Matrix computations for query expansion in information retrieval
Information retrieval (IR) is the task of identifying information items (documents) that are relevant to a user query from a collection. The most popular IR research technique, the vector space model (VSM), is a word-matching approach: it uses the words in common between the query and the document as a basic way of determining their similarity. Because the same concept can be expressed in the query and document using very different vocabularies, synonymy can cause a document to be judged as irrelevant by VSM. 
Query-expansion methods deal with this problem by automatically supplying the query with additional words that are related to those already in it. Latent semantic indexing (LSI) is a statistical method that derives term associations through a reduced dimensional singular value decomposition (SVD) of a matrix formed from the collection. LSI has equaled or outperformed VSM on many relatively small retrieval collections. But, with the growing size of modern information repositories, LSI has failed to demonstrate its advantage over traditional word-matching methods on some of these large corpora. 
In this work, I provide evidence that LSI is not reaching its potential for large collections because existing SVD implementations are not able to compute a sufficiently large number of dimensions. I establish a unified framework of vector-based information retrieval called dimension equalization . Through this, I present approximate dimension equalization (ADE), a method that “extrapolates” the result of a high-dimensional SVD based on a relatively small number of computed dimensions. Experiments indicate that ADE improves retrieval performance over LSI and has great utility in cross-language applications. 
I also investigate sampling approaches to reducing LSI computation, which use only a subset of the document collection to build LSI term-associations. My focus is on local LSI, a variation of the ever-popular local feedback approaches in the IR community. This method computes an SVD on a subset of documents that are related to the query. Experiments show that local LSI outperforms not only the global sampling methods but also the baseline VSM or LSI without sampling. I extend the existing local LSI approach to cross-language retrieval and present its high-quality results.