Laplacian Mixture Modeling for Network Analysis and Unsupervised Learning on Graphs
This addresses unsupervised learning challenges in network analysis, offering a method for probabilistic dimensionality reduction and domain decomposition, but it appears incremental as it combines existing Laplacian and mixture modeling techniques.
The paper tackles the problem of identifying overlapping regions of influence in unlabeled graph and network data by proposing Laplacian mixture models, which provide scalable and computationally efficient low-dimensional representations, with provable optimal recovery shown for a class of cluster graphs.
Laplacian mixture models identify overlapping regions of influence in unlabeled graph and network data in a scalable and computationally efficient way, yielding useful low-dimensional representations. By combining Laplacian eigenspace and finite mixture modeling methods, they provide probabilistic or fuzzy dimensionality reductions or domain decompositions for a variety of input data types, including mixture distributions, feature vectors, and graphs or networks. Provable optimal recovery using the algorithm is analytically shown for a nontrivial class of cluster graphs. Heuristic approximations for scalable high-performance implementations are described and empirically tested. Connections to PageRank and community detection in network analysis demonstrate the wide applicability of this approach. The origins of fuzzy spectral methods, beginning with generalized heat or diffusion equations in physics, are reviewed and summarized. Comparisons to other dimensionality reduction and clustering methods for challenging unsupervised machine learning problems are also discussed.