GDL

The vector space information retrieval system, originated by Gerard Salton [Sal71,

SM83J, represents documents as vectors in a vector space. The document set

comprises an m x n term-document matrix A, in which each column represents a

document, and each entry A(i, j) represents the weighted frequency of term i in

document j. A major benefit of this representation is that the algebraic structure

of the vector space can be exploited [BDO95J. To achieve higher efficiency in manipulating the data, it is often necessary to reduce the dimension dramatically.

Especially when the data set is huge, we can assume that the data have a cluster

structure, and it is often necessary to cluster the data [DHS01] first to utilize the

tremendous amount of information in an efficient way. Once the columns of A are

grouped into clusters, rather than treating each column equally regardless of its

membership in a specific cluster, as is done in the singular value decomposition

(SVD) [GV96], the dimension reduction methods we discuss attempt to preserve

this information.

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