Corpora and Vector Spaces

Demonstrates transforming text into a vector space representation.

Also introduces corpus streaming and persistence to disk in various formats.

import logging
logging.basicConfig(format='%(asctime)s : %(levelname)s : %(message)s', level=logging.INFO)

First, let’s create a small corpus of nine short documents 1:

From Strings to Vectors

This time, let’s start from documents represented as strings:

documents = [
    "Human machine interface for lab abc computer applications",
    "A survey of user opinion of computer system response time",
    "The EPS user interface management system",
    "System and human system engineering testing of EPS",
    "Relation of user perceived response time to error measurement",
    "The generation of random binary unordered trees",
    "The intersection graph of paths in trees",
    "Graph minors IV Widths of trees and well quasi ordering",
    "Graph minors A survey",
]

This is a tiny corpus of nine documents, each consisting of only a single sentence.

First, let’s tokenize the documents, remove common words (using a toy stoplist) as well as words that only appear once in the corpus:

from pprint import pprint  # pretty-printer
from collections import defaultdict

# remove common words and tokenize
stoplist = set('for a of the and to in'.split())
texts = [
    [word for word in document.lower().split() if word not in stoplist]
    for document in documents
]

# remove words that appear only once
frequency = defaultdict(int)
for text in texts:
    for token in text:
        frequency[token] += 1

texts = [
    [token for token in text if frequency[token] > 1]
    for text in texts
]

pprint(texts)

Out:

[['human', 'interface', 'computer'],
 ['survey', 'user', 'computer', 'system', 'response', 'time'],
 ['eps', 'user', 'interface', 'system'],
 ['system', 'human', 'system', 'eps'],
 ['user', 'response', 'time'],
 ['trees'],
 ['graph', 'trees'],
 ['graph', 'minors', 'trees'],
 ['graph', 'minors', 'survey']]

Your way of processing the documents will likely vary; here, I only split on whitespace to tokenize, followed by lowercasing each word. In fact, I use this particular (simplistic and inefficient) setup to mimic the experiment done in Deerwester et al.’s original LSA article 1.

The ways to process documents are so varied and application- and language-dependent that I decided to not constrain them by any interface. Instead, a document is represented by the features extracted from it, not by its “surface” string form: how you get to the features is up to you. Below I describe one common, general-purpose approach (called bag-of-words), but keep in mind that different application domains call for different features, and, as always, it’s garbage in, garbage out

To convert documents to vectors, we’ll use a document representation called bag-of-words. In this representation, each document is represented by one vector where each vector element represents a question-answer pair, in the style of:

  • Question: How many times does the word system appear in the document?

  • Answer: Once.

It is advantageous to represent the questions only by their (integer) ids. The mapping between the questions and ids is called a dictionary:

from gensim import corpora
dictionary = corpora.Dictionary(texts)
dictionary.save('/tmp/deerwester.dict')  # store the dictionary, for future reference
print(dictionary)

Out:

2020-10-28 00:52:02,550 : INFO : adding document #0 to Dictionary(0 unique tokens: [])
2020-10-28 00:52:02,550 : INFO : built Dictionary(12 unique tokens: ['computer', 'human', 'interface', 'response', 'survey']...) from 9 documents (total 29 corpus positions)
2020-10-28 00:52:02,550 : INFO : saving Dictionary(12 unique tokens: ['computer', 'human', 'interface', 'response', 'survey']...) under /tmp/deerwester.dict, separately None
2020-10-28 00:52:02,552 : INFO : saved /tmp/deerwester.dict
Dictionary(12 unique tokens: ['computer', 'human', 'interface', 'response', 'survey']...)

