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distributedwordreps.html
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distributedwordreps.html
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<!DOCTYPE html>
<html>
<head>
<meta charset="utf-8" />
<title>distributedwordreps</title>
<script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.1.10/require.min.js"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/2.0.3/jquery.min.js"></script>
<style type="text/css">
/*!
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* Twitter Bootstrap
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<div class=" highlight hl-ipython2"><pre><span class="c"># -*- coding: utf-8 -*-</span>
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<h1 id="Distributed-word-representations">Distributed word representations<a class="anchor-link" href="#Distributed-word-representations">¶</a></h1>
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<p>This codelab is about methods for creating effective distributed semantic word representations. Here, "distributed" just means that the representations are vectors of real numbers, and these models are also often called <strong>vector space models</strong> (VSMs). My focus is largely on methods derived from co-occurrence patterns in text, but the section <a href="#Supervised-signals">Supervised signals</a> illustrates a simple method for imbuing distributional word vectors with label information.</p>
<p>A usage note: the term <strong>distributional representatation</strong> is sometimes reserved for those derived purely from count data, and <strong>distributed representation</strong> is sometimes reserved for those that involve some kind of supervised optimization. Here, I use <strong>distributed representation</strong> in its most general form. As we will see, many models blur the supervised/distributional distinction.</p>
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<h2 id="Code-and-data-requirements">Code and data requirements<a class="anchor-link" href="#Code-and-data-requirements">¶</a></h2>
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<p>Download or clone <a href="https://github.com/cgpotts/cs224u">this Github repository</a> so that you have all the files it includes.</p>
<p>Download <a href="https://web.stanford.edu/class/cs224u/data/distributedwordreps-data.zip">the data distribution for this unit</a>, unpack it, and place it in the directory containing the above Github directory.</p>
<p>In addition, make sure you have the following installed:</p>
<ul>
<li><a href="http://www.scipy.org/install.html">Numpy, Scipy, and matplotlib</a>. (Mac users: I suggest <a href="http://stronginference.com/ScipySuperpack/">the Scipy Superpack</a>)</li>
<li><a href="http://scikit-learn.org/">scikit.learn</a></li>
</ul>
<p>If you want to work in and modify this notebook, you should also install <a href="http://ipython.org">the latest iPython</a>.</p>
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<h2 id="Contents">Contents<a class="anchor-link" href="#Contents">¶</a></h2><ol>
<li><a href="#Distributional-matrices">Distributional matrices</a></li>
<li><a href="#Vector comparison">Vector comparison</a><ol>
<li><a href="#Euclidean-distance">Euclidean distance</a></li>
<li><a href="#Length-normalization">Length normalization</a></li>
<li><a href="#Cosine-distance">Cosine distance</a></li>
<li><a href="#Matching-based-methods">Matching-based methods</a></li>
<li><a href="#Summary">Summary</a></li>
</ol>
</li>
<li><a href="#Distributional-neighbors">Distributional neighbors</a> </li>
<li><a href="#Matrix-reweighting">Matrix reweighting</a><ol>
<li><a href="#Normalization">Normalization</a></li>
<li><a href="#Pointwise-Mutual-Information">Pointwise Mutual Information</a></li>
<li><a href="#TF-IDF">TF-IDF</a></li>
</ol>
</li>
<li><a href="#Dimensionality-reduction">Dimensionality reduction</a></li>
<li><a href="#Visualization">Visualization</a></li>
<li><a href="#The-semantic-orientation-method">The semantic orientation method</a></li>
<li><a href="#Word-sense-ambiguities">Word-sense ambiguities</a></li>
<li><a href="#GloVe-word-representations">GloVe word representations</a></li>
<li><a href="#Supervised-signals">Supervised signals</a><ol>
<li><a href="#Shallow-neural-network-model">Shallow neural network model</a></li>
<li><a href="#Logical-operator-example">Logical operator example</a></li>
<li><a href="#Sentiment-lexicon-example">Sentiment lexicon example</a></li>
<li><a href="#Word-level-inference-relations"> Word-level inference relations</a></li>
</ol>
</li>
<li><a href="#Word-similarity-evaluation">Word similarity evaluation</a></li>
