Query expansion and dimensionality reduction: Notions of optimality in Rocchio relevance feedback and latent semantic indexing

Rocchio relevance feedback and latent semantic indexing (LSI) are well-known extensions of the vector space model for information retrieval (IR). This paper analyzes the statistical relationship between these extensions. The analysis focuses on each method’s basis in least-squares optimization. Noting that LSI and Rocchio relevance feedback both alter the vector space model in a way that is in some sense least-squares optimal, we ask: what is the relationship between LSI’s and Rocchio’s notions of optimality? What does this relationship imply for IR? Using an analytical approach, we argue that Rocchio relevance feedback is optimal if we understand retrieval as a simplified classification problem. On the other hand, LSI’s motivation comes to the fore if we understand it as a biased regression technique, where projection onto a low-dimensional orthogonal subspace of the documents reduces model variance.