Topic: Spectral partitioning

This talk establishes a general reduction from nonlinear spectral gaps of metric spaces to data-dependent space partitions in the form of locality-sensitive hashing. The reduction yields an approach to high-dimensional approximate near-neighbor search and a data structure for any d-dimensional norm whose query algorithm makes a sublinear number of probes. Its approximation factor is O(log d), improving on the square-root-of-d factor available from the generic approach based on John’s ellipsoid. The presentation connects spectral properties, geometric partitions, and efficient approximate searc

This two-part tutorial considers the problem of indexing points in a metric space so that a query can efficiently retrieve an approximately closest stored point. It surveys established and newer data structures for high-dimensional nearest-neighbor search. The first part examines search under the l1 and Euclidean l2 distances, including locality-sensitive hashing and data-dependent hashing. The second part turns to non-Euclidean geometries and recent approaches such as spectral partitioning for metric spaces.