A computer-implemented method for building an object index used for retrieving an object matching a given query is disclosed. In the method, the computer system initializes a set of clusters, each of which represents at least one base object of a collection. The computer system also enumerates one or more additional clusters by combining multiple clusters from among the set. Each additional cluster represents at least one combinatorial object that has two or more base objects of the collection. The computer system further selects a new set of new clusters by clustering the set of the clusters and the one or more additional clusters, in which each new cluster represents at least one base or combinatorial object. Then, the computer system builds an object index based on the centers of the new clusters such that the object index covers the combinatorial object as a target of retrieval.