because of all the distances that would need to be recomputed for every value of <code>n_neighbors</code>. So we introduce <strong><code>WordMoversKNNCV</code></strong>, which, when fitted, performs <em>cross-validation</em> to find the best value of <code>n_neighbors</code> (under any given evaluation metric), while only computing the <span class="caps">WMD</span> once per fold, and only across folds (saving <code>n_folds * fold_size ** 2</code> evaluations).</p>
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<div class="highlight hl-ipython3"><pre><span></span><span class="sd">"""%%file word_movers_knn.py"""</span>
<span class="c1"># Authors: Vlad Niculae, Matt Kusner</span>
<span class="c1"># License: Simplified BSD</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.metrics</span> <span class="kn">import</span> <span class="n">euclidean_distances</span>
<span class="kn">from</span> <span class="nn">sklearn.externals.joblib</span> <span class="kn">import</span> <span class="n">Parallel</span><span class="p">,</span> <span class="n">delayed</span>
<span class="kn">from</span> <span class="nn">sklearn.neighbors</span> <span class="kn">import</span> <span class="n">KNeighborsClassifier</span>
<span class="kn">from</span> <span class="nn">sklearn.utils</span> <span class="kn">import</span> <span class="n">check_array</span>
<span class="kn">from</span> <span class="nn">sklearn.cross_validation</span> <span class="kn">import</span> <span class="n">check_cv</span>
<span class="kn">from</span> <span class="nn">sklearn.metrics.scorer</span> <span class="kn">import</span> <span class="n">check_scoring</span>
<span class="kn">from</span> <span class="nn">sklearn.preprocessing</span> <span class="kn">import</span> <span class="n">normalize</span>
<span class="kn">from</span> <span class="nn">pyemd</span> <span class="kn">import</span> <span class="n">emd</span>
<span class="k">class</span> <span class="nc">WordMoversKNN</span><span class="p">(</span><span class="n">KNeighborsClassifier</span><span class="p">):</span>
<span class="w"> </span><span class="sd">"""K nearest neighbors classifier using the Word Mover's Distance.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> </span>
<span class="sd"> W_embed : array, shape: (vocab_size, embed_size)</span>
<span class="sd"> Precomputed word embeddings between vocabulary items.</span>
<span class="sd"> Row indices should correspond to the columns in the bag-of-words input.</span>
<span class="sd"> n_neighbors : int, optional (default = 5)</span>
<span class="sd"> Number of neighbors to use by default for :meth:`k_neighbors` queries.</span>
<span class="sd"> n_jobs : int, optional (default = 1)</span>
<span class="sd"> The number of parallel jobs to run for Word Mover's Distance computation.</span>
<span class="sd"> If ``-1``, then the number of jobs is set to the number of CPU cores.</span>
<span class="sd"> </span>
<span class="sd"> verbose : int, optional</span>
<span class="sd"> Controls the verbosity; the higher, the more messages. Defaults to 0.</span>
<span class="sd"> </span>
<span class="sd"> References</span>
<span class="sd"> ----------</span>
<span class="sd"> </span>
<span class="sd"> Matt J. Kusner, Yu Sun, Nicholas I. Kolkin, Kilian Q. Weinberger</span>
<span class="sd"> From Word Embeddings To Document Distances</span>
<span class="sd"> The International Conference on Machine Learning (ICML), 2015</span>
<span class="sd"> http://mkusner.github.io/publications/WMD.pdf</span>
<span class="sd"> </span>
<span class="sd"> """</span>
<span class="n">_pairwise</span> <span class="o">=</span> <span class="kc">False</span>
<span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">W_embed</span><span class="p">,</span> <span class="n">n_neighbors</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">n_jobs</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">verbose</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
<span class="bp">self</span><span class="o">.</span><span class="n">W_embed</span> <span class="o">=</span> <span class="n">W_embed</span>
<span class="bp">self</span><span class="o">.</span><span class="n">verbose</span> <span class="o">=</span> <span class="n">verbose</span>
<span class="nb">super</span><span class="p">(</span><span class="n">WordMoversKNN</span><span class="p">,</span> <span class="bp">self</span><span class="p">)</span><span class="o">.</span><span class="fm">__init__</span><span class="p">(</span><span class="n">n_neighbors</span><span class="o">=</span><span class="n">n_neighbors</span><span class="p">,</span> <span class="n">n_jobs</span><span class="o">=</span><span class="n">n_jobs</span><span class="p">,</span>
