HOMALS for Dimension Reduction in Information Retrieval

Abstract

The usual data base for multiple correspondence analysis/homogeneity analysis consists of objects, characterised by categorical attributes. Its aims and ends are visualisation, dimension reduction and, to some extent, factor analysis using alternating least squares. As for dimension reduction, there are strong parallels between vector-based methods in Information Retrieval (IR) like the Vector Space Model (VSM) or Latent Semantic Analysis (LSA). The latter uses singular value decomposition (SVD) to discard a number of the smallest singular values and that way generates a lower-dimensional retrieval space. In this paper, the HOMALS technique is exploited for use in IR by categorising metric term frequencies in term-document matrices. In this context, dimension reduction is achieved by minimising the difference in distances between objects in the dimensionally reduced space compared to the full-dimensional space. An exemplary set of documents will be submitted to the process and later used for retrieval.