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44
Spectral Clustering and Transductive Learning with Multiple Views
"... We consider spectral clustering and transductive inference for data with multiple views. A typical example is the web, which can be described by either the hyperlinks between web pages or the words occurring in web pages. When each view is represented as a graph, one may convexly combine the weight ..."
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Cited by 76 (2 self)
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We consider spectral clustering and transductive inference for data with multiple views. A typical example is the web, which can be described by either the hyperlinks between web pages or the words occurring in web pages. When each view is represented as a graph, one may convexly combine the weight matrices or the discrete Laplacians for each graph, and then proceed with existing clustering or classification techniques. Such a solution might sound natural, but its underlying principle is not clear. Unlike this kind of methodology, we develop multiview spectral clustering via generalizing the normalized cut from a single view to multiple views. We further build multiview transductive inference on the basis of multiview spectral clustering. Our framework leads to a mixture of Markov chains defined on every graph. The experimental evaluation on realworld web classification demonstrates promising results that validate our method. 1.
A New Analysis of CoTraining
"... In this paper, we present a new analysis on cotraining, a representative paradigm of disagreementbased semisupervised learning methods. In our analysis the cotraining process is viewed as a combinative label propagation over two views; this provides a possibility to bring the graphbased and dis ..."
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Cited by 24 (7 self)
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In this paper, we present a new analysis on cotraining, a representative paradigm of disagreementbased semisupervised learning methods. In our analysis the cotraining process is viewed as a combinative label propagation over two views; this provides a possibility to bring the graphbased and disagreementbased semisupervised methods into a unified framework. With the analysis we get some insight that has not been disclosed by previous theoretical studies. In particular, we provide the sufficient and necessary condition for cotraining to succeed. We also discuss the relationship to previous theoretical results and give some other interesting implications of our results, such as combination of weight matrices and view split. 1.
Fast Prediction on a Tree
"... Given an nvertex weighted tree with structural diameter S and a subset of m vertices, we present a technique to compute a corresponding m × m Gram matrix of the pseudoinverse of the graph Laplacian in O(n + m 2 + mS) time. We discuss the application of this technique to fast label prediction on a g ..."
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Cited by 17 (1 self)
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Given an nvertex weighted tree with structural diameter S and a subset of m vertices, we present a technique to compute a corresponding m × m Gram matrix of the pseudoinverse of the graph Laplacian in O(n + m 2 + mS) time. We discuss the application of this technique to fast label prediction on a generic graph. We approximate the graph with a spanning tree and then we predict with the kernel perceptron. We address the approximation of the graph with either a minimum spanning tree or a shortest path tree. The fast computation of the pseudoinverse enables us to address prediction problems on large graphs. We present experiments on two webspam classification tasks, one of which includes a graph with 400,000 vertices and more than 10,000,000 edges. The results indicate that the accuracy of our technique is competitive with previous methods using the full graph information. 1
A Heterogeneous Label Propagation Algorithm for Disease Gene Discovery
"... Label propagation is an effective and efficient technique to utilize local and global features in a network for semisupervised learning. In the literature, one challenge is how to propagate information in heterogeneous networks comprising several subnetworks, each of which has its own cluster struc ..."
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Cited by 16 (7 self)
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Label propagation is an effective and efficient technique to utilize local and global features in a network for semisupervised learning. In the literature, one challenge is how to propagate information in heterogeneous networks comprising several subnetworks, each of which has its own cluster structures that need to be explored independently. In this paper, we introduce an intutitive algorithm MINProp (Mutual Interactionbased Network Propagation) and a simple regularization framework for propagating information between subnetworks in a heterogeneous network. MINProp sequentially performs label propagation on each individual subnetwork with the current label information derived from the other subnetworks and repeats this step until convergence to the global optimal solution to the convex objective function of the regularization framework. The independent label propagation on each subnetwork explores the cluster structure in the subnetwork. The label information from the other subnetworks is used to capture mutual interactions (bicluster structures) between the vertices in each pair of the subnetworks. MINProp algorithm is applied to disease gene discovery from a heterogeneus network of disease phenotypes and genes. In the experiments, MINProp significantly outputperformed the original label propagation algorithm on a single network and the stateoftheart methods for discovering disease genes. The results also suggest that MINProp is more effective in utilizing the modular structures in a heterogenous network. Finally, MINProp discovered new diseasegene associations that are only reported recently.
Fitting a Graph to Vector Data
"... We introduce a measure of how well a combinatorial graph fits a collection of vectors. The optimal graphs under this measure may be computed by solving convex quadratic programs and have many interesting properties. For vectors in d dimensional space, the graphs always have average degree at most 2( ..."