<span class="n">metric</span><span class="o">=</span><span class="s1">'precomputed'</span><span class="p">,</span> <span class="n">algorithm</span><span class="o">=</span><span class="s1">'brute'</span><span class="p">)</span>
<span class="k">def</span> <span class="nf">_wmd</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">i</span><span class="p">,</span> <span class="n">row</span><span class="p">,</span> <span class="n">X_train</span><span class="p">):</span>
<span class="w"> </span><span class="sd">"""Compute the WMD between training sample i and given test row.</span>
<span class="sd"> </span>
<span class="sd"> Assumes that `row` and train samples are sparse BOW vectors summing to 1.</span>
<span class="sd"> """</span>
<span class="n">union_idx</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">union1d</span><span class="p">(</span><span class="n">X_train</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="o">.</span><span class="n">indices</span><span class="p">,</span> <span class="n">row</span><span class="o">.</span><span class="n">indices</span><span class="p">)</span>
<span class="n">W_minimal</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">W_embed</span><span class="p">[</span><span class="n">union_idx</span><span class="p">]</span>
<span class="n">W_dist</span> <span class="o">=</span> <span class="n">euclidean_distances</span><span class="p">(</span><span class="n">W_minimal</span><span class="p">)</span>
<span class="n">bow_i</span> <span class="o">=</span> <span class="n">X_train</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="n">union_idx</span><span class="p">]</span><span class="o">.</span><span class="n">A</span><span class="o">.</span><span class="n">ravel</span><span class="p">()</span>
<span class="n">bow_j</span> <span class="o">=</span> <span class="n">row</span><span class="p">[:,</span> <span class="n">union_idx</span><span class="p">]</span><span class="o">.</span><span class="n">A</span><span class="o">.</span><span class="n">ravel</span><span class="p">()</span>
<span class="k">return</span> <span class="n">emd</span><span class="p">(</span><span class="n">bow_i</span><span class="p">,</span> <span class="n">bow_j</span><span class="p">,</span> <span class="n">W_dist</span><span class="p">)</span>
<span class="k">def</span> <span class="nf">_wmd_row</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">row</span><span class="p">,</span> <span class="n">X_train</span><span class="p">):</span>
<span class="w"> </span><span class="sd">"""Wrapper to compute the WMD of a row with all training samples.</span>
<span class="sd"> </span>
<span class="sd"> Assumes that `row` and train samples are sparse BOW vectors summing to 1.</span>
<span class="sd"> Useful for parallelization.</span>
<span class="sd"> """</span>
<span class="n">n_samples_train</span> <span class="o">=</span> <span class="n">X_train</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="k">return</span> <span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">_wmd</span><span class="p">(</span><span class="n">i</span><span class="p">,</span> <span class="n">row</span><span class="p">,</span> <span class="n">X_train</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">n_samples_train</span><span class="p">)]</span>
<span class="k">def</span> <span class="nf">_pairwise_wmd</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">X_test</span><span class="p">,</span> <span class="n">X_train</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
<span class="w"> </span><span class="sd">"""Computes the word mover's distance between all train and test points.</span>
<span class="sd"> </span>
<span class="sd"> Parallelized over rows of X_test.</span>
<span class="sd"> </span>
<span class="sd"> Assumes that train and test samples are sparse BOW vectors summing to 1.</span>
<span class="sd"> </span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> X_test: scipy.sparse matrix, shape: (n_test_samples, vocab_size)</span>
<span class="sd"> Test samples.</span>
<span class="sd"> </span>
<span class="sd"> X_train: scipy.sparse matrix, shape: (n_train_samples, vocab_size)</span>
<span class="sd"> Training samples. If `None`, uses the samples the estimator was fit with.</span>
<span class="sd"> </span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> dist : array, shape: (n_test_samples, n_train_samples)</span>
<span class="sd"> Distances between all test samples and all train samples.</span>
<span class="sd"> </span>
