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471
Reinforcement Learning I: Introduction
, 1998
"... In which we try to give a basic intuitive sense of what reinforcement learning is and how it differs and relates to other fields, e.g., supervised learning and neural networks, genetic algorithms and artificial life, control theory. Intuitively, RL is trial and error (variation and selection, search ..."
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Cited by 5500 (118 self)
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In which we try to give a basic intuitive sense of what reinforcement learning is and how it differs and relates to other fields, e.g., supervised learning and neural networks, genetic algorithms and artificial life, control theory. Intuitively, RL is trial and error (variation and selection, search) plus learning (association, memory). We argue that RL is the only field that seriously addresses the special features of the problem of learning from interaction to achieve longterm goals.
SemiSupervised Learning Using Gaussian Fields and Harmonic Functions
 IN ICML
, 2003
"... An approach to semisupervised learning is proposed that is based on a Gaussian random field model. Labeled and unlabeled data are represented as vertices in a weighted graph, with edge weights encoding the similarity between instances. The learning ..."
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Cited by 729 (14 self)
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An approach to semisupervised learning is proposed that is based on a Gaussian random field model. Labeled and unlabeled data are represented as vertices in a weighted graph, with edge weights encoding the similarity between instances. The learning
Random walks for image segmentation
 IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
, 2006
"... A novel method is proposed for performing multilabel, interactive image segmentation. Given a small number of pixels with userdefined (or predefined) labels, one can analytically and quickly determine the probability that a random walker starting at each unlabeled pixel will first reach one of the ..."
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Cited by 379 (21 self)
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A novel method is proposed for performing multilabel, interactive image segmentation. Given a small number of pixels with userdefined (or predefined) labels, one can analytically and quickly determine the probability that a random walker starting at each unlabeled pixel will first reach one of the prelabeled pixels. By assigning each pixel to the label for which the greatest probability is calculated, a highquality image segmentation may be obtained. Theoretical properties of this algorithm are developed along with the corresponding connections to discrete potential theory and electrical circuits. This algorithm is formulated in discrete space (i.e., on a graph) using combinatorial analogues of standard operators and principles from continuous potential theory, allowing it to be applied in arbitrary dimension on arbitrary graphs.
Geometric AdHoc Routing: Of Theory and Practice
, 2003
"... All too often a seemingly insurmountable divide between theory and practice can be witnessed. In this paper we try to contribute to narrowing this gap in the field of adhoc routing. In particular we consider two aspects: We propose a new geometric routing algorithm which is outstandingly efficient ..."
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Cited by 307 (13 self)
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All too often a seemingly insurmountable divide between theory and practice can be witnessed. In this paper we try to contribute to narrowing this gap in the field of adhoc routing. In particular we consider two aspects: We propose a new geometric routing algorithm which is outstandingly efficient on practical averagecase networks, however is also in theory asymptotically worstcase optimal. On the other hand we are able to drop the formerly necessary assumption that the distance between network nodes may not fall below a constant value, an assumption that cannot be maintained for practical networks. Abandoning this assumption we identify from a theoretical point of view two fundamentamentally different classes of cost metrics for routing in adhoc networks.
Visualizing Data using tSNE
, 2008
"... We present a new technique called “tSNE” that visualizes highdimensional data by giving each datapoint a location in a two or threedimensional map. The technique is a variation of Stochastic Neighbor Embedding (Hinton and Roweis, 2002) that is much easier to optimize, and produces significantly b ..."
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Cited by 272 (13 self)
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We present a new technique called “tSNE” that visualizes highdimensional data by giving each datapoint a location in a two or threedimensional map. The technique is a variation of Stochastic Neighbor Embedding (Hinton and Roweis, 2002) that is much easier to optimize, and produces significantly better visualizations by reducing the tendency to crowd points together in the center of the map. tSNE is better than existing techniques at creating a single map that reveals structure at many different scales. This is particularly important for highdimensional data that lie on several different, but related, lowdimensional manifolds, such as images of objects from multiple classes seen from multiple viewpoints. For visualizing the structure of very large data sets, we show how tSNE can use random walks on neighborhood graphs to allow the implicit structure of all of the data to influence the way in which a subset of the data is displayed. We illustrate the performance of tSNE on a wide variety of data sets and compare it with many other nonparametric visualization techniques, including Sammon mapping, Isomap, and Locally Linear Embedding. The visualizations produced by tSNE are significantly better than those produced by the other techniques on almost all of the data sets.
