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<div class="section" id="clustering-the-enron-e-mail-corpus-using-the-infinite-relational-model">
<h1>Clustering the <a class="reference external" href="http://www.cs.cmu.edu/~./enron/">Enron e-mail corpus</a> using the Infinite Relational Model<a class="headerlink" href="#clustering-the-enron-e-mail-corpus-using-the-infinite-relational-model" title="Permalink to this headline">¶</a></h1>
<hr class="docutils" />
<p>Let’s setup our environment</p>
<div class="code python highlight-python"><div class="highlight"><pre>%matplotlib inline
import pickle
import time
import itertools as it
import numpy as np
import matplotlib.pylab as plt
import matplotlib.patches as patches
from multiprocessing import cpu_count
import seaborn as sns
sns.set_context('talk')
</pre></div>
</div>
<p>Below are the functions from datamicroscopes we’ll be using to cluster
the data</p>
<div class="code python highlight-python"><div class="highlight"><pre><span class="kn">from</span> <span class="nn">microscopes.common.rng</span> <span class="kn">import</span> <span class="n">rng</span>
<span class="kn">from</span> <span class="nn">microscopes.common.relation.dataview</span> <span class="kn">import</span> <span class="n">numpy_dataview</span>
<span class="kn">from</span> <span class="nn">microscopes.models</span> <span class="kn">import</span> <span class="n">bb</span> <span class="k">as</span> <span class="n">beta_bernoulli</span>
<span class="kn">from</span> <span class="nn">microscopes.irm.definition</span> <span class="kn">import</span> <span class="n">model_definition</span>
<span class="kn">from</span> <span class="nn">microscopes.irm</span> <span class="kn">import</span> <span class="n">model</span><span class="p">,</span> <span class="n">runner</span><span class="p">,</span> <span class="n">query</span>
<span class="kn">from</span> <span class="nn">microscopes.kernels</span> <span class="kn">import</span> <span class="n">parallel</span>
<span class="kn">from</span> <span class="nn">microscopes.common.query</span> <span class="kn">import</span> <span class="n">groups</span><span class="p">,</span> <span class="n">zmatrix_heuristic_block_ordering</span><span class="p">,</span> <span class="n">zmatrix_reorder</span>
</pre></div>
</div>
<p>We’ve made a set of utilities especially for this dataset,
<tt class="docutils literal"><span class="pre">enron_utils</span></tt>. We’ll include these as well.</p>
<p>We have downloaded the data and preprocessed it as suggested by
<a class="reference external" href="http://www.kecl.ntt.co.jp/as/members/ishiguro/open/2012AISTATS.pdf">Ishiguro et al.
2012</a>.
The results of the scirpt have been stored in the <tt class="docutils literal"><span class="pre">results.p</span></tt>.</p>
<p><tt class="docutils literal"><span class="pre">enron_crawler.py</span></tt> in the kernels repo includes the script to create
<tt class="docutils literal"><span class="pre">results.p</span></tt></p>
<div class="code python highlight-python"><div class="highlight"><pre><span class="kn">import</span> <span class="nn">enron_utils</span>
</pre></div>
</div>
<p>Let’s load the data and make a binary matrix to represent email
communication between individuals</p>
<p>In this matrix, <span class="math">\(X_{i,j} = 1\)</span> if and only if person<span class="math">\(_{i}\)</span>
sent an email to person<span class="math">\(_{j}\)</span></p>
<div class="code python highlight-python"><div class="highlight"><pre><span class="k">with</span> <span class="nb">open</span><span class="p">(</span><span class="s">'results.p'</span><span class="p">)</span> <span class="k">as</span> <span class="n">fp</span><span class="p">:</span>
<span class="n">communications</span> <span class="o">=</span> <span class="n">pickle</span><span class="o">.</span><span class="n">load</span><span class="p">(</span><span class="n">fp</span><span class="p">)</span>
<span class="k">def</span> <span class="nf">allnames</span><span class="p">(</span><span class="n">o</span><span class="p">):</span>
<span class="k">for</span> <span class="n">k</span><span class="p">,</span> <span class="n">v</span> <span class="ow">in</span> <span class="n">o</span><span class="p">:</span>
<span class="k">yield</span> <span class="p">[</span><span class="n">k</span><span class="p">]</span> <span class="o">+</span> <span class="nb">list</span><span class="p">(</span><span class="n">v</span><span class="p">)</span>
<span class="n">names</span> <span class="o">=</span> <span class="nb">set</span><span class="p">(</span><span class="n">it</span><span class="o">.</span><span class="n">chain</span><span class="o">.</span><span class="n">from_iterable</span><span class="p">(</span><span class="n">allnames</span><span class="p">(</span><span class="n">communications</span><span class="p">)))</span>
