The vector-space models for information retrieval are just one subclass of retrieval techniques that have been studied in recent years. The taxonomy provided in [4] labels the class of techniques that resemble vector-space models ``formal, feature-based, individual, partial match'' retrieval techniques since they typically rely on an underlying, formal mathematical model for retrieval, model the documents as sets of terms that can be individually weighted and manipulated, perform queries by comparing the representation of the query to the representation of each document in the space, and can retrieve documents that don't necessarily contain one of the search terms. Although the vector-space techniques share common characteristics with other techniques in the information retrieval hierarchy, they all share a core set of similarities that justify their own class.
Vector-space models rely on the premise that the meaning of
a document can be derived from the document's constituent
terms. They represent documents as vectors of terms
where 
is a non-negative value denoting the single or multiple occurrences
of term i in document d. Thus, each unique
term in the document collection corresponds to a dimension
in the space. Similarly, a query is represented as a vector
where term 
is a non-negative value denoting the
number of occurrences of 
(or, merely a 1 to signify
the occurrence of term 
) in the query [4].
Both the document vectors and the query vector provide
the locations of the objects in the term-document space. By
computing the distance between the query and other objects
in the space, objects with similar semantic content to the
query presumably will be retrieved.
Vector-space models that don't attempt to collapse the dimensions of the space treat each term independently, essentially mimicking an inverted index [11]. However, vector-space models are more flexible than inverted indices since each term can be individually weighted, allowing that term to become more or less important within a document or the entire document collection as a whole. Also, by applying different similarity measures to compare queries to terms and documents, properties of the document collection can be emphasized or deemphasized. For example, the dot product (or, inner product) similarity measure finds the Euclidean distance between the query and a term or document in the space. The cosine similarity measure, on the other hand, by computing the angle between the query and a term or document rather than the distance, deemphasizes the lengths of the vectors. In some cases, the directions of the vectors are a more reliable indication of the semantic similarities of the objects than the distance between the objects in the term-document space [11].
Vector-space models were developed to eliminate many of the problems associated with exact, lexical matching techniques. In particular, since words often have multiple meanings (polysemy), it is difficult for a lexical matching technique to differentiate between two documents that share a given word, but use it differently, without understanding the context in which the word was used. Also, since there are many ways to describe a given concept (synonomy), related documents may not use the same terminology to describe their shared concepts. A query using the terminology of one document will not retrieve the other related documents. In the worst case, a query using terminology different than that used by related documents in the collection may not retrieve any documents using lexical matching, even though the collection contains related documents [5].
Vector-space models, by placing terms, documents, and queries in a term-document space and computing similarities between the queries and the terms or documents, allow the results of a query to be ranked according to the similarity measure used. Unlike lexical matching techniques that provide no ranking or a very crude ranking scheme (for example, ranking one document before another document because it contains more occurrences of the search terms), the vector-space models, by basing their rankings on the Euclidean distance or the angle measure between the query and terms or documents in the space, are able to automatically guide the user to documents that might be more conceptually similar and of greater use than other documents. Also, by representing terms and documents in the same space, vector-space models often provide an elegant method of implementing relevance feedback [21]. Relevance feedback, by allowing documents as well as terms to form the query, and using the terms in those documents to supplement the query, increases the length and precision of the query, helping the user to more accurately specify what he or she desires from the search.
Information retrieval models typically express the retrieval performance of the system in terms of two quantities: precision and recall. Precision is the ratio of the number of relevant documents retrieved by the system to the total number of documents retrieved. Recall is the ratio of the number of relevant documents retrieved for a query to the number of documents relevant to that query in the entire document collection. Both precision and recall are expressed as values between 0 and 1. An optimal retrieval system would provide precision and recall values of 1, although precision tends to decrease with greater recall in real-world systems [11].