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As Section §3.5 has already suggested, our interest in matching queries and documents within a vector space can benefit greatly from other kinds of matching that have arisen in other kinds of vector spaces [Schutze93] . We review several other basic features of the mathematical topic of linear algebra before applying them to the problem of FOA.

It is worth
remembering that similarity information can come from many sources. For
example, we will later (cf. Section §6.1
) have much to say about how **CITATION** structure can be
represented as a graph, with each document represented by a node in the
graph and a directed edge going from $d_{i}$ to $d_{j}$, when $d_{j}$
appears in the bibliography of $d_{i}$. Note that the documents'
citation information is entirely independent of the words they contain,
and can be the basis for another characterization of the topical
similarity between documents: Two documents are about the same topic to
the extent that they share the same documents in their bibliographies.
For now, such bibliometric data need only seem like a plausible, new way
to analyze document content. Chapter 6 will discuss other features that
we might also exploit.

Our goal in casting similarity matching of queries with documents in general, mathematical terms is to make the resulting solutions sufficiently broad to handle any kind of features, keywords or bibliographic citations.

- 5.2.1 A simple example
- 5.2.2 Formal notions of similarity
- 5.2.3 Singular value decomposition
- 5.2.4 How many dimensions $k$ to reduce to?
- 5.2.5 Other uses of vector space
- 5.2.6 Computational considerations
- 5.2.7 ``Latent semantic'' claims

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