Last week, we introduced the concept of natural language processing, and in particular the "bag of words" model for representing and quantifying text for later analysis. In this lecture, we'll expand on those topics, including some additional preprocessing and text representation methods. By the end of this lecture, you should be able to
The "bag of words" model: why do we do it? what does it give us?
It's a way of representing documents in a format that is convenient and amenable to sophisticated analysis.
You're interested in blogs. Specifically, you're interested in how blogs link to each other. Do politically-liberal blogs tend to link to politically-conservative blogs, and vice versa? Or do they mostly link to themselves?
Imagine you have a list of a few hundred blogs. To get their political leanings, you'd need to analyze the blogs and see how similar they are.
To do that, you need some notion of similarity...
We need to be able to represent the blogs as feature vectors.
If you can come up with a quantitative representation of your "thing" of interest, then you can compare it to other instances of that thing.
The bag-of-words model is just one way of turning a document into a feature vector that can be used in analysis. By considering each blog to be a single document, you can therefore convert each blog to its own bag-of-words and compare them directly.
(in fact, this has actually been done)
If you have some data point $\vec{x}$ that is an $n$-dimensional vector (pictured above: a three-dimensional vector), each dimension is a single feature.
(Hint: what does this correspond to with NumPy arrays?)
Therefore, a bag-of-words model is just a way of representing a document as a vector, where the dimensions are word counts!
Pictured above are three separate documents, and the number of times each of the words appears is given by the height of the histogram bar. Stare at this until you get some understanding of what's happening--these are three documents that share the same words (as you can see, they have the same x-axes), but what differs are the relative heights of the bars, meaning they have different values along the x-axes.
Of course there are other ways of representing documents as vectors, but bag-of-words is the easiest.
What is "preprocessing"?
Name some preprocessing techniques with text we've covered!
There are a few more that can be very powerful.
To start, let's go back to the Alice in Wonderland example from the previous lecture, but this time, we'll add a few more books for comparison:
Hopefully this variety should give us a good idea what we're dealing with!
First, we'll read all the books' raw contents into a dictionary.
In [1]:
books = {} # We'll use a dictionary to store all the text from the books.
files = ['Lecture18/alice.txt',
'Lecture18/pride.txt',
'Lecture18/frank.txt',
'Lecture18/bwulf.txt',
'Lecture18/holmes.txt',
'Lecture18/tom.txt',
'Lecture18/finn.txt']
for f in files:
# This weird line just takes the part of the filename between the "/" and "." as the dict key.
prefix = f.split("/")[-1].split(".")[0]
try:
with open(f, "r", encoding = "ISO-8859-1") as descriptor:
books[prefix] = descriptor.read()
except:
print("File '{}' had an error!".format(f))
books[prefix] = None
In [2]:
# Here you can see the dict keys (i.e. the results of the weird line of code in the last cell)
print(books.keys())
Just like before, let's go ahead and lower case everything, strip out whitespace, then count all the words.
In [3]:
def preprocess(book):
# First, lowercase everything.
lower = book.lower()
# Second, split into lines.
lines = lower.split("\n")
# Third, split each line into words.
words = []
for line in lines:
words.extend(line.strip().split(" "))
# That's it!
return count(words)
In [4]:
from collections import defaultdict # Our good friend from the last lecture, defaultdict!
def count(words):
counts = defaultdict(int)
for w in words:
counts[w] += 1
return counts
In [5]:
counts = {}
for k, v in books.items():
counts[k] = preprocess(v)
Let's see how our basic preprocessing techniques from the last lecture worked out.
In [6]:
from collections import Counter
def print_results(counts):
for key, bag_of_words in counts.items():
word_counts = Counter(bag_of_words)
mc_word, mc_count = word_counts.most_common(1)[0]
print("'{}' has {} unique words, and the most common is '{}', occuring {} times."
.format(key, len(bag_of_words.keys()), mc_word, mc_count))
print_results(counts)
Yeesh.
Not only are the most common words among the most boring ("the"? "and"?), but there are occasions where the most common word isn't even a word, but rather a blank space. (How do you think that could happen?)
A great first step is to implement stop words. (I used this list of 319 stop words)
In [7]:
with open("Lecture18/stopwords.txt", "r") as f:
lines = f.read().split("\n")
stopwords = [w.strip() for w in lines]
print(stopwords[:5])
Now we'll augment our preprocess function to include stop word processing.
In [8]:
def preprocess_v2(book, stopwords): # Note the "_v2"--this is a new function!
# First, lowercase everything.
lower = book.lower()
# Second, split into lines.
lines = lower.split("\n")
# Third, split each line into words.
words = []
for line in lines:
tokens = line.strip().split(" ")
# Check for stopwords.
for t in tokens:
if t in stopwords: continue # This "continue" SKIPS the stopword entirely!
words.append(t)
# That's it!
return count(words)
Now let's see what we have!