<span class="n">names</span> <span class="o">=</span> <span class="nb">sorted</span><span class="p">(</span><span class="nb">list</span><span class="p">(</span><span class="n">names</span><span class="p">))</span>
<span class="n">namemap</span> <span class="o">=</span> <span class="p">{</span> <span class="n">name</span> <span class="p">:</span> <span class="n">idx</span> <span class="k">for</span> <span class="n">idx</span><span class="p">,</span> <span class="n">name</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">names</span><span class="p">)</span> <span class="p">}</span>
<span class="n">N</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">names</span><span class="p">)</span>
<span class="n">communications_relation</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="n">N</span><span class="p">,</span> <span class="n">N</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">bool</span><span class="p">)</span>
<span class="k">for</span> <span class="n">sender</span><span class="p">,</span> <span class="n">receivers</span> <span class="ow">in</span> <span class="n">communications</span><span class="p">:</span>
<span class="n">sender_id</span> <span class="o">=</span> <span class="n">namemap</span><span class="p">[</span><span class="n">sender</span><span class="p">]</span>
<span class="k">for</span> <span class="n">receiver</span> <span class="ow">in</span> <span class="n">receivers</span><span class="p">:</span>
<span class="n">receiver_id</span> <span class="o">=</span> <span class="n">namemap</span><span class="p">[</span><span class="n">receiver</span><span class="p">]</span>
<span class="n">communications_relation</span><span class="p">[</span><span class="n">sender_id</span><span class="p">,</span> <span class="n">receiver_id</span><span class="p">]</span> <span class="o">=</span> <span class="bp">True</span>
<span class="k">print</span> <span class="s">"</span><span class="si">%d</span><span class="s"> names in the corpus"</span> <span class="o">%</span> <span class="n">N</span>
</pre></div>
</div>
<div class="highlight-python"><div class="highlight"><pre>115 names in the corpus
</pre></div>
</div>
<p>Let’s visualize the communication matrix</p>
<div class="code python highlight-python"><div class="highlight"><pre><span class="n">blue_cmap</span> <span class="o">=</span> <span class="n">sns</span><span class="o">.</span><span class="n">light_palette</span><span class="p">(</span><span class="s">"#34495e"</span><span class="p">,</span> <span class="n">as_cmap</span><span class="o">=</span><span class="bp">True</span><span class="p">)</span>
<span class="n">labels</span> <span class="o">=</span> <span class="p">[</span><span class="n">i</span> <span class="k">if</span> <span class="n">i</span><span class="o">%</span><span class="mi">20</span> <span class="o">==</span> <span class="mi">0</span> <span class="k">else</span> <span class="s">''</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">xrange</span><span class="p">(</span><span class="n">N</span><span class="p">)]</span>
<span class="n">sns</span><span class="o">.</span><span class="n">heatmap</span><span class="p">(</span><span class="n">communications_relation</span><span class="p">,</span> <span class="n">cmap</span><span class="o">=</span><span class="n">blue_cmap</span><span class="p">,</span> <span class="n">linewidths</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">cbar</span><span class="o">=</span><span class="bp">False</span><span class="p">,</span> <span class="n">xticklabels</span><span class="o">=</span><span class="n">labels</span><span class="p">,</span> <span class="n">yticklabels</span><span class="o">=</span><span class="n">labels</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="s">'person number'</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">ylabel</span><span class="p">(</span><span class="s">'person number'</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s">'Email Communication Matrix'</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-python"><div class="highlight"><pre><matplotlib.text.Text at 0x10aacbf10>
</pre></div>
</div>
<img alt="_images/enron-email_9_1.png" src="_images/enron-email_9_1.png" />
<p>Now, let’s learn the underlying clusters using the Inifinite Relational
Model</p>
<p>Let’s import the necessary functions from datamicroscopes</p>
<p>There are 5 steps necessary in inferring a model with datamicroscopes:
1. define the model 2. load the data 3. initialize the model 4. define
the runners (MCMC chains) 5. run the runners</p>
<p>Let’s start by defining the model and loading the data</p>
<p>To define our model, we need to specify our domains and relations</p>
<p>Our domains are described in a list of the cardinalities of each domain</p>
<p>Our releations are in a list of tuples which refer to the indicies of
each domain and the model type</p>
<p>In this case, the our domain is users, which is of size <span class="math">\(N\)</span></p>
<p>Our relations are users to users, both of cardinality <span class="math">\(N\)</span>, and we