<li><a href="#Word-analogies-evaluation">Word analogies evaluation</a></li>
<li><a href="#Exercises">Exercises</a><ol>
<li><a href="#Exploratory-and-open-ended">Exploratory and open-ended</a></li>
<li><a href="#Straightforward">Straightforward</a></li>
<li><a href="#Challenging">Challenging</a></li>
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</li>
</ol>
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<div class=" highlight hl-ipython2"><pre><span class="kn">import</span> <span class="nn">os</span>
<span class="kn">import</span> <span class="nn">sys</span>
<span class="kn">import</span> <span class="nn">csv</span>
<span class="kn">import</span> <span class="nn">copy</span>
<span class="kn">import</span> <span class="nn">random</span>
<span class="kn">import</span> <span class="nn">itertools</span>
<span class="kn">from</span> <span class="nn">operator</span> <span class="kn">import</span> <span class="n">itemgetter</span>
<span class="kn">from</span> <span class="nn">collections</span> <span class="kn">import</span> <span class="n">defaultdict</span>
<span class="c"># Make sure you've got Numpy and Scipy installed:</span>
<span class="kn">import</span> <span class="nn">numpy</span> <span class="kn">as</span> <span class="nn">np</span>
<span class="kn">import</span> <span class="nn">scipy</span>
<span class="kn">import</span> <span class="nn">scipy.spatial.distance</span>
<span class="kn">from</span> <span class="nn">numpy.linalg</span> <span class="kn">import</span> <span class="n">svd</span>
<span class="c"># For visualization:</span>
<span class="kn">from</span> <span class="nn">tsne</span> <span class="kn">import</span> <span class="n">tsne</span> <span class="c"># See http://lvdmaaten.github.io/tsne/#implementations</span>
<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="kn">as</span> <span class="nn">plt</span>
<span class="c"># For clustering in the 'Word-sense ambiguities' section:</span>
<span class="kn">from</span> <span class="nn">sklearn.cluster</span> <span class="kn">import</span> <span class="n">AffinityPropagation</span>
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<div class=" highlight hl-ipython2"><pre><span class="o">%</span><span class="k">matplotlib</span> inline
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<h2 id="Distributional-matrices">Distributional matrices<a class="anchor-link" href="#Distributional-matrices">¶</a></h2>
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<p>Here's a basic recipe for building a word $\times$ word matrix:</p>
<ol>
<li>Define a notion of co-occurrence context. This could be an entire document, a paragraph, a sentence, a clause, an NP — whatever domain seems likely to capture the associations you care about.</li>
<li>Scan through your corpus building a dictionary $d$ mapping word-pairs to counts. Every time a pair of words $w$ and $w'$ occur in the same context (as you defined it in 1), increment $d[(w, w')]$ by $1$.</li>
<li>Using the count dictionary $d$ that you collected in 2, establish your full vocabulary $V$, an ordered list of words types. For large collections of documents, $|V|$ will typically be huge. You will probably want to winnow the vocabulary at this point. You might do this by filtering to a specific subset, or just imposing a minimum count threshold. You might impose a minimum count threshold even if $|V|$ is small — for words with very low counts, you simply don't have enough evidence to say anything interesting.</li>
<li>Now build a matrix $M$ of dimension $|V| \times |V|$. Both the rows and the columns of $M$ represent words. Each cell $M[i, j]$ is filled with the count $d[(w_i, w_j)]$.</li>
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<p>For different design matrices, the procedure differs slightly. For example, if you are building a word $\times$ document matrix, then the rows of $M$ represent words and the columns of $M$ represent documents. The scan in step 2 then just keeps track of (<em>word</em>, <em>document</em>) pairs — compiling the number of times that <em>word</em> appears in <em>document</em>. Such matrices are often used in information retrieval, because the columns are multi-set representations of documents. They are much sparser than the the word $\times$ word matrices we will work with here. (In my experience, they yield lower quality lexicons, but others have reported good results with them.)</p>
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<p>This codebook is distributed with two pre-computed matrices of co-occurrence counts in IMDB move reviews. The <code>build</code> function allows you to read them in:</p>
