.. _enron_email: Clustering the `Enron e-mail corpus `__ using the Infinite Relational Model ============================================================================================================ -------------- Let's setup our environment .. code:: python %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') Below are the functions from datamicroscopes we'll be using to cluster the data .. code:: python from microscopes.common.rng import rng from microscopes.common.relation.dataview import numpy_dataview from microscopes.models import bb as beta_bernoulli from microscopes.irm.definition import model_definition from microscopes.irm import model, runner, query from microscopes.kernels import parallel from microscopes.common.query import groups, zmatrix_heuristic_block_ordering, zmatrix_reorder We've made a set of utilities especially for this dataset, ``enron_utils``. We'll include these as well. We have downloaded the data and preprocessed it as suggested by `Ishiguro et al. 2012 `__. The results of the scirpt have been stored in the ``results.p``. ``enron_crawler.py`` in the kernels repo includes the script to create ``results.p`` .. code:: python import enron_utils Let's load the data and make a binary matrix to represent email communication between individuals In this matrix, :math:`X_{i,j} = 1` if and only if person\ :math:`_{i}` sent an email to person\ :math:`_{j}` .. code:: python with open('results.p') as fp: communications = pickle.load(fp) def allnames(o): for k, v in o: yield [k] + list(v) names = set(it.chain.from_iterable(allnames(communications))) names = sorted(list(names)) namemap = { name : idx for idx, name in enumerate(names) } N = len(names) communications_relation = np.zeros((N, N), dtype=np.bool) for sender, receivers in communications: sender_id = namemap[sender] for receiver in receivers: receiver_id = namemap[receiver] communications_relation[sender_id, receiver_id] = True print "%d names in the corpus" % N .. parsed-literal:: 115 names in the corpus Let's visualize the communication matrix .. code:: python blue_cmap = sns.light_palette("#34495e", as_cmap=True) labels = [i if i%20 == 0 else '' for i in xrange(N)] sns.heatmap(communications_relation, cmap=blue_cmap, linewidths=0, cbar=False, xticklabels=labels, yticklabels=labels) plt.xlabel('person number') plt.ylabel('person number') plt.title('Email Communication Matrix') .. parsed-literal:: .. image:: enron-email_files/enron-email_9_1.png Now, let's learn the underlying clusters using the Inifinite Relational Model Let's import the necessary functions from datamicroscopes 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 Let's start by defining the model and loading the data To define our model, we need to specify our domains and relations Our domains are described in a list of the cardinalities of each domain Our releations are in a list of tuples which refer to the indicies of each domain and the model type In this case, the our domain is users, which is of size :math:`N` Our relations are users to users, both of cardinality :math:`N`, and we model the relation with beta-bernoulli distribution since our data is binary .. code:: python defn = model_definition([N], [((0, 0), beta_bernoulli)]) views = [numpy_dataview(communications_relation)] prng = rng() Next, let's initialize the model and define the runners. These runners are our MCMC chains. We'll use ``cpu_count`` to define our number of chains. .. code:: python nchains = cpu_count() latents = [model.initialize(defn, views, r=prng, cluster_hps=[{'alpha':1e-3}]) for _ in xrange(nchains)] kc = runner.default_assign_kernel_config(defn) runners = [runner.runner(defn, views, latent, kc) for latent in latents] r = parallel.runner(runners) From here, we can finally run each chain of the sampler 1000 times .. code:: python start = time.time() r.run(r=prng, niters=1000) print "inference took {} seconds".format(time.time() - start) .. parsed-literal:: inference took 128.098203897 seconds Now that we have learned our model let's get our cluster assignments .. code:: python infers = r.get_latents() clusters = groups(infers[0].assignments(0), sort=True) ordering = list(it.chain.from_iterable(clusters)) Let's sort the communications matrix to highlight our inferred clusters .. code:: python z = communications_relation.copy() z = z[ordering] z = z[:,ordering] sizes = map(len, clusters) boundaries = np.cumsum(sizes)[:-1] Our model finds suspicious cluster based on the communication data. Let's color and label these clusters in our communications matrix. .. code:: python def cluster_with_name(clusters, name, payload=None): ident = namemap[name] for idx, cluster in enumerate(clusters): if ident in cluster: return idx, (cluster, payload) raise ValueError("could not find name") suspicious = [ cluster_with_name(clusters, "horton-s", {"color":"#66CC66", "desc":"The pipeline/regulatory group"}), cluster_with_name(clusters, "skilling-j", {"color":"#FF6600", "desc":"The VIP/executives group"}), ] suspicious = dict(suspicious) for idx, (boundary, size) in enumerate(zip(boundaries, sizes)): if size < 5: continue plt.plot(range(N), boundary*np.ones(N), color='#0066CC') plt.plot(boundary*np.ones(N), range(N), color='#0066CC') if idx in suspicious: rect = patches.Rectangle((boundary-size, boundary-size), width=size, height=size, alpha=0.5, fc=suspicious[idx][1]["color"]) plt.gca().add_patch(rect) plt.imshow(z, cmap=blue_cmap, interpolation='nearest', aspect='auto') .. parsed-literal:: .. image:: enron-email_files/enron-email_21_1.png We've identified two suspicious clusters. Let's look at the data to find out who these individuals are .. code:: python def cluster_names(cluster): return [names[idx] for idx in cluster] def get_full_name(name): return enron_utils.FULLNAMES.get(name, name) def get_title(name): return enron_utils.TITLES.get(name, "?") for cluster, payload in suspicious.values(): cnames = cluster_names(cluster) ctitles = map(get_title, cnames) print payload["desc"] for n, t in zip(cnames, ctitles): print "\t", get_full_name(n), '\t\t"{}"'.format(t) print .. parsed-literal:: 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 "?" Given the uncertainty behind these latent clusters, we can visualize the variablity within these assignments with a z-matrix Ordering the z-matrix allows us to group members of each possible cluster together .. code:: python zmat = query.zmatrix(domain=0, latents=infers) zmat = zmatrix_reorder(zmat, zmatrix_heuristic_block_ordering(zmat)) .. code:: python sns.heatmap(zmat, cmap=blue_cmap, cbar=False, xticklabels=labels, yticklabels=labels) plt.xlabel('people (sorted)') plt.ylabel('people (sorted)') plt.title('Z-Matrix of IRM Cluster Assignments') .. parsed-literal:: .. image:: enron-email_files/enron-email_26_1.png