Concepts inGeneralized vector spaces model in information retrieval
Vector space model
Vector space model or term vector model is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as, for example, index terms. It is used in information filtering, information retrieval, indexing and relevancy rankings. Its first use was in the SMART Information Retrieval System.
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Orthogonality
Orthogonality comes from the Greek orthos, meaning "straight", and gonia, meaning "angle". It has somewhat different meanings depending on the context, but most involve the idea of perpendicular, non-overlapping, varying independently, or uncorrelated. In mathematics, two lines or curves are orthogonal if they are perpendicular at their point of intersection. Two vectors are orthogonal if and only if their dot product is zero.
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Information retrieval
Information retrieval (IR) is the area of study concerned with searching for documents, for information within documents, and for metadata about documents, as well as that of searching structured storage, relational databases, and the World Wide Web. There is overlap in the usage of the terms data retrieval, document retrieval, information retrieval, and text retrieval, but each also has its own body of literature, theory, praxis, and technologies.
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Euclidean vector
In mathematics, physics, and engineering, a Euclidean vector (sometimes called a geometric or spatial vector, or – as here – simply a vector) is a geometric object that has a magnitude and direction and can be added according to the parallelogram law of addition.
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Correlation and dependence
In statistics, dependence refers to any statistical relationship between two random variables or two sets of data. Correlation refers to any of a broad class of statistical relationships involving dependence. Familiar examples of dependent phenomena include the correlation between the physical statures of parents and their offspring, and the correlation between the demand for a product and its price.
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Vector space
A vector space is a mathematical structure formed by a collection of elements called vectors, which may be added together and multiplied ("scaled") by numbers, called scalars in this context. Scalars are often taken to be real numbers, but there are also vector spaces with scalar multiplication by complex numbers, rational numbers, or generally any field. The operations of vector addition and scalar multiplication must satisfy certain requirements, called axioms, listed below.
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Generalized vector space model
The Generalized vector space model is a generalization of the vector space model used in information retrieval. Wong et al. presented an analysis of the problems that the pairwise orthogonality assumption of the Vector space model(VSM) creates. From here they extended the VSM to the generalized vector space model (GVSM).
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A priori and a posteriori
The terms a priori ("from the earlier") and a posteriori ("from the later") are used in philosophy to distinguish two types of knowledge, justifications or arguments. A priori knowledge or justification is independent of experience (for example "All bachelors are unmarried"); a posteriori knowledge or justification is dependent on experience or empirical evidence (for example "Some bachelors are very happy").
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