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<div class=" highlight hl-ipython2"><pre><span class="k">def</span> <span class="nf">build</span><span class="p">(</span><span class="n">src_filename</span><span class="p">,</span> <span class="n">delimiter</span><span class="o">=</span><span class="s">','</span><span class="p">,</span> <span class="n">header</span><span class="o">=</span><span class="bp">True</span><span class="p">,</span> <span class="n">quoting</span><span class="o">=</span><span class="n">csv</span><span class="o">.</span><span class="n">QUOTE_MINIMAL</span><span class="p">):</span>
<span class="n">reader</span> <span class="o">=</span> <span class="n">csv</span><span class="o">.</span><span class="n">reader</span><span class="p">(</span><span class="nb">file</span><span class="p">(</span><span class="n">src_filename</span><span class="p">),</span> <span class="n">delimiter</span><span class="o">=</span><span class="n">delimiter</span><span class="p">,</span> <span class="n">quoting</span><span class="o">=</span><span class="n">quoting</span><span class="p">)</span>
<span class="n">colnames</span> <span class="o">=</span> <span class="bp">None</span>
<span class="k">if</span> <span class="n">header</span><span class="p">:</span>
<span class="n">colnames</span> <span class="o">=</span> <span class="n">reader</span><span class="o">.</span><span class="n">next</span><span class="p">()</span>
<span class="n">colnames</span> <span class="o">=</span> <span class="n">colnames</span><span class="p">[</span><span class="mi">1</span><span class="p">:</span> <span class="p">]</span>
<span class="n">mat</span> <span class="o">=</span> <span class="p">[]</span>
<span class="n">rownames</span> <span class="o">=</span> <span class="p">[]</span>
<span class="k">for</span> <span class="n">line</span> <span class="ow">in</span> <span class="n">reader</span><span class="p">:</span>
<span class="n">rownames</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">line</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
<span class="n">mat</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="nb">map</span><span class="p">(</span><span class="nb">float</span><span class="p">,</span> <span class="n">line</span><span class="p">[</span><span class="mi">1</span><span class="p">:</span> <span class="p">])))</span>
<span class="k">return</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">mat</span><span class="p">),</span> <span class="n">rownames</span><span class="p">,</span> <span class="n">colnames</span><span class="p">)</span>
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<p>Let's read these in now for use in later examples:</p>
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<div class=" highlight hl-ipython2"><pre><span class="n">ww</span> <span class="o">=</span> <span class="n">build</span><span class="p">(</span><span class="s">'distributedwordreps-data/imdb-wordword.csv'</span><span class="p">)</span>
<span class="n">wd</span> <span class="o">=</span> <span class="n">build</span><span class="p">(</span><span class="s">'distributedwordreps-data/imdb-worddoc.csv'</span><span class="p">)</span>
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<p>There are some great pre-computed matrices available online too. These aren't matrices of counts, but rather more abstract values computed using methods like those under discussion here. Just for kicks, load in the GloVe vectors
included in the data distribution:</p>
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<div class=" highlight hl-ipython2"><pre><span class="n">glv</span> <span class="o">=</span> <span class="n">build</span><span class="p">(</span><span class="s">'distributedwordreps-data/glove.6B.50d.txt'</span><span class="p">,</span> <span class="n">delimiter</span><span class="o">=</span><span class="s">' '</span><span class="p">,</span> <span class="n">header</span><span class="o">=</span><span class="bp">False</span><span class="p">,</span> <span class="n">quoting</span><span class="o">=</span><span class="n">csv</span><span class="o">.</span><span class="n">QUOTE_NONE</span><span class="p">)</span>
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<h2 id="Vector-comparison">Vector comparison<a class="anchor-link" href="#Vector-comparison">¶</a></h2>
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<p>Vector comparisons form the heart of our analyses in this context. For the most part, we are interested in measuring the <em>distance</em> between vectors. The guiding idea is that semantically related words should be close together in the vector spaces we build, and semantically unrelated words should be far apart.</p>
