1. In a system including one or more reduced dimensionality indexes to multidimensional data, a method for performing an exact search for specified data using the one or more indexes, the method comprising the following steps in the sequence set forth: associating specified data to a data cluster based on clustering information, said data cluster being a partition of an original data input set; reducing a dimensionality of the specified data, based on dimensionality reduction information for a reduced dimensionality version of the cluster; recursively applying said associating and reducing steps unitl a corresponding lowest level of a hierarchy of reduced dimensionality clusters has been reached; and searching, using low dimensional indexes to said lowest level and a reduced dimensionality specified data, for cluster elements of the reduced dimensionality version of the cluster matching the specified data.