Document-term matrix

Document-term matrices are used in natural language processing programs. They represent natural language documents as mathematical objects (a matrix) and make it possible to process them as a whole.

General Concept

When creating a database of terms that appear in a set of documents the document-term matrix contains rows corresponding to the documents and columns corresponding to the terms. For instance if one has the following two (short) documents:

• D1 = "I like databases"
• D2 = "I hate databases",

then the document-term matrix would be:

	I	like	hate	databases
D1	1	1	0	1
D2	1	0	2	1

which shows which documents contain which terms and how many times they appear.

Note that more sophisticated weights can be used; one typical example, among others, would be tf-idf.

Choice of Terms

A point of view on the matrix is that each row represents a document. In the vectorial semantic model which is normally the one used when computing a document-term matrix, the goal is to represent the topic of a document by the frequency of semantically significant terms. The terms are semantic units of the documents. It is often assumed, for Indo-European languages, that nouns, verbs and adjectives are the more significant categories , and that words from those categories should be kept as terms. Adding collocation as terms improves the quality of the vectors, especially when computing similarities between documents.

Applications

Improving search results

Latent semantic analysis (performing eigenvalue decomposition on the document-term matrix) can improve search results by disambiguating polysemous words and searching for synonyms of the query. However, searching in the high-dimensional continuous space is much slower than searching the standard trie data structure of search engines.

Finding topics

Multivariate analysis of the document-term matrix can reveal topics/themes of the corpus. Specifically, latent semantic analysis and data clustering can be used, and more recently probabilistic latent semantic analysis and non-negative matrix factorization have been found to perform well for this task.