Manifold matching using shortest-path distance and joint neighborhood selection

• Published in: Pattern recognition letters 2017-06, Vol.92, p.41-48
• Main Authors: Shen, Cencheng, Vogelstein, Joshua T., Priebe, Carey E.
• Format: Article
• Language: English
• Subjects: Algorithms; Data analysis; Data processing; Datasets; Embedding; Euclidean geometry; Geodesic distance; Graphs; Information processing; k-nearest-neighbor; Manifolds (mathematics); Matching; Nearest-neighbor; Nonlinear systems; Nonlinear transformation; Pattern recognition; Seeded graph matching; Shortest-path problems
• ISSN: 0167-8655; 1872-7344
• DOI: 10.1016/j.patrec.2017.04.005

•We propose a new manifold matching method, that is superior than existing methods based on single modality.•Our method is robust against noise and different types of geometry in matching.•The method is particularly useful for graph and network matching. Matching datasets of multiple modalities has become an important task in data analysis. Existing methods often rely on the embedding and transformation of each single modality without utilizing any correspondence information, which often results in sub-optimal matching performance. In this paper, we propose a nonlinear manifold matching algorithm using shortest-path distance and joint neighborhood selection. Specifically, a joint nearest-neighbor graph is built for all modalities. Then the shortest-path distance within each modality is calculated from the joint neighborhood graph, followed by embedding into and matching in a common low-dimensional Euclidean space. Compared to existing algorithms, our approach exhibits superior performance for matching disparate datasets of multiple modalities.