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Organizational overlap on social networks and its applications.
 Proceedings of the 22nd international conference on World Wide Web, International World Wide Web Conferences Steering Committee.
, 2013
"... ABSTRACT Online social networks have become important for networking, communication, sharing, and discovery. A considerable challenge these networks face is the fact that an online social network is partially observed because two individuals might know each other, but may not have established a con ..."
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ABSTRACT Online social networks have become important for networking, communication, sharing, and discovery. A considerable challenge these networks face is the fact that an online social network is partially observed because two individuals might know each other, but may not have established a connection on the site. Therefore, link prediction and recommendations are important tasks for any online social network. In this paper, we address the problem of computing edge affinity between two users on a social network, based on the users belonging to organizations such as companies, schools, and online groups. We present experimental insights from social network data on organizational overlap, a novel mathematical model to compute the probability of connection between two people based on organizational overlap, and experimental validation of this model based on real social network data. We also present novel ways in which the organization overlap model can be applied to link prediction and community detection, which in itself could be useful for recommending entities to follow and generating personalized news feed.
PU Learning for Matrix Completion
 Inderjit S. Dhillon Dept of Computer Science UT Austin LowRank Bilinear Prediction
, 2015
"... In this paper, we consider the matrix completion problem when the observations are onebit measurements of some underlying matrix M, and in particular the observed samples consist only of ones and no zeros. This problem is motivated by modern applications such as recommender systems and social net ..."
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In this paper, we consider the matrix completion problem when the observations are onebit measurements of some underlying matrix M, and in particular the observed samples consist only of ones and no zeros. This problem is motivated by modern applications such as recommender systems and social networks where only “likes ” or “friendships ” are observed. The problem is an instance of PU (positiveunlabeled) learning, i.e. learning from only positive and unlabeled examples that has been studied in the context of binary classification. Under the assumption thatM has bounded nuclear norm, we provide recovery guarantees for two different observation models: 1) M parameterizes a distribution that generates a binary matrix, 2) M is thresholded to obtain a binary matrix. For the first case, we propose a “shifted matrix completion ” method that recovers M using only a subset of indices corresponding to ones; for the second case, we propose a “biased matrix completion ” method that recovers the (thresholded) binary matrix. Both methods yield strong error bounds — if M ∈ Rn×n, the error is bounded as O
Towards More Efficient SPSD Matrix Approximation and CUR Matrix Decomposition
, 2016
"... Abstract Symmetric positive semidefinite (SPSD) matrix approximation methods have been extensively used to speed up largescale eigenvalue computation and kernel learning methods. The standard sketch based method, which we call the prototype model, produces relatively accurate approximations, but ..."
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Abstract Symmetric positive semidefinite (SPSD) matrix approximation methods have been extensively used to speed up largescale eigenvalue computation and kernel learning methods. The standard sketch based method, which we call the prototype model, produces relatively accurate approximations, but is inefficient on large square matrices. The Nyström method is highly efficient, but can only achieve low accuracy. In this paper we propose a novel model that we call the fast SPSD matrix approximation model. The fast model is nearly as efficient as the Nyström method and as accurate as the prototype model. We show that the fast model can potentially solve eigenvalue problems and kernel learning problems in linear time with respect to the matrix size n to achieve 1 + relativeerror, whereas both the prototype model and the Nyström method cost at least quadratic time to attain comparable error bound. Empirical comparisons among the prototype model, the Nyström method, and our fast model demonstrate the superiority of the fast model. We also contribute new understandings of the Nyström method. The Nyström method is a special instance of our fast model and is approximation to the prototype model. Our technique can be straightforwardly applied to make the CUR matrix decomposition more efficiently computed without much affecting the accuracy.
MultiScale Spectral Decomposition of Massive Graphs
"... Computing the k dominant eigenvalues and eigenvectors of massive graphs is a key operation in numerous machine learning applications; however, popular solvers suffer from slow convergence, especially when k is reasonably large. In this paper, we propose and analyze a novel multiscale spectral decom ..."
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Computing the k dominant eigenvalues and eigenvectors of massive graphs is a key operation in numerous machine learning applications; however, popular solvers suffer from slow convergence, especially when k is reasonably large. In this paper, we propose and analyze a novel multiscale spectral decomposition method (MSEIGS), which first clusters the graph into smaller clusters whose spectral decomposition can be computed efficiently and independently. We show theoretically as well as empirically that the union of all cluster’s subspaces has significant overlap with the dominant subspace of the original graph, provided that the graph is clustered appropriately. Thus, eigenvectors of the clusters serve as good initializations to a block Lanczos algorithm that is used to compute spectral decomposition of the original graph. We further use hierarchical clustering to speed up the computation and adopt a fast early termination strategy to compute quality approximations. Our method outperforms widely used solvers in terms of convergence speed and approximation quality. Furthermore, our method is naturally parallelizable and exhibits significant speedups in sharedmemory parallel settings. For example, on a graph with more than 82 million nodes and 3.6 billion edges, MSEIGS takes less than 3 hours on a singlecore machine while Randomized SVD takes more than 6 hours, to obtain a similar approximation of the top50 eigenvectors. Using 16 cores, we can reduce this time to less than 40 minutes. 1