2. The method of claim 1, further comprising the steps of: (a) generating cluster boundaries, which correspond to a zeroth-order approximation to a geometry of said clusters; (b) approximating the geometry of each of the clusters by means of a minimum bounding box and generating a first-order approximation to the geometry of each cluster; (c) partitioning the bounding box into 2 k hyper rectangles, wherein said partitioning is at a midpoint of each dimension; (d) retaining only those hyper rectangles that contain data points and generating a second-order approximation to the geometry of the cluster; and (e) repeating said steps (c) and (d) for each retained hyper rectangle to generate successively the third-, fourth-, . . . , n-th approximations to the geometry of the cluster.
3. The method of claim 2, for searching a hierarchy of approximations to the geometric structure of each cluster, further comprising the steps of: reducing the dimensionality of the specified data using the dimensionality reduction information associated with the database; finding the cluster to which reduced dimensionality specified data belongs, based on the clustering information; reducing the dimensionality of the reduced dimensionality specified data based on the dimensionality reduction information for an identified cluster; searching for a reduced-dimensionality version of the cluster to which the further reduced dimensionality specified data belongs; retrieving via the multidimensional index, k records most similar to the further reduced dimensionality specified data in the cluster; assessing whether one or more other clusters can contain records closer to the specified data than the farthest of the k records retrieved; retaining an other cluster only if it can contain any of k-nearest neighbors of specified data based on boundaries of the cluster; iteratively determining if a retained cluster could contain any of the k-nearest neighbors, based on increasingly finer approximations to the geometry, and retaining the retained cluster only if the cluster is accepted at the finest level of the hierarchy of successive approximations; and identifying a retained cluster as a candidate cluster containing one or more of the k-nearest neighbors of the data, in response to said step of iteratively determining.