Here we assigned a unique integer id to all words appearing in the corpus with the gensim.corpora.dictionary.Dictionary class. This sweeps across the texts, collecting word counts and relevant statistics. In the end, we see there are twelve distinct words in the processed corpus, which means each document will be represented by twelve numbers (ie., by a 12-D vector). To see the mapping between words and their ids:

print(dictionary.token2id)

Out:

{'computer': 0, 'human': 1, 'interface': 2, 'response': 3, 'survey': 4, 'system': 5, 'time': 6, 'user': 7, 'eps': 8, 'trees': 9, 'graph': 10, 'minors': 11}

To actually convert tokenized documents to vectors:

new_doc = "Human computer interaction"
new_vec = dictionary.doc2bow(new_doc.lower().split())
print(new_vec)  # the word "interaction" does not appear in the dictionary and is ignored

Out:

[(0, 1), (1, 1)]

The function doc2bow() simply counts the number of occurrences of each distinct word, converts the word to its integer word id and returns the result as a sparse vector. The sparse vector [(0, 1), (1, 1)] therefore reads: in the document “Human computer interaction”, the words computer (id 0) and human (id 1) appear once; the other ten dictionary words appear (implicitly) zero times.

corpus = [dictionary.doc2bow(text) for text in texts]
corpora.MmCorpus.serialize('/tmp/deerwester.mm', corpus)  # store to disk, for later use
print(corpus)

Out:

2020-10-28 00:52:02,830 : INFO : storing corpus in Matrix Market format to /tmp/deerwester.mm
2020-10-28 00:52:02,832 : INFO : saving sparse matrix to /tmp/deerwester.mm
2020-10-28 00:52:02,832 : INFO : PROGRESS: saving document #0
2020-10-28 00:52:02,834 : INFO : saved 9x12 matrix, density=25.926% (28/108)
2020-10-28 00:52:02,834 : INFO : saving MmCorpus index to /tmp/deerwester.mm.index
[[(0, 1), (1, 1), (2, 1)], [(0, 1), (3, 1), (4, 1), (5, 1), (6, 1), (7, 1)], [(2, 1), (5, 1), (7, 1), (8, 1)], [(1, 1), (5, 2), (8, 1)], [(3, 1), (6, 1), (7, 1)], [(9, 1)], [(9, 1), (10, 1)], [(9, 1), (10, 1), (11, 1)], [(4, 1), (10, 1), (11, 1)]]

By now it should be clear that the vector feature with id=10 stands for the question “How many times does the word graph appear in the document?” and that the answer is “zero” for the first six documents and “one” for the remaining three.

Corpus Streaming – One Document at a Time

Note that corpus above resides fully in memory, as a plain Python list. In this simple example, it doesn’t matter much, but just to make things clear, let’s assume there are millions of documents in the corpus. Storing all of them in RAM won’t do. Instead, let’s assume the documents are stored in a file on disk, one document per line. Gensim only requires that a corpus must be able to return one document vector at a time:

from smart_open import open  # for transparently opening remote files


class MyCorpus:
    def __iter__(self):
        for line in open('https://radimrehurek.com/gensim/mycorpus.txt'):
            # assume there's one document per line, tokens separated by whitespace
            yield dictionary.doc2bow(line.lower().split())

The full power of Gensim comes from the fact that a corpus doesn’t have to be a list, or a NumPy array, or a Pandas dataframe, or whatever. Gensim accepts any object that, when iterated over, successively yields documents.

# This flexibility allows you to create your own corpus classes that stream the
# documents directly from disk, network, database, dataframes... The models
# in Gensim are implemented such that they don't require all vectors to reside
# in RAM at once. You can even create the documents on the fly!

Download the sample mycorpus.txt file here. The assumption that each document occupies one line in a single file is not important; you can mold the __iter__ function to fit your input format, whatever it is. Walking directories, parsing XML, accessing the network… Just parse your input to retrieve a clean list of tokens in each document, then convert the tokens via a dictionary to their ids and yield the resulting sparse vector inside __iter__.

corpus_memory_friendly = MyCorpus()  # doesn't load the corpus into memory!
print(corpus_memory_friendly)

Out:

<__main__.MyCorpus object at 0x11e77bb38>

Corpus is now an object. We didn’t define any way to print it, so print just outputs address of the object in memory. Not very useful. To see the constituent vectors, let’s iterate over the corpus and print each document vector (one at a time):

for vector in corpus_memory_friendly:  # load one vector into memory at a time
    print(vector)

Out:

[(0, 1), (1, 1), (2, 1)]
[(0, 1), (3, 1), (4, 1), (5, 1), (6, 1), (7, 1)]
[(2, 1), (5, 1), (7, 1), (8, 1)]
[(1, 1), (5, 2), (8, 1)]
[(3, 1), (6, 1), (7, 1)]
[(9, 1)]
[(9, 1), (10, 1)]
[(9, 1), (10, 1), (11, 1)]
[(4, 1), (10, 1), (11, 1)]

Although the output is the same as for the plain Python list, the corpus is now much more memory friendly, because at most one vector resides in RAM at a time. Your corpus can now be as large as you want.