<span class="sd"> """</span>
<span class="n">n_samples_test</span> <span class="o">=</span> <span class="n">X_test</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="k">if</span> <span class="n">X_train</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
<span class="n">X_train</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_fit_X</span>
<span class="n">dist</span> <span class="o">=</span> <span class="n">Parallel</span><span class="p">(</span><span class="n">n_jobs</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">n_jobs</span><span class="p">,</span> <span class="n">verbose</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">verbose</span><span class="p">)(</span>
<span class="n">delayed</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">_wmd_row</span><span class="p">)(</span><span class="n">test_sample</span><span class="p">,</span> <span class="n">X_train</span><span class="p">)</span>
<span class="k">for</span> <span class="n">test_sample</span> <span class="ow">in</span> <span class="n">X_test</span><span class="p">)</span>
<span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">dist</span><span class="p">)</span>
<span class="k">def</span> <span class="nf">fit</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">X</span><span class="p">,</span> <span class="n">y</span><span class="p">):</span>
<span class="w"> </span><span class="sd">"""Fit the model using X as training data and y as target values</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> X : scipy sparse matrix, shape: (n_samples, n_features)</span>
<span class="sd"> Training data. </span>
<span class="sd"> y : {array-like, sparse matrix}</span>
<span class="sd"> Target values of shape = [n_samples] or [n_samples, n_outputs]</span>
<span class="sd"> """</span>
<span class="n">X</span> <span class="o">=</span> <span class="n">check_array</span><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">accept_sparse</span><span class="o">=</span><span class="s1">'csr'</span><span class="p">,</span> <span class="n">copy</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="n">X</span> <span class="o">=</span> <span class="n">normalize</span><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">norm</span><span class="o">=</span><span class="s1">'l1'</span><span class="p">,</span> <span class="n">copy</span><span class="o">=</span><span class="kc">False</span><span class="p">)</span>
<span class="k">return</span> <span class="nb">super</span><span class="p">(</span><span class="n">WordMoversKNN</span><span class="p">,</span> <span class="bp">self</span><span class="p">)</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">y</span><span class="p">)</span>
<span class="k">def</span> <span class="nf">predict</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">X</span><span class="p">):</span>
<span class="w"> </span><span class="sd">"""Predict the class labels for the provided data</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> X : scipy.sparse matrix, shape (n_test_samples, vocab_size)</span>
<span class="sd"> Test samples.</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> y : array of shape [n_samples]</span>
<span class="sd"> Class labels for each data sample.</span>
<span class="sd"> """</span>
<span class="n">X</span> <span class="o">=</span> <span class="n">check_array</span><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">accept_sparse</span><span class="o">=</span><span class="s1">'csr'</span><span class="p">,</span> <span class="n">copy</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="n">X</span> <span class="o">=</span> <span class="n">normalize</span><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">norm</span><span class="o">=</span><span class="s1">'l1'</span><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">dist</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_pairwise_wmd</span><span class="p">(</span><span class="n">X</span><span class="p">)</span>
<span class="k">return</span> <span class="nb">super</span><span class="p">(</span><span class="n">WordMoversKNN</span><span class="p">,</span> <span class="bp">self</span><span class="p">)</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="n">dist</span><span class="p">)</span>
<span class="k">class</span> <span class="nc">WordMoversKNNCV</span><span class="p">(</span><span class="n">WordMoversKNN</span><span class="p">):</span>
<span class="w"> </span><span class="sd">"""Cross-validated KNN classifier using the Word Mover's Distance.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> W_embed : array, shape: (vocab_size, embed_size)</span>
