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Natural Language Processing with Python by Edward Loper, Steven Bird, Ewan Klein

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Computing with Language: Simple Statistics

Let’s return to our exploration of the ways we can bring our computational resources to bear on large quantities of text. We began this discussion in Computing with Language: Texts and Words, and saw how to search for words in context, how to compile the vocabulary of a text, how to generate random text in the same style, and so on.

In this section, we pick up the question of what makes a text distinct, and use automatic methods to find characteristic words and expressions of a text. As in Computing with Language: Texts and Words, you can try new features of the Python language by copying them into the interpreter, and you’ll learn about these features systematically in the following section.

Before continuing further, you might like to check your understanding of the last section by predicting the output of the following code. You can use the interpreter to check whether you got it right. If you’re not sure how to do this task, it would be a good idea to review the previous section before continuing further.

>>> saying = ['After', 'all', 'is', 'said', 'and', 'done',
...           'more', 'is', 'said', 'than', 'done']
>>> tokens = set(saying)
>>> tokens = sorted(tokens)
>>> tokens[-2:]
what output do you expect here?
>>>

Frequency Distributions

How can we automatically identify the words of a text that are most informative about the topic and genre of the text? Imagine how you might go about finding the 50 most frequent words of a book. One method would be to keep a tally for each vocabulary item, like that shown in Figure 1-3. The tally would need thousands of rows, and it would be an exceedingly laborious process—so laborious that we would rather assign the task to a machine.

Counting words appearing in a text (a frequency distribution).

Figure 1-3. Counting words appearing in a text (a frequency distribution).

The table in Figure 1-3 is known as a frequency distribution , and it tells us the frequency of each vocabulary item in the text. (In general, it could count any kind of observable event.) It is a “distribution” since it tells us how the total number of word tokens in the text are distributed across the vocabulary items. Since we often need frequency distributions in language processing, NLTK provides built-in support for them. Let’s use a FreqDist to find the 50 most frequent words of Moby Dick. Try to work out what is going on here, then read the explanation that follows.

>>> fdist1 = FreqDist(text1) 1
>>> fdist1 2
<FreqDist with 260819 outcomes>
>>> vocabulary1 = fdist1.keys() 3
>>> vocabulary1[:50] 4
[',', 'the', '.', 'of', 'and', 'a', 'to', ';', 'in', 'that', "'", '-',
'his', 'it', 'I', 's', 'is', 'he', 'with', 'was', 'as', '"', 'all', 'for',
'this', '!', 'at', 'by', 'but', 'not', '--', 'him', 'from', 'be', 'on',
'so', 'whale', 'one', 'you', 'had', 'have', 'there', 'But', 'or', 'were',
'now', 'which', '?', 'me', 'like']
>>> fdist1['whale']
906
>>>

When we first invoke FreqDist, we pass the name of the text as an argument 1. We can inspect the total number of words (“outcomes”) that have been counted up 2—260,819 in the case of Moby Dick. The expression keys() gives us a list of all the distinct types in the text 3, and we can look at the first 50 of these by slicing the list 4.

Note

Your Turn: Try the preceding frequency distribution example for yourself, for text2. Be careful to use the correct parentheses and uppercase letters. If you get an error message NameError: name 'FreqDist' is not defined, you need to start your work with from nltk.book import *.

Do any words produced in the last example help us grasp the topic or genre of this text? Only one word, whale, is slightly informative! It occurs over 900 times. The rest of the words tell us nothing about the text; they’re just English “plumbing.” What proportion of the text is taken up with such words? We can generate a cumulative frequency plot for these words, using fdist1.plot(50, cumulative=True), to produce the graph in Figure 1-4. These 50 words account for nearly half the book!

Cumulative frequency plot for the 50 most frequently used words in Moby Dick, which account for nearly half of the tokens.

Figure 1-4. Cumulative frequency plot for the 50 most frequently used words in Moby Dick, which account for nearly half of the tokens.