<p>The <a href="http://docs.scipy.org/doc/scipy-0.14.0/reference/spatial.distance.html">scipy.spatial.distance</a> module has a lot of vector comparison methods, so you might check them out if you want to go beyond the functions defined and explored here. Read the documentation closely, though: many of those methods are defined only for binary vectors, whereas the VSMs we'll use allow all float values in principle.</p>
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<h3 id="Euclidean-distance">Euclidean distance<a class="anchor-link" href="#Euclidean-distance">¶</a></h3>
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<p>The most basic and intuitive distance measure between vectors is <strong>euclidean distance</strong>. The euclidean distance between two vectors $u$ and $v$ of dimension $n$ is</p>
$$\sqrt{\sum_{i=1}^{n} |u_{i}-v_{i}|^2}$$<p></p>
<p>In two-dimensions, this corresponds to the length of the most direct line between the two points. Here, we just rely on
<code>scipy</code> to define it:</p>
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<div class=" highlight hl-ipython2"><pre><span class="k">def</span> <span class="nf">euclidean</span><span class="p">(</span><span class="n">u</span><span class="p">,</span> <span class="n">v</span><span class="p">):</span>
<span class="c"># Use scipy's method:</span>
<span class="k">return</span> <span class="n">scipy</span><span class="o">.</span><span class="n">spatial</span><span class="o">.</span><span class="n">distance</span><span class="o">.</span><span class="n">euclidean</span><span class="p">(</span><span class="n">u</span><span class="p">,</span> <span class="n">v</span><span class="p">)</span>
<span class="c"># Or define it yourself:</span>
<span class="c"># return vector_length(u - v) </span>
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<p>The comment above shows how to define this measure yourself. The function used there is the <strong>length</strong> of a vector $u$ of dimension $n$, which is defined as</p>
$$\|u\| = \sqrt{\sum_{i=1}^{n} u_{i}^{2}}$$<p></p>
<p>Here's the code:</p>
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<div class=" highlight hl-ipython2"><pre><span class="k">def</span> <span class="nf">vector_length</span><span class="p">(</span><span class="n">u</span><span class="p">):</span>
<span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">u</span><span class="p">,</span> <span class="n">u</span><span class="p">))</span>
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<p>Here's the tiny vector space from the screencast on vector comparisons associated
with this codelab:</p>
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<div class=" highlight hl-ipython2"><pre><span class="n">ABC</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="p">[</span> <span class="mf">2.0</span><span class="p">,</span> <span class="mf">4.0</span><span class="p">],</span> <span class="c"># A</span>
<span class="p">[</span><span class="mf">10.0</span><span class="p">,</span> <span class="mf">15.0</span><span class="p">],</span> <span class="c"># B</span>
<span class="p">[</span><span class="mf">14.0</span><span class="p">,</span> <span class="mf">10.0</span><span class="p">]])</span> <span class="c"># C</span>
<span class="k">def</span> <span class="nf">plot_ABC</span><span class="p">(</span><span class="n">m</span><span class="p">):</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">m</span><span class="p">[:,</span><span class="mi">0</span><span class="p">],</span> <span class="n">m</span><span class="p">[:,</span><span class="mi">1</span><span class="p">],</span> <span class="n">marker</span><span class="o">=</span><span class="s">''</span><span class="p">,</span> <span class="n">linestyle</span><span class="o">=</span><span class="s">''</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">xlim</span><span class="p">([</span><span class="mi">0</span><span class="p">,</span><span class="n">np</span><span class="o">.</span><span class="n">max</span><span class="p">(</span><span class="n">m</span><span class="p">)</span><span class="o">*</span><span class="mf">1.2</span><span class="p">])</span>
<span class="n">plt</span><span class="o">.</span><span class="n">ylim</span><span class="p">([</span><span class="mi">0</span><span class="p">,</span><span class="n">np</span><span class="o">.</span><span class="n">max</span><span class="p">(</span><span class="n">m</span><span class="p">)</span><span class="o">*</span><span class="mf">1.2</span><span class="p">])</span>