Similarly, to construct the dictionary without loading all texts into memory:

# collect statistics about all tokens
dictionary = corpora.Dictionary(line.lower().split() for line in open('https://radimrehurek.com/gensim/mycorpus.txt'))
# remove stop words and words that appear only once
stop_ids = [
    dictionary.token2id[stopword]
    for stopword in stoplist
    if stopword in dictionary.token2id
]
once_ids = [tokenid for tokenid, docfreq in dictionary.dfs.items() if docfreq == 1]
dictionary.filter_tokens(stop_ids + once_ids)  # remove stop words and words that appear only once
dictionary.compactify()  # remove gaps in id sequence after words that were removed
print(dictionary)

Out:

2020-10-28 00:52:04,241 : INFO : adding document #0 to Dictionary(0 unique tokens: [])
2020-10-28 00:52:04,243 : INFO : built Dictionary(42 unique tokens: ['abc', 'applications', 'computer', 'for', 'human']...) from 9 documents (total 69 corpus positions)
Dictionary(12 unique tokens: ['computer', 'human', 'interface', 'response', 'survey']...)

And that is all there is to it! At least as far as bag-of-words representation is concerned. Of course, what we do with such a corpus is another question; it is not at all clear how counting the frequency of distinct words could be useful. As it turns out, it isn’t, and we will need to apply a transformation on this simple representation first, before we can use it to compute any meaningful document vs. document similarities. Transformations are covered in the next tutorial (Topics and Transformations), but before that, let’s briefly turn our attention to corpus persistency.

Corpus Formats

There exist several file formats for serializing a Vector Space corpus (~sequence of vectors) to disk. Gensim implements them via the streaming corpus interface mentioned earlier: documents are read from (resp. stored to) disk in a lazy fashion, one document at a time, without the whole corpus being read into main memory at once.

One of the more notable file formats is the Market Matrix format. To save a corpus in the Matrix Market format:

create a toy corpus of 2 documents, as a plain Python list

corpus = [[(1, 0.5)], []]  # make one document empty, for the heck of it

corpora.MmCorpus.serialize('/tmp/corpus.mm', corpus)

Out:

2020-10-28 00:52:04,368 : INFO : storing corpus in Matrix Market format to /tmp/corpus.mm
2020-10-28 00:52:04,370 : INFO : saving sparse matrix to /tmp/corpus.mm
2020-10-28 00:52:04,370 : INFO : PROGRESS: saving document #0
2020-10-28 00:52:04,370 : INFO : saved 2x2 matrix, density=25.000% (1/4)
2020-10-28 00:52:04,370 : INFO : saving MmCorpus index to /tmp/corpus.mm.index

Other formats include Joachim’s SVMlight format, Blei’s LDA-C format and GibbsLDA++ format.

corpora.SvmLightCorpus.serialize('/tmp/corpus.svmlight', corpus)
corpora.BleiCorpus.serialize('/tmp/corpus.lda-c', corpus)
corpora.LowCorpus.serialize('/tmp/corpus.low', corpus)

Out:

