Definitions

For the purposes of this paper, I will use the following definitions:

is a set of N documents in the collection. d will refer to an arbitrary document .

is a set of m terms indexed in D. In this paper will generally be a single word, but richer definitions may be used without impacting the underlying theory. t will refer to an arbitrary term .

is the weight of term . Weight is simply a numeric quantity that indicates the importance of a term.

is an individual document, represented by the vector of length m

where is the weight of term in document . In the simplest case, each is a term indexed from one or more documents, and is either 1 or 0, depending if the term is present or absent from document .

is a set of documents restricted to those documents that contain the term t. Note that represents the Document Frequency of term t.

Q

is a Query containing terms . The specific structure of Q is model dependent and will be further defined.

|X|

is the size of set X. |V| will also be used to denote the length of a vector V.

is the number of times term appears in document . This is the Term Frequency of .