<span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">x</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">([</span><span class="s">'A'</span><span class="p">,</span><span class="s">'B'</span><span class="p">,</span><span class="s">'C'</span><span class="p">]):</span>
<span class="n">plt</span><span class="o">.</span><span class="n">annotate</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">m</span><span class="p">[</span><span class="n">i</span><span class="p">,:])</span>
<span class="n">plot_ABC</span><span class="p">(</span><span class="n">ABC</span><span class="p">)</span>
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<p>The euclidean distances align well with the raw visual distance in the plot:</p>
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<div class=" highlight hl-ipython2"><pre><span class="n">euclidean</span><span class="p">(</span><span class="n">ABC</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">ABC</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
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<pre>13.601470508735444</pre>
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<div class=" highlight hl-ipython2"><pre><span class="n">euclidean</span><span class="p">(</span><span class="n">ABC</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">ABC</span><span class="p">[</span><span class="mi">2</span><span class="p">])</span>
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<pre>6.4031242374328485</pre>
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<p>However, suppose we think of the vectors as word meanings in the vector-space sense. In that case, the values don't look good: the distributions of B and C are more or less directly opposed, suggesting very different meanings, whereas A and B are rather closely aligned, abstracting away from the fact that the first is far less frequent than the second. In terms of the large
models we will soon explore, A and B resemble a pair like <strong>superb</strong> and <strong>good</strong>, which have similar meanings but very different frequencies. In contrast, B and C are like <strong>good</strong> and <strong>disappointing</strong> — similar overall frequencies but different distributions with respect to the overall vocabulary.</p>
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<h3 id="Length-normalization">Length normalization<a class="anchor-link" href="#Length-normalization">¶</a></h3>
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<p>These affinities are immediately apparent if we normalize the vectors by their length. To do this, we use <code>vector_length</code>
to define <code>length_norm</code>:</p>
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<div class=" highlight hl-ipython2"><pre><span class="k">def</span> <span class="nf">length_norm</span><span class="p">(</span><span class="n">u</span><span class="p">):</span>
<span class="k">return</span> <span class="n">u</span> <span class="o">/</span> <span class="n">vector_length</span><span class="p">(</span><span class="n">u</span><span class="p">)</span>
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<div class=" highlight hl-ipython2"><pre><span class="n">plot_ABC</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="n">length_norm</span><span class="p">(</span><span class="n">row</span><span class="p">)</span> <span class="k">for</span> <span class="n">row</span> <span class="ow">in</span> <span class="n">ABC</span><span class="p">]))</span>
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<p>Here, the connection between A and B is more apparent, as is the opposition between B and C.</p>
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<h3 id="Cosine-distance">Cosine distance<a class="anchor-link" href="#Cosine-distance">¶</a></h3>
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<p><strong>Cosine distance</strong> takes overall length into account. The cosine distance between two vectors $u$ and $v$ of dimension $n$ is</p>
$$1 - \left(\frac{\sum_{i=1}^{n} u_{i} \cdot v_{i}}{\|u\|\cdot \|v\|}\right)$$<p>The similarity part of this (the righthand term of the subtraction) is actually measuring the <em>angles</em> between the two vectors. The result is the same (in terms of rank order) as one gets from first normalizing both vectors using <code>vector_length</code> and then calculating their Euclidean distance.</p>
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<div class=" highlight hl-ipython2"><pre><span class="k">def</span> <span class="nf">cosine</span><span class="p">(</span><span class="n">u</span><span class="p">,</span> <span class="n">v</span><span class="p">):</span>
<span class="c"># Use scipy's method:</span>
