An information retrieval system that deals with the problems of synonymy, polysemy, and retrieval by concept by allowing for a wide margin of uncertainty in the initial choice of keywords in a query. For each input query vector and an information matrix, the disclosed system solves an optimization problem which maximizes the stability of a solution at a given level of misfit. The disclosed system may include a decomposition of the information matrix in terms of orthogonal basis functions. Each basis encodes groups of conceptually related keywords. The bases are arranged in order of decreasing statistical relevance to a query. The disclosed search engine approximates the input query with a weighted sum of the first few bases. Other commercial applications than the disclosed search engine can also be built on the disclosed techniques.