Laplacian and vibrational spectra for homogeneous graphs
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Approximating s-t minimum cuts in Õ(n2) time
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Matrix computations (3rd ed.)
The anatomy of a large-scale hypertextual Web search engine
WWW7 Proceedings of the seventh international conference on World Wide Web 7
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SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Random Sampling in Cut, Flow, and Network Design Problems
Mathematics of Operations Research
Minimum cuts in near-linear time
Journal of the ACM (JACM)
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PODS '01 Proceedings of the twentieth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Scaling personalized web search
WWW '03 Proceedings of the 12th international conference on World Wide Web
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ICCV '99 Proceedings of the International Conference on Computer Vision-Volume 2 - Volume 2
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Local Graph Partitioning using PageRank Vectors
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
IEEE Transactions on Knowledge and Data Engineering
Genetic clustering of social networks using random walks
Computational Statistics & Data Analysis
Expansion properties of random Cayley graphs and vertex transitive graphs via matrix martingales
Random Structures & Algorithms
Graph sparsification by effective resistances
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Spectral norm of random matrices
Combinatorica
Approaching Optimality for Solving SDD Linear Systems
FOCS '10 Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
Viewing Angle Classification of Cryo-Electron Microscopy Images Using Eigenvectors
SIAM Journal on Imaging Sciences
A Simpler Approach to Matrix Completion
The Journal of Machine Learning Research
Sensor network localization by eigenvector synchronization over the euclidean group
ACM Transactions on Sensor Networks (TOSN)
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Many problems arising in dealing with high-dimensional data sets involve connection graphs in which each edge is associated with both an edge weight and a d-dimensional linear transformation. We consider vectorized versions of the PageRank and effective resistance which can be used as basic tools for organizing and analyzing complex data sets. For example, the generalized PageRank and effective resistance can be utilized to derive and modify diffusion distances for vector diffusion maps in data and image processing. Furthermore, the edge ranking of the connection graphs determined by the vectorized PageRank and effective resistance are an essential part of sparsification algorithms which simplify and preserve the global structure of connection graphs.