Term-document matrix

Term-document matrices, or term-by-document matrices, are used in natural language processing programs. They represent natural language documents as mathematical objects 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 term-document matrix contains rows corresponding to the terms and columns corresponding to the documents (or contexts). The cell values represent the occurrence of a particular term in a particular document.

For instance, if one has the following two (short) documents:

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

then the term-document matrix would be:

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

which shows which terms are contained in which documents (we start reading at the rows) and which documents contain which terms (we start reading at the columns), 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 term-document 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 term-document 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.