model the relation with beta-bernoulli distribution since our data is
binary</p>
<div class="code python highlight-python"><div class="highlight"><pre><span class="n">defn</span> <span class="o">=</span> <span class="n">model_definition</span><span class="p">([</span><span class="n">N</span><span class="p">],</span> <span class="p">[((</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">),</span> <span class="n">beta_bernoulli</span><span class="p">)])</span>
<span class="n">views</span> <span class="o">=</span> <span class="p">[</span><span class="n">numpy_dataview</span><span class="p">(</span><span class="n">communications_relation</span><span class="p">)]</span>
<span class="n">prng</span> <span class="o">=</span> <span class="n">rng</span><span class="p">()</span>
</pre></div>
</div>
<p>Next, let’s initialize the model and define the runners.</p>
<p>These runners are our MCMC chains. We’ll use <tt class="docutils literal"><span class="pre">cpu_count</span></tt> to define our
number of chains.</p>
<div class="code python highlight-python"><div class="highlight"><pre><span class="n">nchains</span> <span class="o">=</span> <span class="n">cpu_count</span><span class="p">()</span>
<span class="n">latents</span> <span class="o">=</span> <span class="p">[</span><span class="n">model</span><span class="o">.</span><span class="n">initialize</span><span class="p">(</span><span class="n">defn</span><span class="p">,</span> <span class="n">views</span><span class="p">,</span> <span class="n">r</span><span class="o">=</span><span class="n">prng</span><span class="p">,</span> <span class="n">cluster_hps</span><span class="o">=</span><span class="p">[{</span><span class="s">'alpha'</span><span class="p">:</span><span class="mf">1e-3</span><span class="p">}])</span> <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">xrange</span><span class="p">(</span><span class="n">nchains</span><span class="p">)]</span>
<span class="n">kc</span> <span class="o">=</span> <span class="n">runner</span><span class="o">.</span><span class="n">default_assign_kernel_config</span><span class="p">(</span><span class="n">defn</span><span class="p">)</span>
<span class="n">runners</span> <span class="o">=</span> <span class="p">[</span><span class="n">runner</span><span class="o">.</span><span class="n">runner</span><span class="p">(</span><span class="n">defn</span><span class="p">,</span> <span class="n">views</span><span class="p">,</span> <span class="n">latent</span><span class="p">,</span> <span class="n">kc</span><span class="p">)</span> <span class="k">for</span> <span class="n">latent</span> <span class="ow">in</span> <span class="n">latents</span><span class="p">]</span>
<span class="n">r</span> <span class="o">=</span> <span class="n">parallel</span><span class="o">.</span><span class="n">runner</span><span class="p">(</span><span class="n">runners</span><span class="p">)</span>
</pre></div>
</div>
<p>From here, we can finally run each chain of the sampler 1000 times</p>
<div class="code python highlight-python"><div class="highlight"><pre><span class="n">start</span> <span class="o">=</span> <span class="n">time</span><span class="o">.</span><span class="n">time</span><span class="p">()</span>
<span class="n">r</span><span class="o">.</span><span class="n">run</span><span class="p">(</span><span class="n">r</span><span class="o">=</span><span class="n">prng</span><span class="p">,</span> <span class="n">niters</span><span class="o">=</span><span class="mi">1000</span><span class="p">)</span>
<span class="k">print</span> <span class="s">"inference took {} seconds"</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">time</span><span class="o">.</span><span class="n">time</span><span class="p">()</span> <span class="o">-</span> <span class="n">start</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-python"><div class="highlight"><pre>inference took 128.098203897 seconds
</pre></div>
</div>
<p>Now that we have learned our model let’s get our cluster assignments</p>
<div class="code python highlight-python"><div class="highlight"><pre><span class="n">infers</span> <span class="o">=</span> <span class="n">r</span><span class="o">.</span><span class="n">get_latents</span><span class="p">()</span>
<span class="n">clusters</span> <span class="o">=</span> <span class="n">groups</span><span class="p">(</span><span class="n">infers</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">assignments</span><span class="p">(</span><span class="mi">0</span><span class="p">),</span> <span class="n">sort</span><span class="o">=</span><span class="bp">True</span><span class="p">)</span>
<span class="n">ordering</span> <span class="o">=</span> <span class="nb">list</span><span class="p">(</span><span class="n">it</span><span class="o">.</span><span class="n">chain</span><span class="o">.</span><span class="n">from_iterable</span><span class="p">(</span><span class="n">clusters</span><span class="p">))</span>
