A Semi-Discrete Matrix Decomposition for Latent Semantic Indexing in Information Retrieval

The vast amount of textual information available today is useless unless it can be e ectively and e ciently searched. In information retrieval, we wish to match queries with relevant documents. Documents can be represented by the terms that appear within them, but literal matching of terms does not necessarily retrieve all relevant documents. Latent Semantic Indexing represents documents by approximations and tends to cluster documents on similar topics even if their term pro les are somewhat different. This approximate representation is usually accomplished using a low-rank singular value decomposition (SVD) approximation. In this paper, we use an alternate decomposition, the semi-discrete decomposition (SDD). In our tests, for equal query times, the SDD does as well as the SVD and uses less than one-tenth the storage. Additionally, we show how to update the SDD for a dynamically changing document collection.