If the frequent words don’t help us, how about the words that occur once only, the so-called hapaxes? View them by typing fdist1.hapaxes(). This list contains lexicographer, cetological, contraband, expostulations, and about 9,000 others. It seems that there are too many rare words, and without seeing the context we probably can’t guess what half of the hapaxes mean in any case! Since neither frequent nor infrequent words help, we need to try something else.

Fine-Grained Selection of Words

Next, let’s look at the long words of a text; perhaps these will be more characteristic and informative. For this we adapt some notation from set theory. We would like to find the words from the vocabulary of the text that are more than 15 characters long. Let’s call this property P, so that P(w) is true if and only if w is more than 15 characters long. Now we can express the words of interest using mathematical set notation as shown in a. This means “the set of all w such that w is an element of V (the vocabulary) and w has property P.”

Example 1-1. 

  1. {w | wV & P(w)}

  2. [w for w in V if p(w)]

The corresponding Python expression is given in b. (Note that it produces a list, not a set, which means that duplicates are possible.) Observe how similar the two notations are. Let’s go one more step and write executable Python code:

>>> V = set(text1)
>>> long_words = [w for w in V if len(w) > 15]
>>> sorted(long_words)
['CIRCUMNAVIGATION', 'Physiognomically', 'apprehensiveness', 'cannibalistically',
'characteristically', 'circumnavigating', 'circumnavigation', 'circumnavigations',
'comprehensiveness', 'hermaphroditical', 'indiscriminately', 'indispensableness',
'irresistibleness', 'physiognomically', 'preternaturalness', 'responsibilities',
'simultaneousness', 'subterraneousness', 'supernaturalness', 'superstitiousness',
'uncomfortableness', 'uncompromisedness', 'undiscriminating', 'uninterpenetratingly']
>>>

For each word w in the vocabulary V, we check whether len(w) is greater than 15; all other words will be ignored. We will discuss this syntax more carefully later.

Note

Your Turn: Try out the previous statements in the Python interpreter, and experiment with changing the text and changing the length condition. Does it make an difference to your results if you change the variable names, e.g., using [word for word in vocab if ...]?

Let’s return to our task of finding words that characterize a text. Notice that the long words in text4 reflect its national focus—constitutionally, transcontinental—whereas those in text5 reflect its informal content: boooooooooooglyyyyyy and yuuuuuuuuuuuummmmmmmmmmmm. Have we succeeded in automatically extracting words that typify a text? Well, these very long words are often hapaxes (i.e., unique) and perhaps it would be better to find frequently occurring long words. This seems promising since it eliminates frequent short words (e.g., the) and infrequent long words (e.g., antiphilosophists). Here are all words from the chat corpus that are longer than seven characters, that occur more than seven times:

>>> fdist5 = FreqDist(text5)
>>> sorted([w for w in set(text5) if len(w) > 7 and fdist5[w] > 7])
['#14-19teens', '#talkcity_adults', '((((((((((', '........', 'Question',
'actually', 'anything', 'computer', 'cute.-ass', 'everyone', 'football',
'innocent', 'listening', 'remember', 'seriously', 'something', 'together',
'tomorrow', 'watching']
>>>

Notice how we have used two conditions: len(w) > 7 ensures that the words are longer than seven letters, and fdist5[w] > 7 ensures that these words occur more than seven times. At last we have managed to automatically identify the frequently occurring content-bearing words of the text. It is a modest but important milestone: a tiny piece of code, processing tens of thousands of words, produces some informative output.

Collocations and Bigrams

A collocation is a sequence of words that occur together unusually often. Thus red wine is a collocation, whereas the wine is not. A characteristic of collocations is that they are resistant to substitution with words that have similar senses; for example, maroon wine sounds very odd.