<span class="sd"> Precomputed word embeddings between vocabulary items.</span>
<span class="sd"> Row indices should correspond to the columns in the bag-of-words input.</span>
<span class="sd"> n_neighbors_try : sequence, optional</span>
<span class="sd"> List of ``n_neighbors`` values to try.</span>
<span class="sd"> If None, tries 1-5 neighbors.</span>
<span class="sd"> scoring : string, callable or None, optional, default: None</span>
<span class="sd"> A string (see model evaluation documentation) or</span>
<span class="sd"> a scorer callable object / function with signature</span>
<span class="sd"> ``scorer(estimator, X, y)``.</span>
<span class="sd"> cv : int, cross-validation generator or an iterable, optional</span>
<span class="sd"> Determines the cross-validation splitting strategy.</span>
<span class="sd"> Possible inputs for cv are:</span>
<span class="sd"> - None, to use the default 3-fold cross-validation,</span>
<span class="sd"> - integer, to specify the number of folds.</span>
<span class="sd"> - An object to be used as a cross-validation generator.</span>
<span class="sd"> - An iterable yielding train/test splits.</span>
<span class="sd"> For integer/None inputs, StratifiedKFold is used.</span>
<span class="sd"> n_jobs : int, optional (default = 1)</span>
<span class="sd"> The number of parallel jobs to run for Word Mover's Distance computation.</span>
<span class="sd"> If ``-1``, then the number of jobs is set to the number of CPU cores.</span>
<span class="sd"> verbose : int, optional</span>
<span class="sd"> Controls the verbosity; the higher, the more messages. Defaults to 0.</span>
<span class="sd"> Attributes</span>
<span class="sd"> ----------</span>
<span class="sd"> cv_scores_ : array, shape (n_folds, len(n_neighbors_try))</span>
<span class="sd"> Test set scores for each fold.</span>
<span class="sd"> n_neighbors_ : int,</span>
<span class="sd"> The best `n_neighbors` value found.</span>
<span class="sd"> References</span>
<span class="sd"> ----------</span>
<span class="sd"> Matt J. Kusner, Yu Sun, Nicholas I. Kolkin, Kilian Q. Weinberger</span>
<span class="sd"> From Word Embeddings To Document Distances</span>
<span class="sd"> The International Conference on Machine Learning (ICML), 2015</span>
<span class="sd"> http://mkusner.github.io/publications/WMD.pdf</span>
<span class="sd"> </span>
<span class="sd"> """</span>
<span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">W_embed</span><span class="p">,</span> <span class="n">n_neighbors_try</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">scoring</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">cv</span><span class="o">=</span><span class="mi">3</span><span class="p">,</span>
<span class="n">n_jobs</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">verbose</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
<span class="bp">self</span><span class="o">.</span><span class="n">cv</span> <span class="o">=</span> <span class="n">cv</span>
<span class="bp">self</span><span class="o">.</span><span class="n">n_neighbors_try</span> <span class="o">=</span> <span class="n">n_neighbors_try</span>
<span class="bp">self</span><span class="o">.</span><span class="n">scoring</span> <span class="o">=</span> <span class="n">scoring</span>
<span class="nb">super</span><span class="p">(</span><span class="n">WordMoversKNNCV</span><span class="p">,</span> <span class="bp">self</span><span class="p">)</span><span class="o">.</span><span class="fm">__init__</span><span class="p">(</span><span class="n">W_embed</span><span class="p">,</span>
<span class="n">n_neighbors</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
<span class="n">n_jobs</span><span class="o">=</span><span class="n">n_jobs</span><span class="p">,</span>
<span class="n">verbose</span><span class="o">=</span><span class="n">verbose</span><span class="p">)</span>
<span class="k">def</span> <span class="nf">fit</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">X</span><span class="p">,</span> <span class="n">y</span><span class="p">):</span>
<span class="w"> </span><span class="sd">"""Fit KNN model by choosing the best `n_neighbors`.</span>
<span class="sd"> </span>
<span class="sd"> Parameters</span>
<span class="sd"> -----------</span>
<span class="sd"> X : scipy.sparse matrix, (n_samples, vocab_size)</span>
<span class="sd"> Data</span>
<span class="sd"> y : ndarray, shape (n_samples,) or (n_samples, n_targets)</span>
<span class="sd"> Target</span>
<span class="sd"> """</span>