<span class="k">return</span> <span class="n">scipy</span><span class="o">.</span><span class="n">spatial</span><span class="o">.</span><span class="n">distance</span><span class="o">.</span><span class="n">cosine</span><span class="p">(</span><span class="n">u</span><span class="p">,</span> <span class="n">v</span><span class="p">)</span>
<span class="c"># Or define it yourself:</span>
<span class="c"># return 1.0 - (np.dot(u, v) / (vector_length(u) * vector_length(v)))</span>
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<h3 id="Matching-based-methods">Matching-based methods<a class="anchor-link" href="#Matching-based-methods">¶</a></h3>
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<p>Matching-based methods are also common in the literature. The basic <code>matching</code> measure effectively creates a vector consisting of all of the smaller of the two values at each coordinate, and then sums them:</p>
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<div class=" highlight hl-ipython2"><pre><span class="k">def</span> <span class="nf">matching</span><span class="p">(</span><span class="n">u</span><span class="p">,</span> <span class="n">v</span><span class="p">):</span>
<span class="c"># The scipy implementation is for binary vectors only. This version is more general.</span>
<span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">minimum</span><span class="p">(</span><span class="n">u</span><span class="p">,</span> <span class="n">v</span><span class="p">))</span>
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<p>One approach to normalizing the <code>matching</code> values is the <strong>Jaccard coefficient</strong>. The numerator is the matching coefficient. The denominator — the normalizer — is intuitively like the set union: for binary vectors it gives the cardinality of the union of the two being compared:</p>
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<div class=" highlight hl-ipython2"><pre><span class="k">def</span> <span class="nf">jaccard</span><span class="p">(</span><span class="n">u</span><span class="p">,</span> <span class="n">v</span><span class="p">):</span>
<span class="c"># The scipy implementation is for binary vectors only. This version is more general.</span>
<span class="k">return</span> <span class="mf">1.0</span> <span class="o">-</span> <span class="p">(</span><span class="n">matching</span><span class="p">(</span><span class="n">u</span><span class="p">,</span> <span class="n">v</span><span class="p">)</span> <span class="o">/</span> <span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">maximum</span><span class="p">(</span><span class="n">u</span><span class="p">,</span> <span class="n">v</span><span class="p">)))</span>
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<h3 id="Summary">Summary<a class="anchor-link" href="#Summary">¶</a></h3>
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<p>Suppose we set for ourselves the goal of associating A with B and disassociating B from C, in keeping with the semantic intuition expressed above. Then we can assess distance measures by whether they achieve this goal:</p>
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<div class=" highlight hl-ipython2"><pre><span class="k">for</span> <span class="n">m</span> <span class="ow">in</span> <span class="p">(</span><span class="n">euclidean</span><span class="p">,</span> <span class="n">cosine</span><span class="p">,</span> <span class="n">matching</span><span class="p">,</span> <span class="n">jaccard</span><span class="p">):</span>
<span class="n">fmt</span> <span class="o">=</span> <span class="p">{</span><span class="s">'name'</span><span class="p">:</span> <span class="n">m</span><span class="o">.</span><span class="n">__name__</span><span class="p">,</span> <span class="s">'AB'</span><span class="p">:</span> <span class="n">m</span><span class="p">(</span><span class="n">ABC</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">ABC</span><span class="p">[</span><span class="mi">1</span><span class="p">]),</span> <span class="s">'BC'</span><span class="p">:</span> <span class="n">m</span><span class="p">(</span><span class="n">ABC</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">ABC</span><span class="p">[</span><span class="mi">2</span><span class="p">])}</span>
<span class="k">print</span> <span class="s">'</span><span class="si">%(name)15s</span><span class="s">(A, B) = </span><span class="si">%(AB)5.2f</span><span class="s"> </span><span class="si">%(name)15s</span><span class="s">(B, C) = </span><span class="si">%(BC)5.2f</span><span class="s">'</span> <span class="o">%</span> <span class="n">fmt</span>
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