13. The method of claim 10 , wherein the selecting step comprises matching the estimated singular values corresponding to at least one of a plurality of probabilistic distributions on parts with the actual singular values of matrix A.
10. A method for generating a reduced rank approximation for information retrieval, comprising: forming on a computer a part-by-collection matrix A, wherein the elements of the matrix represent the existence of one or more parts within one or more collections; estimating via the computer a plurality of singular values corresponding to at least one of a plurality of probabilistic distributions on parts; identifying via the computer a plurality of actual singular values each having a corresponding singular vector; selecting via the computer a subset of the actual singular values based on actual singular values that correspond to at least one of the estimated singular values; and determining via the computer a set of singular vectors based on the selected singular values, wherein the singular vectors provide an index for use during information retrieval.