<span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">n_neighbors_try</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
<span class="n">n_neighbors_try</span> <span class="o">=</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">6</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">n_neighbors_try</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">n_neighbors_try</span>
<span class="n">X</span> <span class="o">=</span> <span class="n">check_array</span><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">accept_sparse</span><span class="o">=</span><span class="s1">'csr'</span><span class="p">,</span> <span class="n">copy</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="n">X</span> <span class="o">=</span> <span class="n">normalize</span><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">norm</span><span class="o">=</span><span class="s1">'l1'</span><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">cv</span> <span class="o">=</span> <span class="n">check_cv</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">cv</span><span class="p">,</span> <span class="n">X</span><span class="p">,</span> <span class="n">y</span><span class="p">)</span>
<span class="n">knn</span> <span class="o">=</span> <span class="n">KNeighborsClassifier</span><span class="p">(</span><span class="n">metric</span><span class="o">=</span><span class="s1">'precomputed'</span><span class="p">,</span> <span class="n">algorithm</span><span class="o">=</span><span class="s1">'brute'</span><span class="p">)</span>
<span class="n">scorer</span> <span class="o">=</span> <span class="n">check_scoring</span><span class="p">(</span><span class="n">knn</span><span class="p">,</span> <span class="n">scoring</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">scoring</span><span class="p">)</span>
<span class="n">scores</span> <span class="o">=</span> <span class="p">[]</span>
<span class="k">for</span> <span class="n">train_ix</span><span class="p">,</span> <span class="n">test_ix</span> <span class="ow">in</span> <span class="n">cv</span><span class="p">:</span>
<span class="n">dist</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_pairwise_wmd</span><span class="p">(</span><span class="n">X</span><span class="p">[</span><span class="n">test_ix</span><span class="p">],</span> <span class="n">X</span><span class="p">[</span><span class="n">train_ix</span><span class="p">])</span>
<span class="n">knn</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_ix</span><span class="p">],</span> <span class="n">y</span><span class="p">[</span><span class="n">train_ix</span><span class="p">])</span>
<span class="n">scores</span><span class="o">.</span><span class="n">append</span><span class="p">([</span>
<span class="n">scorer</span><span class="p">(</span><span class="n">knn</span><span class="o">.</span><span class="n">set_params</span><span class="p">(</span><span class="n">n_neighbors</span><span class="o">=</span><span class="n">k</span><span class="p">),</span> <span class="n">dist</span><span class="p">,</span> <span class="n">y</span><span class="p">[</span><span class="n">test_ix</span><span class="p">])</span>
<span class="k">for</span> <span class="n">k</span> <span class="ow">in</span> <span class="n">n_neighbors_try</span>
<span class="p">])</span>
<span class="n">scores</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">scores</span><span class="p">)</span>
<span class="bp">self</span><span class="o">.</span><span class="n">cv_scores_</span> <span class="o">=</span> <span class="n">scores</span>
<span class="n">best_k_ix</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">argmax</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">scores</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">))</span>
<span class="n">best_k</span> <span class="o">=</span> <span class="n">n_neighbors_try</span><span class="p">[</span><span class="n">best_k_ix</span><span class="p">]</span>
<span class="bp">self</span><span class="o">.</span><span class="n">n_neighbors</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">n_neighbors_</span> <span class="o">=</span> <span class="n">best_k</span>
<span class="k">return</span> <span class="nb">super</span><span class="p">(</span><span class="n">WordMoversKNNCV</span><span class="p">,</span> <span class="bp">self</span><span class="p">)</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">y</span><span class="p">)</span>
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<pre>Overwriting word_movers_knn.py