In [9]:
counts = {}
for k, v in books.items():
counts[k] = preprocess_v2(v, stopwords)
print_results(counts)
Well, this seems even worse! What could we try next?
Pretty straightforward: cut out all the words under a certain length; say, 2. After all--how many words do you know that are semantically super-important to a book, and yet are fewer than 2 letters long?
(I'm sure you can think of a few; my point being, they're so few they're unlikely to matter much)
In [10]:
def preprocess_v3(book, stopwords): # We've reached "_v3"!
# First, lowercase everything.
lower = book.lower()
# Second, split into lines.
lines = lower.split("\n")
# Third, split each line into words.
words = []
for line in lines:
tokens = line.strip().split(" ")
# Check for stopwords.
for t in tokens:
if t in stopwords or len(t) <= 2: continue # Skip stopwords AND words with length under 2
words.append(t)
# That's it!
return count(words)
Maybe this will be better?
In [11]:
counts = {}
for k, v in books.items():
counts[k] = preprocess_v3(v, stopwords)
print_results(counts)
Ooh! Definite improvement! Though clearly, punctuation is getting in the way; you can see it in at least two of the top words in the list above.
We spoke last time about how removing punctuation could be a little dangerous; what if the punctuation is inherent to the meaning of the word (i.e., a contraction)?
Here, we'll compromise a little: we'll get the "easy" punctuation, like exclamation marks, periods, and commas, and leave the rest.
In [12]:
def preprocess_v4(book, stopwords):
# First, lowercase everything.
lower = book.lower()
# Second, split into lines.
lines = lower.split("\n")
# Third, split each line into words.
words = []
for line in lines:
tokens = line.strip().split(" ")
# Check for stopwords.
for t in tokens:
# Cut off any end-of-sentence punctuation.
if t.endswith(",") or t.endswith("!") or t.endswith(".") or \
t.endswith(":") or t.endswith(";") or t.endswith("?"):
t = t[:-1] # This says: take everything except the last letter
if t in stopwords or len(t) <= 2: continue
words.append(t)
# That's it!
return count(words)
Alright, let's check it out again.
In [13]:
counts = {}
for k, v in books.items():
counts[k] = preprocess_v4(v, stopwords)
print_results(counts)
Now we're getting somewhere! But this introduces a new concept--in looking at this list, wouldn't you say that "says" and "said" are probably, semantically, more or less the same word?
Stemming is the process by which we convert words with similar meaning into the same word, so their similarity is reflected in our analysis. Words like "imaging" and "images", or "says" and "said" should probably be considered the same thing.
To do this, we'll need an external Python package: the Natural Language Toolkit, or NLTK. (it's installed on JupyterHub, so go ahead and play with it!)
In [14]:
import nltk # This package!
def preprocess_v5(book, stopwords):
lower = book.lower()
lines = lower.split("\n")
# Create the stemmer.
stemmer = nltk.stem.SnowballStemmer('english')
words = []
for line in lines:
tokens = line.strip().split(" ")
for t in tokens:
if t.endswith(",") or t.endswith("!") or t.endswith(".") or \
t.endswith(":") or t.endswith(";") or t.endswith("?"):
t = t[:-1]
if t in stopwords or len(t) <= 2: continue
stemmed = stemmer.stem(t) # This is all that is required--nltk does the rest!
words.append(stemmed)
# That's it!
return count(words)
How did this go?
In [15]:
counts = {}
for k, v in books.items():
counts[k] = preprocess_v5(v, stopwords)
print_results(counts)
Well, this kinda helped--"says" was reduced to "say", and its count clearly increased from the 628 it was before, meaning stemmed versions that were previously viewed as different words were merged. But "said" is still there; clearly, there are limitations to this stemmer.
As one final step--it's convenient sometimes to simply drop words that occur only once or twice. This can dramatically help with processing time, as quite a few words (usually proper nouns) will only be seen a few times.
In [16]:
def preprocess_v6(book, stopwords):
lower = book.lower()
lines = lower.split("\n")
# Create the stemmer.
stemmer = nltk.stem.SnowballStemmer('english')
words = []
for line in lines:
tokens = line.strip().split(" ")
for t in tokens:
if t.endswith(",") or t.endswith("!") or t.endswith(".") or \
t.endswith(":") or t.endswith(";") or t.endswith("?"):
t = t[:-1]
if t in stopwords or len(t) <= 2: continue
stemmed = stemmer.stem(t)
words.append(stemmed)
# Only keep words that were observed more than once.
word_counts = count(words)
return {k: v for k, v in word_counts.items() if v > 1}
One final check:
In [17]:
counts = {}
for k, v in books.items():
counts[k] = preprocess_v6(v, stopwords)
print_results(counts)
The most common words and their counts haven't changed, but hopefully you can see there's a big difference in the number of unique words!
Now that we have the document vectors in bag of words format, fully preprocessed, we can do some analysis, right?
First, let's step back and discuss again what these features actually mean.