To get a handle on collocations, we start off by extracting from a text a list of word pairs, also known as bigrams. This is easily accomplished with the function bigrams():

>>> bigrams(['more', 'is', 'said', 'than', 'done'])
[('more', 'is'), ('is', 'said'), ('said', 'than'), ('than', 'done')]
>>>

Here we see that the pair of words than-done is a bigram, and we write it in Python as ('than', 'done'). Now, collocations are essentially just frequent bigrams, except that we want to pay more attention to the cases that involve rare words. In particular, we want to find bigrams that occur more often than we would expect based on the frequency of individual words. The collocations() function does this for us (we will see how it works later):

>>> text4.collocations()
Building collocations list
United States; fellow citizens; years ago; Federal Government; General
Government; American people; Vice President; Almighty God; Fellow
citizens; Chief Magistrate; Chief Justice; God bless; Indian tribes;
public debt; foreign nations; political parties; State governments;
National Government; United Nations; public money
>>> text8.collocations()
Building collocations list
medium build; social drinker; quiet nights; long term; age open;
financially secure; fun times; similar interests; Age open; poss
rship; single mum; permanent relationship; slim build; seeks lady;
Late 30s; Photo pls; Vibrant personality; European background; ASIAN
LADY; country drives
>>>

The collocations that emerge are very specific to the genre of the texts. In order to find red wine as a collocation, we would need to process a much larger body of text.

Counting Other Things

Counting words is useful, but we can count other things too. For example, we can look at the distribution of word lengths in a text, by creating a FreqDist out of a long list of numbers, where each number is the length of the corresponding word in the text:

>>> [len(w) for w in text1] 1
[1, 4, 4, 2, 6, 8, 4, 1, 9, 1, 1, 8, 2, 1, 4, 11, 5, 2, 1, 7, 6, 1, 3, 4, 5, 2, ...]
>>> fdist = FreqDist([len(w) for w in text1])  2
>>> fdist  3
<FreqDist with 260819 outcomes>
>>> fdist.keys()
[3, 1, 4, 2, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20]
>>>

We start by deriving a list of the lengths of words in text1 1, and the FreqDist then counts the number of times each of these occurs 2. The result 3 is a distribution containing a quarter of a million items, each of which is a number corresponding to a word token in the text. But there are only 20 distinct items being counted, the numbers 1 through 20, because there are only 20 different word lengths. I.e., there are words consisting of just 1 character, 2 characters, ..., 20 characters, but none with 21 or more characters. One might wonder how frequent the different lengths of words are (e.g., how many words of length 4 appear in the text, are there more words of length 5 than length 4, etc.). We can do this as follows:

>>> fdist.items()
[(3, 50223), (1, 47933), (4, 42345), (2, 38513), (5, 26597), (6, 17111), (7, 14399),
(8, 9966), (9, 6428), (10, 3528), (11, 1873), (12, 1053), (13, 567), (14, 177),
(15, 70), (16, 22), (17, 12), (18, 1), (20, 1)]
>>> fdist.max()
3
>>> fdist[3]
50223
>>> fdist.freq(3)
0.19255882431878046
>>>

From this we see that the most frequent word length is 3, and that words of length 3 account for roughly 50,000 (or 20%) of the words making up the book. Although we will not pursue it here, further analysis of word length might help us understand differences between authors, genres, or languages. Table 1-2 summarizes the functions defined in frequency distributions.

Table 1-2. Functions defined for NLTK’s frequency distributions

Example

Description

fdist = FreqDist(samples)

Create a frequency distribution containing the given samples

fdist.inc(sample)

Increment the count for this sample

fdist['monstrous']

Count of the number of times a given sample occurred

fdist.freq('monstrous')

Frequency of a given sample

fdist.N()

Total number of samples

fdist.keys()

The samples sorted in order of decreasing frequency

for sample in fdist:

Iterate over the samples, in order of decreasing frequency

fdist.max()

Sample with the greatest count

fdist.tabulate()

Tabulate the frequency distribution

fdist.plot()

Graphical plot of the frequency distribution

fdist.plot(cumulative=True)

Cumulative plot of the frequency distribution

fdist1 < fdist2

Test if samples in fdist1 occur less frequently than in fdist2

Our discussion of frequency distributions has introduced some important Python concepts, and we will look at them systematically in Back to Python: Making Decisions and Taking Control.

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