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<div class="highlight hl-ipython3"><pre><span></span><span class="n">knn_cv</span> <span class="o">=</span> <span class="n">WordMoversKNNCV</span><span class="p">(</span><span class="n">cv</span><span class="o">=</span><span class="mi">3</span><span class="p">,</span>
<span class="n">n_neighbors_try</span><span class="o">=</span><span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">20</span><span class="p">),</span>
<span class="n">W_embed</span><span class="o">=</span><span class="n">W_common</span><span class="p">,</span> <span class="n">verbose</span><span class="o">=</span><span class="mi">5</span><span class="p">,</span> <span class="n">n_jobs</span><span class="o">=</span><span class="mi">3</span><span class="p">)</span>
<span class="n">knn_cv</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_train</span><span class="p">,</span> <span class="n">y_train</span><span class="p">)</span>
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<pre>[Parallel(n_jobs=3)]: Done 12 tasks | elapsed: 30.8s
[Parallel(n_jobs=3)]: Done 34 out of 34 | elapsed: 2.0min finished
[Parallel(n_jobs=3)]: Done 12 tasks | elapsed: 25.7s
[Parallel(n_jobs=3)]: Done 33 out of 33 | elapsed: 2.9min finished
[Parallel(n_jobs=3)]: Done 12 tasks | elapsed: 53.3s
[Parallel(n_jobs=3)]: Done 33 out of 33 | elapsed: 2.0min finished
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<pre>WordMoversKNNCV(W_embed=memmap([[ 0.04283, -0.01124, ..., -0.05679, -0.00763],
[ 0.02884, -0.05923, ..., -0.04744, 0.06698],
...,
[ 0.08428, -0.15534, ..., -0.01413, 0.04561],
[-0.02052, 0.08666, ..., 0.03659, 0.10445]]),
cv=3, n_jobs=3, n_neighbors_try=range(1, 20), scoring=None,
verbose=5)</pre>
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<div class="highlight hl-ipython3"><pre><span></span><span class="nb">print</span><span class="p">(</span><span class="s2">"CV score: </span><span class="si">{:.2f}</span><span class="s2">"</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">knn_cv</span><span class="o">.</span><span class="n">cv_scores_</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span><span class="o">.</span><span class="n">max</span><span class="p">()))</span>
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<pre>CV score: 0.38
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<div class="highlight hl-ipython3"><pre><span></span><span class="nb">print</span><span class="p">(</span><span class="s2">"Test score: </span><span class="si">{:.2f}</span><span class="s2">"</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">knn_cv</span><span class="o">.</span><span class="n">score</span><span class="p">(</span><span class="n">X_test</span><span class="p">,</span> <span class="n">y_test</span><span class="p">)))</span>
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<pre>[Parallel(n_jobs=3)]: Done 12 tasks | elapsed: 32.2s
[Parallel(n_jobs=3)]: Done 66 tasks | elapsed: 4.3min
[Parallel(n_jobs=3)]: Done 156 tasks | elapsed: 12.5min
[Parallel(n_jobs=3)]: Done 282 tasks | elapsed: 30.5min
[Parallel(n_jobs=3)]: Done 300 out of 300 | elapsed: 48.9min finished
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<pre>Test score: 0.31
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<h2 id="Comparison-with-other-models">Comparison with other models<a class="anchor-link" href="#Comparison-with-other-models">¶</a></h2><p>Now let’s see how <span class="caps">WMD</span> compares with some common approaches, on bag of words features. The most apples-to-apples comparison would be
K nearest neighbors with a cosine similarity metric. This approach performs worse than using <span class="caps">WMD</span>. (All scores are accuracies.)</p>
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<div class="highlight hl-ipython3"><pre><span></span><span class="kn">from</span> <span class="nn">sklearn.svm</span> <span class="kn">import</span> <span class="n">LinearSVC</span>
<span class="kn">from</span> <span class="nn">sklearn.neighbors</span> <span class="kn">import</span> <span class="n">KNeighborsClassifier</span>
<span class="kn">from</span> <span class="nn">sklearn.grid_search</span> <span class="kn">import</span> <span class="n">GridSearchCV</span>
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<div class="highlight hl-ipython3"><pre><span></span><span class="n">knn_grid</span> <span class="o">=</span> <span class="n">GridSearchCV</span><span class="p">(</span><span class="n">KNeighborsClassifier</span><span class="p">(</span><span class="n">metric</span><span class="o">=</span><span class="s1">'cosine'</span><span class="p">,</span> <span class="n">algorithm</span><span class="o">=</span><span class="s1">'brute'</span><span class="p">),</span>