Here's food for thought: if we are assuming high word count = high importance, what do we do about those two books that both have "said" as their most frequent word?
We could just add it to our stop list. But as we saw last time, another word that may only be slightly more meaningful will take its place. How do we know when to stop adding words to our stoplist?
Maybe, like we did with cutting out words that only appeared once, we could cut out the top 5% of words. But then why not 4% or 6%? Where do we set that threshold?
What is it we're really hoping these word counts tell us?
So far, what we've computed in our bag of words, is term frequencies.
Each individual word is a term, and we've simply counted how many times those terms appeared, or how frequent they were.
The underlying assumption of using word frequencies as features is that some number of shared words will appear across ALL the documents, but vary considerably in how frequently they appear. Remember our feature vectors plot from earlier in the lecture:
You'll notice the x-axes for these three plots are the same! It's the relative frequencies of those x-values that differ over the three documents. That's what we're hoping for.
But since documents, in general, don't have an upper limit to the number of words they can have, you can run into the following situation:
In [18]:
document1 = ["Happy", "Halloween"]
document2 = ["Happy", "Happy", "Happy", "Halloween", "Halloween", "Halloween"]
This is an admittedly blunt example, but using just term frequencies, which document would you say would be more important if I searched for the word "Halloween"? What should the relative importance of the word "Halloween" to these two documents be?
To handle this problem, we combine term frequency (TF) with inverse document frequency (IDF).
This quantity consists of two terms (TF and IDF) that are multiplied together.
You already know how to compute TF: just the count of how many times $word_i$ appears in document $d$ (though this is usually normalized by the total number of words in the document, so it becomes a probability!).
IDF is a little more involved. To compute it, you need access to all the documents.
IDF is a fraction:
Let's think about this.
This has the effect of weighting the words by how often they're found across all documents.
To do the TF-IDF computation, let's first convert our counts to a matrix: the rows are documents (so there will be 7 rows), and the columns are the counts for each word.
In [19]:
import numpy as np
all_words = set([w for d in counts.values() for w in d.keys()])
count_matrix = np.zeros(shape = (len(counts.keys()), len(all_words)))
for i, word in enumerate(all_words):
for j, doc in enumerate(counts.keys()):
doc_counts = counts[doc]
if word in doc_counts:
count_matrix[j][i] = doc_counts[word]
In [20]:
print(count_matrix[0, :5])
Now we'll compute the inverse document frequencies.
In [21]:
tfidf = np.zeros(shape = (len(counts.keys()), len(all_words)))
normalizers = count_matrix.sum(axis = 1)
num_docs = len(counts.keys())
for j in range(count_matrix.shape[1]):
column = count_matrix[:, j]
greater_than_zero = len(column[column > 0])
tf = column / normalizers
idf = num_docs / greater_than_zero
tfidf[:, j] = tf * idf
TF-IDF may have a fancy name and a cool looking acronym, but it's still a glorified word count, just with weights.
Word counts are nothing more than histograms, so we should be able to make some bar plots of our 7 TF-IDF vectors, one for each book.
In [22]:
%matplotlib inline
import matplotlib.pyplot as plt
import seaborn as sns
x = np.arange(len(all_words)) + 1
books = list(counts.keys())
for i in range(tfidf.shape[0]):
book_tfidf = tfidf[i]
plt.subplot(2, 4, i + 1)
plt.plot(x, book_tfidf)
plt.title(books[i])
plt.ylim([0, 0.12])
plt.xlim([0, x.shape[0] + 1])
plt.xticks([])
plt.yticks([])
One final bit of introspective magic: the above histograms are great, but they don't really give us a good intuition for what's really going on in these books.
Ever seen a word cloud before?
In [23]:
from wordcloud import WordCloud
for i in range(tfidf.shape[0]):
book_tfidf = tfidf[i]
freqs = []
for j, word in enumerate(all_words):
if book_tfidf[j] > 0:
freqs.append((word, book_tfidf[j]))
wc = WordCloud().generate_from_frequencies(freqs)
#plt.subplot(4, 2, i + 1)
plt.figure(i)
plt.imshow(wc)
plt.title(books[i])
plt.axis("off")
Some questions to discuss and consider:
1: There are many machine learning algorithms that rely on the probability of a single word, $P(w)$, under some condition (e.g. the probability of a word in a conservative or liberal blog). Explain what this would involve.
2: So far we've considered only nonzero word counts. When you combine all the unique words in a collection of documents together, it's possible (even likely) that quite a few of the words will have counts of 0 in some of the documents. Why is this? What problems might this cause for the later analyses?
3: Another point we haven't even touched on, but which can really generate very powerful features, is the inclusion of $n$-grams. If you consider $n = 1$ to be the case of individual words as we've used them throughout the last two lectures, with $n = 2$ we instead consider a single "token" to be every sequence of 2 consecutive words. What advantages and disadvantages would this approach have (e.g. $n = 2$, or bigrams), over using single words ($n = 1$, or unigrams)?
#questions channel!