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43
Randomwalk computation of similarities between nodes of a graph, with application to collaborative recommendation
 IEEE Transactions on Knowledge and Data Engineering
, 2006
"... Abstract—This work presents a new perspective on characterizing the similarity between elements of a database or, more generally, nodes of a weighted and undirected graph. It is based on a Markovchain model of random walk through the database. More precisely, we compute quantities (the average comm ..."
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Cited by 116 (14 self)
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Abstract—This work presents a new perspective on characterizing the similarity between elements of a database or, more generally, nodes of a weighted and undirected graph. It is based on a Markovchain model of random walk through the database. More precisely, we compute quantities (the average commute time, the pseudoinverse of the Laplacian matrix of the graph, etc.) that provide similarities between any pair of nodes, having the nice property of increasing when the number of paths connecting those elements increases and when the “length ” of paths decreases. It turns out that the square root of the average commute time is a Euclidean distance and that the pseudoinverse of the Laplacian matrix is a kernel matrix (its elements are inner products closely related to commute times). A principal component analysis (PCA) of the graph is introduced for computing the subspace projection of the node vectors in a manner that preserves as much variance as possible in terms of the Euclidean commutetime distance. This graph PCA provides a nice interpretation to the “Fiedler vector, ” widely used for graph partitioning. The model is evaluated on a collaborativerecommendation task where suggestions are made about which movies people should watch based upon what they watched in the past. Experimental results on the MovieLens database show that the Laplacianbased similarities perform well in comparison with other methods. The model, which nicely fits into the socalled “statistical relational learning ” framework, could also be used to compute document or word similarities, and, more generally, it could be applied to machinelearning and patternrecognition tasks involving a relational database. Index Terms—Graph analysis, graph and database mining, collaborative recommendation, graph kernels, spectral clustering, Fiedler vector, proximity measures, statistical relational learning. 1
Learning to Track the Visual Motion of Contours
 Artificial Intelligence
, 1995
"... A development of a method for tracking visual contours is described. Given an "untrained" tracker, a trainingmotion of an object can be observed over some extended time and stored as an image sequence. The image sequence is used to learn parameters in a stochastic differential equation model. Thes ..."
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Cited by 97 (16 self)
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A development of a method for tracking visual contours is described. Given an "untrained" tracker, a trainingmotion of an object can be observed over some extended time and stored as an image sequence. The image sequence is used to learn parameters in a stochastic differential equation model. These are used, in turn, to build a tracker whose predictor imitates the motion in the training set. Tests show that the resulting trackers can be markedly tuned to desired curve shapes and classes of motions. Contents 1 Introduction 2 2 Tracking framework 2 2.1 Curve representation : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 2 2.2 Tracking as estimation over time : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 3 2.3 Rigid body transformations : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 3 2.4 Curves in motion : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 7 2.5 Discretetime model : : : : : : : : : :...
D Position, Attitude and Shape Input Using Video Tracking of Hands and Lips
"... Recent developments in videotracking allow the outlines of moving, natural objects in a videocamera input stream to be tracked live, at full videorate. Previous systems have been available to do this for specially illuminated objects or for naturally illuminated but polyhedral objects. Other syst ..."
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Cited by 70 (12 self)
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Recent developments in videotracking allow the outlines of moving, natural objects in a videocamera input stream to be tracked live, at full videorate. Previous systems have been available to do this for specially illuminated objects or for naturally illuminated but polyhedral objects. Other systems have been able to track nonpolyhedral objects in motion, in some cases from live video, but following only centroids or keypoints rather than tracking whole curves. The system described here can track accurately the curved silhouettes of moving nonpolyhedral objects at framerate, for example hands, lips, legs, vehicles, fruit, and without any special hardware beyond a desktop workstation and a videocamera and framestore. The new algorithms are a synthesis of methods in deformable models, Bspline curve representation and control theory. This paper shows how such a facility can be used to turn parts of the body  for instance, hands and lips  into input devices. Rigid motion of a...
The Principal Components Analysis of a Graph, and its Relationships to Spectral Clustering
 Proceedings of the 15th European Conference on Machine Learning (ECML 2004). Lecture Notes in Artificial Intelligence
, 2004
"... This work presents a novel procedure for computing (1) distances between nodes of a weighted, undirected, graph, called the Euclidean Commute Time Distance (ECTD), and (2) a subspace projection of the nodes of the graph that preserves as much variance as possible, in terms of the ECTD  a princi ..."
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Cited by 66 (15 self)
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This work presents a novel procedure for computing (1) distances between nodes of a weighted, undirected, graph, called the Euclidean Commute Time Distance (ECTD), and (2) a subspace projection of the nodes of the graph that preserves as much variance as possible, in terms of the ECTD  a principal components analysis of the graph. It is based on a Markovchain model of random walk through the graph. The model assigns transition probabilities to the links between nodes, so that a random walker can jump from node to node. A quantity, called the average commute time, computes the average time taken by a random walker for reaching node j when starting from node i, and coming back to node i. The square root of this quantity, the ECTD, is a distance measure between any two nodes, and has the nice property of decreasing when the number of paths connecting two nodes increases and when the "length" of any path decreases. The ECTD can be computed from the pseudoinverse of the Laplacian matrix of the graph, which is a kernel. We finally define the Principal Components Analysis (PCA) of a graph as the subspace projection that preserves as much variance as possible, in terms of the ECTD. This graph PCA has some interesting links with spectral graph theory, in particular spectral clustering.
