Indexing Through Laplacian Spectra

Abstract

With ever growing databases containing multimedia data, indexing has become a necessity to avoid a linear search. We propose a novel technique for indexing multimedia databases in which entries can be represented as graph structures. In our method, the topological structure of a graph as well as that of its subgraphs are represented as vectors whose components correspond to the sorted laplacian eigenvalues of the graph or subgraphs. Given the laplacian spectrum of graph G, we draw from recently developed techniques in the field of spectral integral variation to generate the laplacian spectrum of graph G + e without computing its eigendecomposition, where G + e is a graph obtained by adding edge e to graph G. This process improves the performance of the system for generating the subgraph signatures for 1.8% and 6.5% in datasets of size 420 and 1400, respectively. By doing a nearest neighbor search around the query spectra, similar but not necessarily isomorphic graphs are retrieved. Given a query graph, a voting schema ranks database graphs into an indexing hypothesis to which a final matching process can be applied. The novelties of the proposed method come from the powerful representation of the graph topology and successfully adopting the concept of spectral integral variation in an indexing algorithm. To examine the fitness of the new indexing framework, we have performed a number of experiments using an extensive set of recognition trials in the domain of 2D and 3D object recognition. The experiments, including a comparison with a competing indexing method using two different graph-based object representations, demonstrate both the robustness and efficacy of the overall approach. (C) 2007 Elsevier Inc. All rights reserved.