Authoritybased keyword search in databases
 TODS
"... The ObjectRank system applies authoritybased ranking to keyword search in databases modeled as labeled graphs. Conceptually, authority originates at the nodes (objects) containing the keywords and flows to objects according to their semantic connections. Each node is ranked according to its authori ..."
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Cited by 217 (13 self)
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The ObjectRank system applies authoritybased ranking to keyword search in databases modeled as labeled graphs. Conceptually, authority originates at the nodes (objects) containing the keywords and flows to objects according to their semantic connections. Each node is ranked according to its authority with respect to the particular
THE ELECTRICAL RESISTANCE OF A GRAPH CAPTURES ITS COMMUTE AND COVER TIMES
"... View an nvertex, medge undirected graph as an electrical network with unit resistors as edges. We extend known relations between random walks and electrical networks by showing that resistance in this network is intimately connected with the lengths of random walks on the graph. For example, the c ..."
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Cited by 192 (5 self)
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View an nvertex, medge undirected graph as an electrical network with unit resistors as edges. We extend known relations between random walks and electrical networks by showing that resistance in this network is intimately connected with the lengths of random walks on the graph. For example, the commute time between two vertices s and t (the expected length of a random walk from s to t and back) is precisely characterized by the e ective resistance Rst between s and t: commute time = 2mRst. As a corollary, the cover time (the expected length of a random walk visiting all vertices) is characterized by the maximum resistance R in the graph to within a factor of log n: mR cover time O(mR log n). For many graphs, the bounds on cover time obtained in this manner are better than those obtained from previous techniques such as the eigenvalues of the adjacency matrix. In particular, we improve known bounds on cover times for highdegree graphs and expanders, and give new proofs of known results for multidimensional meshes. Moreover, resistance seems to provide an intuitively appealing and tractable approach to these problems.
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 186 (19 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
Graph sparsification by effective resistances
 SIAM J. Comput
"... We present a nearlylinear time algorithm that produces highquality sparsifiers of weighted graphs. Given as input a weighted graph G = (V, E, w) and a parameter ǫ> 0, we produce a weighted subgraph H = (V, ˜ E, ˜w) of G such that  ˜ E  = O(n log n/ǫ 2) and for all vectors x ∈ R V (1 − ǫ) ∑ ..."
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Cited by 140 (9 self)
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We present a nearlylinear time algorithm that produces highquality sparsifiers of weighted graphs. Given as input a weighted graph G = (V, E, w) and a parameter ǫ> 0, we produce a weighted subgraph H = (V, ˜ E, ˜w) of G such that  ˜ E  = O(n log n/ǫ 2) and for all vectors x ∈ R V (1 − ǫ) ∑ (x(u) − x(v)) 2 wuv ≤ ∑ (x(u) − x(v)) 2 ˜wuv ≤ (1 + ǫ) ∑ (x(u) − x(v)) 2 wuv. (1) uv∈E uv ∈ ˜ E This improves upon the sparsifiers constructed by Spielman and Teng, which had O(n log c n) edges for some large constant c, and upon those of Benczúr and Karger, which only satisfied (1) for x ∈ {0, 1} V. We conjecture the existence of sparsifiers with O(n) edges, noting that these would generalize the notion of expander graphs, which are constantdegree sparsifiers for the complete graph. A key ingredient in our algorithm is a subroutine of independent interest: a nearlylinear time algorithm that builds a data structure from which we can query the approximate effective resistance between any two vertices in a graph in O(log n) time. uv∈E
Automatic Multimedia Crossmodal Correlation Discovery
, 2004
"... Given an image (or video clip, or audio song), how do we automatically assign keywords to it? The general problem is to find correlations across the media in a collection of multimedia objects like video clips, with colors, and/or motion, and/or audio, and/or text scripts. We propose a novel, graph ..."
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Cited by 137 (16 self)
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Given an image (or video clip, or audio song), how do we automatically assign keywords to it? The general problem is to find correlations across the media in a collection of multimedia objects like video clips, with colors, and/or motion, and/or audio, and/or text scripts. We propose a novel, graphbased approach, "MMG", to discover such crossmodal correlations. Our