Terms selection with chi-square

In Natural Language Processing, the identification the most relevant terms in a collection of documents is a common task. It can produce meaningful insights about the data and it can also be useful to improve classification performances and computational efficiency. A popular measure of relevance for terms is the χ² statistic. To compute it we can convert the terms of our document collection and turn them into features of a vectorial model, then χ² can be computed as follow:

Where f is a feature (a term in this case), t is a target variable that we, usually, want to predict, A is the number of times that f and t cooccur, B is the number of times that f occurs without t, C is the number of times that t occurs without f, D is the number of times neither t or f occur and N is the number of observations.

Let's see how χ² can be used through a simple example. We load some posts from 4 different newsgroups categories using the sklearn interface:

from sklearn.datasets import fetch_20newsgroups
 # newsgroups categories
categories = ['alt.atheism','talk.religion.misc',
              'comp.graphics','sci.space']

posts = fetch_20newsgroups(subset='train', categories=categories,
                           shuffle=True, random_state=42,
                           remove=('headers','footers','quotes'))

From the posts loaded, we build a linear model using all the terms in the document collection but the stop words:

from sklearn.feature_extraction.text import CountVectorizer
vectorizer = CountVectorizer(lowercase=True,stop_words='english')
X = vectorizer.fit_transform(posts.data)

Now, X is a document-term matrix where the element X_i,j is the frequency of the term j in the document i. Then, the features are given by the columns of X and we want to compute χ² between the categories of interest and each feature in order to figure out what are the most relevant terms. This can be done as follows

from sklearn.feature_selection import chi2
# compute chi2 for each feature
chi2score = chi2(X,posts.target)[0]

To have a visual insight, we can plot a bar chart where each bar shows the χ² value computed above:

from pylab import barh,plot,yticks,show,grid,xlabel,figure
figure(figsize=(6,6))
wscores = zip(vectorizer.get_feature_names(),chi2score)
wchi2 = sorted(wscores,key=lambda x:x[1]) 
topchi2 = zip(*wchi2[-25:])
x = range(len(topchi2[1]))
labels = topchi2[0]
barh(x,topchi2[1],align='center',alpha=.2,color='g')
plot(topchi2[1],x,'-o',markersize=2,alpha=.8,color='g')
yticks(x,labels)
xlabel('$\chi^2$')
show()

We can observe that the terms with a high χ² can be considered relevant for the newsgroup categories we are analyzing. For example, the terms space, nasa and launch can be considered relevant for the group sci.space. The terms god, jesus and atheism can be considered relevant for the groups alt.atheism and talk.religion.misc. And, the terms image, graphics and jpeg can be considered relevant in the category comp.graphics.

Real-time Twitter analysis

The twitter API is a great tool for analyze tweets by code. In particular, the streaming API gives real time access to the global stream of tweets and, unlike a conventional REST API, it is used through a continuous connection to the Twitter servers. So it requires a persistent HTTP connection open as long as you need to collect tweets. The typical workflow of an application which uses this API is the following:

The easiest way to handle an HTTP streaming in Python is to use PyCurl, the Python bindings for the famous Curl network library. PyCurl allows you to provide a callback function that will be executed every time a new block of data is available. The following code is a simple demonstration of how we can use HTTP streaming with PyCurl in order to analyzie a stream of tweet:

from __future__ import division
from collections import defaultdict
from pylab import barh,show,yticks
import pycurl
import simplejson
import sys
import nltk
import re

def plot_histogram(freq, mean):
 # using dict comprehensions to remove not frequent words
 topwords = {word : count 
             for word,count in freq.items() 
             if count > round(2*mean)}
 # plotting
 y = topwords.values()
 x = range(len(y))
 labels = topwords.keys()
 barh(x,y,align='center')
 yticks(x,labels)
 show()

class TwitterAnalyzer:
 def __init__(self):
  self.freq = defaultdict(int)
  self.cnt = 0
  self.mean = 0.0
  # composing the twitter stream url
  nyc_area = 'locations=-74,40,-73,41'
  self.url = "https://stream.twitter.com/1.1/statuses/filter.json?"+nyc_area

