Social Network Analysis

IEEE Transactions on Pattern Analysis and Machine Intelligence

Transportation Networks. Optimality. Cost Functions. Deterministic User Equilibrium Assignment. Stochastic User Equilibrium Assignment. Trip Table Estimation. Network Reliability. Network Design. Conclusions. References. Index.

Transportation network analysis

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Perturbation Analysis Of Optimization Problems

Bipartite Graph Partitioning and Data Clustering* Hongyuan Zha Xiaofeng He Dept. of Comp. Sci. & Eng. Penn State Univ. State College, PA 16802 {zha,xhe}@cse.psu.edu Chris Ding Horst Simon NERSC Division Berkeley National Lab. Berkeley, CA 94720 {chqding,hdsimon} Qlbl. gov Ming Gu Dept. of Math. U.C. Berkeley Berkeley, CA 94720 mgu@math.berkeley.edu ABSTRACT M a n y data types arising from data mining applications can be modeled as bipartite graphs, examples include terms and documents in a text corpus, customers and purchasing items in market basket analysis and reviewers and movies in a movie recommender system. In this paper, we propose a new data clustering method based on partitioning the underlying bipartite graph. The partition is constructed by minimizing a normalized sum of edge weights between unmatched pairs of vertices of the bipartite graph. We show that an approxi­ mate solution to the minimization problem can be obtained by computing a partial singular value decomposition ( S V D ) of the associated edge weight matrix of the bipartite graph. We point out the connection of our clustering algorithm to correspondence analysis used in multivariate analysis. We also briefly discuss the issue of assigning data objects to multiple clusters. In the experimental results, we apply our clustering algorithm to the problem of document clustering to illustrate its effectiveness and efficiency. 1. INTRODUCTION Cluster analysis is an important tool for exploratory data mining applications arising from many diverse disciplines. Informally, cluster analysis seeks to partition a given data set into compact clusters so that data objects within a clus­ ter are more similar than those in distinct clusters. The liter­ ature on cluster analysis is enormous including contributions from many research communities, (see [6, 9] for recent sur­ veys of some classical approaches.) M a n y traditional clus­ tering algorithms are based on the assumption that the given dataset consists of covariate information (or attributes) for each individual data object, and cluster analysis can be cast as a problem of grouping a set of n-dimensional vectors each representing a data object in the dataset. A familiar ex­ ample is document clustering using the vector space model [1]. Here each document is represented by an n-dimensional vector, and each coordinate of the vector corresponds to a term in a vocabulary of size n. This formulation leads to the so-called term-document matrix A = (oy) for the rep­ resentation of the collection of documents, where o y is the so-called term frequency, i.e., the number of times term i occurs in document j. In this vector space model terms and documents are treated asymmetrically with terms consid­ ered as the covariates or attributes of documents. It is also possible to treat both terms and documents as first-class citizens in a symmetric fashion, and consider a y as the fre­ quency of co-occurrence of term i and document j as is done, for example, in probabilistic latent semantic indexing [12]. In this paper, we follow this basic principle and propose a new approach to model terms and documents as vertices in a bipartite graph with edges of the graph indicating the co-occurrence of terms and documents. In addition we can optionally use edge weights to indicate the frequency of this co-occurrence. Cluster analysis for document collections in this context is based on a very intuitive notion: documents are grouped by topics, on one hand documents in a topic tend to more heavily use the same subset of terms which form a term cluster, and on the other hand a topic usually is characterized by a subset of terms and those documents heavily using those terms tend to be about that particular topic. It is this interplay of terms and documents which gives rise to what we call bi-clustering by which terms and documents are simultaneously grouped into semantically co- Categories and Subject Descriptors 11.3.3 [ I n f o r m a t i o n S e a r c h a n d R e t r i e v a l ] : Clustering; G.1.3 [ N u m e r i c a l L i n e a r A l g e b r a ] : Singular value de­ composition; G.2.2 [ G r a p h T h e o r y ] : G r a p h algorithms General Terms Algorithms, theory Keywords document clustering, bipartite graph, graph partitioning, spectral relaxation, singular value decomposition, correspon­ dence analysis *Part of this work was done while Xiaofeng He was a grad­ uate research assistant at N E R S C , Berkeley National Lab. Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. CIKM '01 November 5-10, 2001, Atlanta, Georgia. U S A Copyright 2001 A C M X - X X X X X - X X - X / X X / X X ...$5.00. O u r clustering algorithm computes an approximate global optimal solution while probabilistic latent semantic indexing relies on the E M algorithm and therefore might be prone to local m i n i m a even with the help of some annealing process. x