</pre></div>
</div>
<p>Let’s sort the communications matrix to highlight our inferred clusters</p>
<div class="code python highlight-python"><div class="highlight"><pre><span class="n">z</span> <span class="o">=</span> <span class="n">communications_relation</span><span class="o">.</span><span class="n">copy</span><span class="p">()</span>
<span class="n">z</span> <span class="o">=</span> <span class="n">z</span><span class="p">[</span><span class="n">ordering</span><span class="p">]</span>
<span class="n">z</span> <span class="o">=</span> <span class="n">z</span><span class="p">[:,</span><span class="n">ordering</span><span class="p">]</span>
<span class="n">sizes</span> <span class="o">=</span> <span class="nb">map</span><span class="p">(</span><span class="nb">len</span><span class="p">,</span> <span class="n">clusters</span><span class="p">)</span>
<span class="n">boundaries</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">cumsum</span><span class="p">(</span><span class="n">sizes</span><span class="p">)[:</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
</pre></div>
</div>
<p>Our model finds suspicious cluster based on the communication data.
Let’s color and label these clusters in our communications matrix.</p>
<div class="code python highlight-python"><div class="highlight"><pre><span class="k">def</span> <span class="nf">cluster_with_name</span><span class="p">(</span><span class="n">clusters</span><span class="p">,</span> <span class="n">name</span><span class="p">,</span> <span class="n">payload</span><span class="o">=</span><span class="bp">None</span><span class="p">):</span>
<span class="n">ident</span> <span class="o">=</span> <span class="n">namemap</span><span class="p">[</span><span class="n">name</span><span class="p">]</span>
<span class="k">for</span> <span class="n">idx</span><span class="p">,</span> <span class="n">cluster</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">clusters</span><span class="p">):</span>
<span class="k">if</span> <span class="n">ident</span> <span class="ow">in</span> <span class="n">cluster</span><span class="p">:</span>
<span class="k">return</span> <span class="n">idx</span><span class="p">,</span> <span class="p">(</span><span class="n">cluster</span><span class="p">,</span> <span class="n">payload</span><span class="p">)</span>
<span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s">"could not find name"</span><span class="p">)</span>
<span class="n">suspicious</span> <span class="o">=</span> <span class="p">[</span>
<span class="n">cluster_with_name</span><span class="p">(</span><span class="n">clusters</span><span class="p">,</span> <span class="s">"horton-s"</span><span class="p">,</span> <span class="p">{</span><span class="s">"color"</span><span class="p">:</span><span class="s">"#66CC66"</span><span class="p">,</span> <span class="s">"desc"</span><span class="p">:</span><span class="s">"The pipeline/regulatory group"</span><span class="p">}),</span>
<span class="n">cluster_with_name</span><span class="p">(</span><span class="n">clusters</span><span class="p">,</span> <span class="s">"skilling-j"</span><span class="p">,</span> <span class="p">{</span><span class="s">"color"</span><span class="p">:</span><span class="s">"#FF6600"</span><span class="p">,</span> <span class="s">"desc"</span><span class="p">:</span><span class="s">"The VIP/executives group"</span><span class="p">}),</span>
<span class="p">]</span>
<span class="n">suspicious</span> <span class="o">=</span> <span class="nb">dict</span><span class="p">(</span><span class="n">suspicious</span><span class="p">)</span>
<span class="k">for</span> <span class="n">idx</span><span class="p">,</span> <span class="p">(</span><span class="n">boundary</span><span class="p">,</span> <span class="n">size</span><span class="p">)</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="nb">zip</span><span class="p">(</span><span class="n">boundaries</span><span class="p">,</span> <span class="n">sizes</span><span class="p">)):</span>
<span class="k">if</span> <span class="n">size</span> <span class="o"><</span> <span class="mi">5</span><span class="p">:</span>
<span class="k">continue</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="n">N</span><span class="p">),</span> <span class="n">boundary</span><span class="o">*</span><span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">(</span><span class="n">N</span><span class="p">),</span> <span class="n">color</span><span class="o">=</span><span class="s">'#0066CC'</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">boundary</span><span class="o">*</span><span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">(</span><span class="n">N</span><span class="p">),</span> <span class="nb">range</span><span class="p">(</span><span class="n">N</span><span class="p">),</span> <span class="n">color</span><span class="o">=</span><span class="s">'#0066CC'</span><span class="p">)</span>