 def begin(self,usr,pws):
  """ 
    init and start the connection with twitter using pycurl
    usr and pws must be valid twitter credentials
  """
  self.conn = pycurl.Curl()
  # we use the basic authentication, 
  # in future oauth2 could be required
  self.conn.setopt(pycurl.USERPWD, "%s:%s" % (usr, pws))
  self.conn.setopt(pycurl.URL, self.url)
  self.conn.setopt(pycurl.WRITEFUNCTION, self.on_receive)
  self.conn.perform()

 def on_receive(self,data):
  """ Handles the arrive of a single tweet """
  self.cnt += 1
  tweet = simplejson.loads(data)
  # a little bit of natural language processing
  tokens = nltk.word_tokenize(tweet['text']) # tokenize
  tagged_sent = nltk.pos_tag(tokens) # Part Of Speech tagging
  for word,tag in tagged_sent:
   # filter sigle chars words and symbols
   if len(word) > 1 and re.match('[A-Za-z0-9 ]+',word):
    # consider only adjectives and nouns
    if tag == 'JJ' or tag == 'NN':
     self.freq[word] += 1 # keep the count
  # print the statistics every 50 tweets
  if self.cnt % 50 == 0:
   self.print_stats()

 def print_stats(self):
  maxc = 0
  sumc = 0
  for word,count in self.freq.items():
   if maxc < count:
    maxc = count
   sumc += count
  self.mean = sumc/len(self.freq)
  print '-------------------------------'
  print ' tweets analyzed:', self.cnt
  print ' words extracted:', len(self.freq)
  print '   max frequency:', maxc
  print '  mean frequency:', self.mean

 def close_and_plot(self,signal,frame):
  print ' Plotting...'  
  plot_histogram(self.freq,self.mean)
  sys.exit(0)

In the constructor of this class we initialize a dictionary that will contain the frequency of each word, a string that contains the url of the service we need to call (composed in order to query twitter for the tweets in NYC) and the variables cnt and mean to keep track of the number of tweets analyzed and of the mean frequency over all the words.
In the method begin, we use the PyCurl library for the authentication to Twitter and start the connection. In particular, we set that the method on_receive is the callback function demanded to processing of the incoming. In this method the actual analysis is done, every tweet is split in tokens and a part of speech tagging is performed. Then, the frequency of all the words that are adjective or nouns is updated.
The method print_stats is used to print the our statistics on the console while close_and_plot plots an histogram using the frequencies in the dictionary and closes the program.
Let's use this class:

import signal
usr = 'supersexytwitteruser'
pws = "yessosexyiam"

ta = TwitterAnalyzer()
# invoke the close_and_plot() method when a Ctrl-D arrives
signal.signal(signal.SIGINT, ta.close_and_plot)
ta.begin(usr,pws) # run the analysis

In the code above, a TwitterAnalyzer object is instantiated, its method close_and_plot is registered as handler for the SIGINT signal and, finally, begin is invoked.
This code starts a program which analyzes all the tweet of the New York Area in real time and prints the statistics every 50 tweets, just like follows:

-------------------------------
 tweets analyzed: 50
 words extracted: 110
   max frequency: 8
  mean frequency: 1.12727272727
-------------------------------
 tweets analyzed: 100
 words extracted: 200
   max frequency: 22
  mean frequency: 1.235
-------------------------------
 tweets analyzed: 150
 words extracted: 286
   max frequency: 29
  mean frequency: 1.26573426573
-------------------------------
 tweets analyzed: 200
 words extracted: 407
   max frequency: 39
  mean frequency: 1.31203931204
-------------------------------
 tweets analyzed: 250
 words extracted: 495
   max frequency: 49
  mean frequency: 1.37575757576

Pressing Cntrl-D we can stop the program and plot a bar chart of adjectives and nouns detected. This is what I got in the morning of March 21, 2013:

We see that is very common to post a link in a tweet (turned out that http is considered as a noun most of the time) and that the words day, today, good and morning were the most used during the analysis.