Blind Separation of Synchronous CoChannel Digital Signals Using an Antenna Array. Part I. Algorithms
 IEEE Transactions on Signal Processing
, 1995
"... We propose a maximumlikelihood approach for separating and estimating multiple synchronous digital signals arriving at an antenna array. The spatial response of the array is assumed to be known imprecisely or unknown. We exploit the finite alphabet (FA) property of digital signals to simultaneou ..."
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Cited by 65 (6 self)
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We propose a maximumlikelihood approach for separating and estimating multiple synchronous digital signals arriving at an antenna array. The spatial response of the array is assumed to be known imprecisely or unknown. We exploit the finite alphabet (FA) property of digital signals to simultaneously determine the array response and the symbol sequence for each signal. Uniqueness of the estimates is established for signals with linear modulation formats. We introduce a signal detection technique based on the FA property which is different from a standard linear combiner. Computationally efficient algorithms for both block and recursive estimation of the signals are presented. This new approach is applicable to an unknown array geometry and propagation environment, which is particularly useful in wireless communication systems. Simulation results demonstrate its promising performance. Email: talwar@sccm.stanford.edu, Ph: (415) 7230061, Fax: (415) 7232411. This work was suppor...
The matrix cookbook
, 2006
"... What is this? These pages are a collection of facts (identities, approximations, inequalities, relations,...) about matrices and matters relating to them. It is collected in this form for the convenience of anyone who wants a quick desktop reference. Disclaimer: The identities, approximations and re ..."
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Cited by 61 (0 self)
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What is this? These pages are a collection of facts (identities, approximations, inequalities, relations,...) about matrices and matters relating to them. It is collected in this form for the convenience of anyone who wants a quick desktop reference. Disclaimer: The identities, approximations and relations presented here were obviously not invented but collected, borrowed and copied from a large amount of sources. These sources include similar but shorter notes found on the internet and appendices in books see the references for a full list. Errors: Very likely there are errors, typos, and mistakes for which we apologize and would be grateful to receive corrections at
Clustering Using a Random Walk Based Distance Measure
, 2005
"... This work proposes a simple way to improve a clustering algorithm. ..."
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Cited by 23 (1 self)
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This work proposes a simple way to improve a clustering algorithm.
A Novel Way of Computing Dissimilarities between Nodes of a Graph, with Application to Collaborative Filtering
, 2004
"... This work presents some general procedures for computing dissimilarities between elements of a database or, more generally, nodes of a weighted, undirected, graph. It is based on a Markovchain model of random walk through the database. The model assigns transition probabilities to the links betw ..."
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Cited by 18 (0 self)
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This work presents some general procedures for computing dissimilarities between elements of a database or, more generally, nodes of a weighted, undirected, graph. It is based on a Markovchain model of random walk through the database. The model assigns transition probabilities to the links between elements, so that a random walker can jump from element to element. A quantity, called the average firstpassage cost, computes the average cost incurred by a random walker for reaching element k for the first time when starting from element i.
Statistical Models of Visual Shape and Motion
 A
, 1998
"... This paper addresses some problems in the interpretation of visually observed shapes in motion, both planar and threedimensional shapes. Mumford (1996), interpreting the "Pattern Theory" developed over a number of years by Grenander (1976), views images as "pure" patterns that have been distorted b ..."
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Cited by 16 (0 self)
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This paper addresses some problems in the interpretation of visually observed shapes in motion, both planar and threedimensional shapes. Mumford (1996), interpreting the "Pattern Theory" developed over a number of years by Grenander (1976), views images as "pure" patterns that have been distorted by a combination of four kinds of degradations. This view applies naturally to the analysis of static, twodimensional images. The four degradations are given here, together with comments on how they need to be extended to take account of threedimensional objects in motion.
Signal propagation in proteins and relation to equilibrium fluctuations
 PLoS Comput Biol
"... Elastic network (EN) models have been widely used in recent years for describing protein dynamics, based on the premise that the motions naturally accessible to native structures are relevant to biological function. We posit that equilibrium motions also determine communication mechanisms inherent t ..."
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Cited by 13 (2 self)
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Elastic network (EN) models have been widely used in recent years for describing protein dynamics, based on the premise that the motions naturally accessible to native structures are relevant to biological function. We posit that equilibrium motions also determine communication mechanisms inherent to the network architecture. To this end, we explore the stochastics of a discretetime, discretestate Markov process of information transfer across the network of residues. We measure the communication abilities of residue pairs in terms of hit and commute times, i.e., the number of steps it takes on an average to send and receive signals. Functionally active residues are found to possess enhanced communication propensities, evidenced by their short hit times. Furthermore, secondary structural elements emerge as efficient mediators of communication. The present findings provide us with insights on the topological basis of communication in proteins and design principles for efficient signal transduction. While hit/commute times are informationtheoretic concepts, a central contribution of this work is to rigorously show that they have physical origins directly relevant to the equilibrium fluctuations of residues predicted by EN models.