<span class="k">if</span> <span class="n">idx</span> <span class="ow">in</span> <span class="n">suspicious</span><span class="p">:</span>
<span class="n">rect</span> <span class="o">=</span> <span class="n">patches</span><span class="o">.</span><span class="n">Rectangle</span><span class="p">((</span><span class="n">boundary</span><span class="o">-</span><span class="n">size</span><span class="p">,</span> <span class="n">boundary</span><span class="o">-</span><span class="n">size</span><span class="p">),</span>
<span class="n">width</span><span class="o">=</span><span class="n">size</span><span class="p">,</span> <span class="n">height</span><span class="o">=</span><span class="n">size</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.5</span><span class="p">,</span> <span class="n">fc</span><span class="o">=</span><span class="n">suspicious</span><span class="p">[</span><span class="n">idx</span><span class="p">][</span><span class="mi">1</span><span class="p">][</span><span class="s">"color"</span><span class="p">])</span>
<span class="n">plt</span><span class="o">.</span><span class="n">gca</span><span class="p">()</span><span class="o">.</span><span class="n">add_patch</span><span class="p">(</span><span class="n">rect</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">imshow</span><span class="p">(</span><span class="n">z</span><span class="p">,</span> <span class="n">cmap</span><span class="o">=</span><span class="n">blue_cmap</span><span class="p">,</span> <span class="n">interpolation</span><span class="o">=</span><span class="s">'nearest'</span><span class="p">,</span> <span class="n">aspect</span><span class="o">=</span><span class="s">'auto'</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-python"><div class="highlight"><pre><matplotlib.image.AxesImage at 0x10af923d0>
</pre></div>
</div>
<img alt="_images/enron-email_21_1.png" src="_images/enron-email_21_1.png" />
<p>We’ve identified two suspicious clusters. Let’s look at the data to find
out who these individuals are</p>
<div class="code python highlight-python"><div class="highlight"><pre><span class="k">def</span> <span class="nf">cluster_names</span><span class="p">(</span><span class="n">cluster</span><span class="p">):</span>
<span class="k">return</span> <span class="p">[</span><span class="n">names</span><span class="p">[</span><span class="n">idx</span><span class="p">]</span> <span class="k">for</span> <span class="n">idx</span> <span class="ow">in</span> <span class="n">cluster</span><span class="p">]</span>
<span class="k">def</span> <span class="nf">get_full_name</span><span class="p">(</span><span class="n">name</span><span class="p">):</span>
<span class="k">return</span> <span class="n">enron_utils</span><span class="o">.</span><span class="n">FULLNAMES</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="n">name</span><span class="p">,</span> <span class="n">name</span><span class="p">)</span>
<span class="k">def</span> <span class="nf">get_title</span><span class="p">(</span><span class="n">name</span><span class="p">):</span>
<span class="k">return</span> <span class="n">enron_utils</span><span class="o">.</span><span class="n">TITLES</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="n">name</span><span class="p">,</span> <span class="s">"?"</span><span class="p">)</span>
<span class="k">for</span> <span class="n">cluster</span><span class="p">,</span> <span class="n">payload</span> <span class="ow">in</span> <span class="n">suspicious</span><span class="o">.</span><span class="n">values</span><span class="p">():</span>
<span class="n">cnames</span> <span class="o">=</span> <span class="n">cluster_names</span><span class="p">(</span><span class="n">cluster</span><span class="p">)</span>
<span class="n">ctitles</span> <span class="o">=</span> <span class="nb">map</span><span class="p">(</span><span class="n">get_title</span><span class="p">,</span> <span class="n">cnames</span><span class="p">)</span>
<span class="k">print</span> <span class="n">payload</span><span class="p">[</span><span class="s">"desc"</span><span class="p">]</span>
<span class="k">for</span> <span class="n">n</span><span class="p">,</span> <span class="n">t</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="n">cnames</span><span class="p">,</span> <span class="n">ctitles</span><span class="p">):</span>
<span class="k">print</span> <span class="s">"</span><span class="se">\t</span><span class="s">"</span><span class="p">,</span> <span class="n">get_full_name</span><span class="p">(</span><span class="n">n</span><span class="p">),</span> <span class="s">'</span><span class="se">\t\t</span><span class="s">"{}"'</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">t</span><span class="p">)</span>
<span class="k">print</span>
</pre></div>
</div>
<div class="highlight-python"><div class="highlight"><pre>The pipeline/regulatory group
Lynn Blair "?"