Bipartite graph partitioning and data clustering

In this paper, we study the sensitivity of discrete-time dynamic programs with nonlinear dynamics and objective to perturbations in the initial conditions and reference parameters. Under uniform co...

Exponential Decay in the Sensitivity Analysis of Nonlinear Dynamic Programming

AEGCN: An Autoencoder-Constrained Graph Convolutional Network

Differential graphical models are designed to represent the difference between the conditional dependence structures of two groups, thus are of particular interest for scientific investigation. Motivated by modern applications, this manuscript considers an extended setting where each group is generated by a latent variable Gaussian graphical model. Due to the existence of latent factors, the differential network is decomposed into sparse and low-rank components, both of which are symmetric indefinite matrices. We estimate these two components simultaneously using a two-stage procedure: (i) an initialization stage, which computes a simple, consistent estimator, and (ii) a convergence stage, implemented using a projected alternating gradient descent algorithm applied to a nonconvex objective, initialized using the output of the first stage. We prove that given the initialization, the estimator converges linearly with a nontrivial, minimax optimal statistical error. Experiments on synthetic and real data illustrate that the proposed nonconvex procedure outperforms existing methods.

Estimating differential latent variable graphical models with applications to brain connectivity

We develop a one-Newton-step-per-horizon, online, lag-$L$, model predictive control (MPC) algorithm for solving discrete-time, equality-constrained, nonlinear dynamic programs. Based on recent sensitivity analysis results for the target problems class, we prove that the approach exhibits a behavior that we call superconvergence; that is, the tracking error with respect to the full horizon solution is not only stable for successive horizon shifts, but also decreases with increasing shift order to a minimum value that decays exponentially in the length of the receding horizon. The key analytical step is the decomposition of the one-step error recursion of our algorithm into algorithmic error and perturbation error. We show that the perturbation error decays exponentially with the lag between two consecutive receding horizons, while the algorithmic error, determined by Newton's method, achieves quadratic convergence instead. Overall this approach induces our local exponential convergence result in terms of the receding horizon length for suitable values of $L$. Numerical experiments validate our theoretical findings.

Superconvergence of Online Optimization for Model Predictive Control.

Interactive news recommendation has been launched and attracted much attention recently. In this scenario, user’s behavior evolves from single click behavior to multiple behaviors including like, comment, share etc. However, most of the existing methods still use single click behavior as the unique criterion of judging user’s preferences. Further, although heterogeneous graphs have been applied in different areas, a proper way to construct a heterogeneous graph for interactive news data with an appropriate learning mechanism on it is still desired. To address the above concerns, we propose a graph-based behavior-aware network, which simultaneously considers six different types of behaviors as well as user’s demand on the news diversity. We have three mainsteps. First, we build an interaction behavior graph for multi-level and multi-category data. Second, we apply DeepWalk on the behavior graph to obtain entity semantics, then build a graph-based convolutional neural network called G-CNN to learn news representations, and an attention-based LSTM to learn behavior sequence representations. Third, we introduce core and coritivity features for the behavior graph, which measure the concentration degree of user’s interests. These features affect the trade-off between accuracy and diversity of our personalized recommendation system. Taking these features into account, our system finally achieves recommending news to different users at their different levels of concentration degrees.

Sen Na

Papers

Exponential Decay in the Sensitivity Analysis of Nonlinear Dynamic Programming

AEGCN: An Autoencoder-Constrained Graph Convolutional Network

Estimating differential latent variable graphical models with applications to brain connectivity

Superconvergence of Online Optimization for Model Predictive Control.

The graph-based behavior-aware recommendation for interactive news