2020-10-28 00:52:04,425 : INFO : converting corpus to SVMlight format: /tmp/corpus.svmlight
2020-10-28 00:52:04,426 : INFO : saving SvmLightCorpus index to /tmp/corpus.svmlight.index
2020-10-28 00:52:04,427 : INFO : no word id mapping provided; initializing from corpus
2020-10-28 00:52:04,427 : INFO : storing corpus in Blei's LDA-C format into /tmp/corpus.lda-c
2020-10-28 00:52:04,427 : INFO : saving vocabulary of 2 words to /tmp/corpus.lda-c.vocab
2020-10-28 00:52:04,427 : INFO : saving BleiCorpus index to /tmp/corpus.lda-c.index
2020-10-28 00:52:04,481 : INFO : no word id mapping provided; initializing from corpus
2020-10-28 00:52:04,481 : INFO : storing corpus in List-Of-Words format into /tmp/corpus.low
2020-10-28 00:52:04,482 : WARNING : List-of-words format can only save vectors with integer elements; 1 float entries were truncated to integer value
2020-10-28 00:52:04,482 : INFO : saving LowCorpus index to /tmp/corpus.low.index

Conversely, to load a corpus iterator from a Matrix Market file:

corpus = corpora.MmCorpus('/tmp/corpus.mm')

Out:

2020-10-28 00:52:04,538 : INFO : loaded corpus index from /tmp/corpus.mm.index
2020-10-28 00:52:04,540 : INFO : initializing cython corpus reader from /tmp/corpus.mm
2020-10-28 00:52:04,540 : INFO : accepted corpus with 2 documents, 2 features, 1 non-zero entries

Corpus objects are streams, so typically you won’t be able to print them directly:

print(corpus)

Out:

MmCorpus(2 documents, 2 features, 1 non-zero entries)

Instead, to view the contents of a corpus:

# one way of printing a corpus: load it entirely into memory
print(list(corpus))  # calling list() will convert any sequence to a plain Python list

Out:

[[(1, 0.5)], []]

or

# another way of doing it: print one document at a time, making use of the streaming interface
for doc in corpus:
    print(doc)

Out:

[(1, 0.5)]
[]

The second way is obviously more memory-friendly, but for testing and development purposes, nothing beats the simplicity of calling list(corpus).

To save the same Matrix Market document stream in Blei’s LDA-C format,

corpora.BleiCorpus.serialize('/tmp/corpus.lda-c', corpus)

Out:

2020-10-28 00:52:04,921 : INFO : no word id mapping provided; initializing from corpus
2020-10-28 00:52:04,922 : INFO : storing corpus in Blei's LDA-C format into /tmp/corpus.lda-c
2020-10-28 00:52:04,923 : INFO : saving vocabulary of 2 words to /tmp/corpus.lda-c.vocab
2020-10-28 00:52:04,923 : INFO : saving BleiCorpus index to /tmp/corpus.lda-c.index

In this way, gensim can also be used as a memory-efficient I/O format conversion tool: just load a document stream using one format and immediately save it in another format. Adding new formats is dead easy, check out the code for the SVMlight corpus for an example.

Compatibility with NumPy and SciPy

Gensim also contains efficient utility functions to help converting from/to numpy matrices

import gensim
import numpy as np
numpy_matrix = np.random.randint(10, size=[5, 2])  # random matrix as an example
corpus = gensim.matutils.Dense2Corpus(numpy_matrix)
# numpy_matrix = gensim.matutils.corpus2dense(corpus, num_terms=number_of_corpus_features)

and from/to scipy.sparse matrices

import scipy.sparse
scipy_sparse_matrix = scipy.sparse.random(5, 2)  # random sparse matrix as example
corpus = gensim.matutils.Sparse2Corpus(scipy_sparse_matrix)
scipy_csc_matrix = gensim.matutils.corpus2csc(corpus)

What Next

Read about Topics and Transformations.

References

For a complete reference (Want to prune the dictionary to a smaller size? Optimize converting between corpora and NumPy/SciPy arrays?), see the API Reference.

1(1,2)

This is the same corpus as used in Deerwester et al. (1990): Indexing by Latent Semantic Analysis, Table 2.

import matplotlib.pyplot as plt
import matplotlib.image as mpimg
img = mpimg.imread('run_corpora_and_vector_spaces.png')
imgplot = plt.imshow(img)
_ = plt.axis('off')
run corpora and vector spaces

Total running time of the script: ( 0 minutes 4.010 seconds)

Estimated memory usage: 40 MB

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