Shelley Corman "Vice President Regulatory Affairs"
Lindy Donoho "Employee"
Drew Fossum "Vice President"
Tracy Geaccone "Employee"
harris-s "?"
Rod Hayslett "Vice President Also Chief Financial Officer and Treasurer"
Stanley Horton "President Enron Gas Pipeline"
Kevin Hyatt "Director Pipeline Business"
Michelle Lokay "Employee Administrative Asisstant"
Teb Lokey "Manager Regulatory Affairs"
Danny McCarty "Vice President"
mcconnell-m "?"
Darrell Schoolcraft "?"
Kimberly Watson "?"
The VIP/executives group
Rick Buy "Manager Chief Risk Management Officer"
Jeff Dasovich "Employee Government Relation Executive"
David Delainey "CEO Enron North America and Enron Enery Services"
Louise Kitchen "President Enron Online"
John Lavorato "CEO Enron America"
Richard Shapiro "Vice President Regulatory Affairs"
Jeffery Skilling "CEO"
Barry Tycholiz "Vice President"
Greg Whalley "President"
williams-j "?"
</pre></div>
</div>
<p>Given the uncertainty behind these latent clusters, we can visualize the
variablity within these assignments with a z-matrix</p>
<p>Ordering the z-matrix allows us to group members of each possible
cluster together</p>
<div class="code python highlight-python"><div class="highlight"><pre><span class="n">zmat</span> <span class="o">=</span> <span class="n">query</span><span class="o">.</span><span class="n">zmatrix</span><span class="p">(</span><span class="n">domain</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">latents</span><span class="o">=</span><span class="n">infers</span><span class="p">)</span>
<span class="n">zmat</span> <span class="o">=</span> <span class="n">zmatrix_reorder</span><span class="p">(</span><span class="n">zmat</span><span class="p">,</span> <span class="n">zmatrix_heuristic_block_ordering</span><span class="p">(</span><span class="n">zmat</span><span class="p">))</span>
</pre></div>
</div>
<div class="code python highlight-python"><div class="highlight"><pre><span class="n">sns</span><span class="o">.</span><span class="n">heatmap</span><span class="p">(</span><span class="n">zmat</span><span class="p">,</span> <span class="n">cmap</span><span class="o">=</span><span class="n">blue_cmap</span><span class="p">,</span> <span class="n">cbar</span><span class="o">=</span><span class="bp">False</span><span class="p">,</span> <span class="n">xticklabels</span><span class="o">=</span><span class="n">labels</span><span class="p">,</span> <span class="n">yticklabels</span><span class="o">=</span><span class="n">labels</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="s">'people (sorted)'</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">ylabel</span><span class="p">(</span><span class="s">'people (sorted)'</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s">'Z-Matrix of IRM Cluster Assignments'</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-python"><div class="highlight"><pre><matplotlib.text.Text at 0x10bc8bc50>
</pre></div>
</div>
<img alt="_images/enron-email_26_1.png" src="_images/enron-email_26_1.png" />
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