<span class="nb">dict</span><span class="p">(</span><span class="n">n_neighbors</span><span class="o">=</span><span class="nb">list</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">20</span><span class="p">))),</span>
<span class="n">cv</span><span class="o">=</span><span class="mi">3</span><span class="p">)</span>
<span class="n">knn_grid</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_train</span><span class="p">,</span> <span class="n">y_train</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">"CV score: </span><span class="si">{:.2f}</span><span class="s2">"</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">knn_grid</span><span class="o">.</span><span class="n">best_score_</span><span class="p">))</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">"Test score: </span><span class="si">{:.2f}</span><span class="s2">"</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">knn_grid</span><span class="o">.</span><span class="n">score</span><span class="p">(</span><span class="n">X_test</span><span class="p">,</span> <span class="n">y_test</span><span class="p">)))</span>
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<pre>CV score: 0.34
Test score: 0.22
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<p>Another common method for text classification is the linear support vector machine on bag of words.
This performs a bit better than vanilla cosine <span class="caps">KNN</span>, but worse than using <span class="caps">WMD</span> in this setting. In our experience,
this seems to depend on the amount of training data available.</p>
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<div class="highlight hl-ipython3"><pre><span></span><span class="n">svc_grid</span> <span class="o">=</span> <span class="n">GridSearchCV</span><span class="p">(</span><span class="n">LinearSVC</span><span class="p">(),</span>
<span class="nb">dict</span><span class="p">(</span><span class="n">C</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">logspace</span><span class="p">(</span><span class="o">-</span><span class="mi">6</span><span class="p">,</span> <span class="mi">6</span><span class="p">,</span> <span class="mi">13</span><span class="p">,</span> <span class="n">base</span><span class="o">=</span><span class="mi">2</span><span class="p">)),</span>
<span class="n">cv</span><span class="o">=</span><span class="mi">3</span><span class="p">)</span>
<span class="n">svc_grid</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_train</span><span class="p">,</span> <span class="n">y_train</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">"CV score: </span><span class="si">{:.2f}</span><span class="s2">"</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">svc_grid</span><span class="o">.</span><span class="n">best_score_</span><span class="p">))</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">"Test score: </span><span class="si">{:.2f}</span><span class="s2">"</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">svc_grid</span><span class="o">.</span><span class="n">score</span><span class="p">(</span><span class="n">X_test</span><span class="p">,</span> <span class="n">y_test</span><span class="p">)))</span>
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<pre>CV score: 0.35
Test score: 0.27
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<h2 id="What-have-we-learned?">What have we learned?<a class="anchor-link" href="#What-have-we-learned?">¶</a></h2><p><span class="caps">WMD</span> is much better at capturing semantic similarity between documents than cosine, due to its ability to generalize to unseen words. The <span class="caps">SVM</span> does somewhat better than cosine <span class="caps">KNN</span>, but still lacks such out-of-vocabulary generalization. Given enough data, <span class="caps">WMD</span> can probably improve this margin, especially using something like metric learning on top.</p>
<p>The exact <span class="caps">WMD</span>, as we have used it here, is pretty slow. This code is not optimized as much as it could be, there is potential through caching and using Cython.
However, a major limitation remains the cost of actually computing the <span class="caps">EMD</span>. To scale even higher, exactness can be relaxed by using lower bounds. In our next post, we will compare such optimization strategies, as discussed in <a href="http://mkusner.github.io/publications/WMD.pdf">the <span class="caps">WMD</span> paper</a>.</p>
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