21. A program storage device readable by a machine which includes one or more reduced dimensionality indexes to multidimensional data, the program storage device tangibly embodying a program of instructions executable by the machine to perform method steps for performing an exact search for specified data using the one or more indexes, said method steps comprising: 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 until 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.
23. The program storage device of claim 21, wherein said reducing step comprises a singular value decomposition, said searching further comprising the step of: searching an index for a matching reduced dimensionality cluster, based on decomposed specified data.