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Cited by 14 (1 self)
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We introduce a measure of how well a combinatorial graph fits a collection of vectors. The optimal graphs under this measure may be computed by solving convex quadratic programs and have many interesting properties. For vectors in d dimensional space, the graphs always have average degree at most 2(d+1), and for vectors in 2 dimensions they are always planar. We compute these graphs for many standard data sets and show that they can be used to obtain good solutions to classification, regression and clustering problems. 1.
Semisupervised Learning by Higher Order Regularization
"... In semisupervised learning, at the limit of infinite unlabeled points while fixing labeled ones, the solutions of several graph Laplacian regularization based algorithms were shown by Nadler et al. (2009) to degenerate to constant functions with “spikes ” at labeled points in R d for d ≥ 2. These o ..."
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Cited by 13 (2 self)
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In semisupervised learning, at the limit of infinite unlabeled points while fixing labeled ones, the solutions of several graph Laplacian regularization based algorithms were shown by Nadler et al. (2009) to degenerate to constant functions with “spikes ” at labeled points in R d for d ≥ 2. These optimization problems all use the graph Laplacian regularizer as a common penalty term. In this paper, we address this problem by using regularization based on an iterated Laplacian, which is equivalent to a higher order Sobolev seminorm. Alternatively, it can be viewed as a generalization of the thin plate spline to an unknown submanifold in high dimensions. We also discuss relationships between Reproducing Kernel Hilbert Spaces and Green’s functions. Experimental results support our analysis by showing consistently improved results using iterated Laplacians. 1
Margin based transductive graph cuts using linear programming
 Proceedings of the Eleventh International Conference on Artificial Intelligence and Statistics, (AISTATS 2007
, 2007
"... This paper studies the problem of inferring a partition (or a graph cut) of an undirected deterministic graph where the labels of some nodes are observed thereby bridging a gap between graph theory and probabilistic inference techniques. Given a weighted graph, we focus on the rules of weighted nei ..."
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Cited by 11 (7 self)
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This paper studies the problem of inferring a partition (or a graph cut) of an undirected deterministic graph where the labels of some nodes are observed thereby bridging a gap between graph theory and probabilistic inference techniques. Given a weighted graph, we focus on the rules of weighted neighbors to predict the label of a particular node. A maximum margin and maximal average margin based argument is used to prove a generalization bound, and is subsequently related to the classical MINCUT approach. From a practical perspective a simple and intuitive, but efficient convex formulation is constructed. This scheme can readily be implemented as a linear program which scales well till a few thousands of (labeled or unlabeled) datapoints. The extremal case is studied where one observes only a single label, and this setting is related to the task of unsupervised clustering.
Clustering with local and global regularization
 in Proc. Assoc. Adv. Artif. Intell
, 2007
"... Abstract—Clustering is an old research topic in data mining and machine learning. Most of the traditional clustering methods can be categorized as local or global ones. In this paper, a novel clustering method that can explore both the local and global information in the data set is proposed. The me ..."
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Cited by 11 (4 self)
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Abstract—Clustering is an old research topic in data mining and machine learning. Most of the traditional clustering methods can be categorized as local or global ones. In this paper, a novel clustering method that can explore both the local and global information in the data set is proposed. The method, Clustering with Local and Global Regularization (CLGR), aims to minimize a cost function that properly trades off the local and global costs. We show that such an optimization problem can be solved by the eigenvalue decomposition of a sparse symmetric matrix, which can be done efficiently using iterative methods. Finally, the experimental results on several data sets are presented to show the effectiveness of our method. Index Terms—Clustering, local learning, smoothness, regularization. Ç 1
Graphbased Semisupervised Learning
 IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE (TPAMI08571206)
"... Graphbased learning provides a useful approach for modeling data in classification problems. In this modeling scenario, the relationship between labeled and unlabeled data impacts the construction and performance of classifiers, and therefore a semisupervised learning framework is adopted. We prop ..."
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Cited by 10 (3 self)
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Graphbased learning provides a useful approach for modeling data in classification problems. In this modeling scenario, the relationship between labeled and unlabeled data impacts the construction and performance of classifiers, and therefore a semisupervised learning framework is adopted. We propose a graph classifier based on kernel smoothing. A regularization framework is also introduced, and it is shown that the proposed classifier optimizes certain loss functions. Its performance is assessed on several synthetic and real benchmark data sets with good results, especially in settings where only a small fraction of the data are labeled.
Laplacian regularized gaussian mixture model for data clustering
 IEEE Transactions on Knowledge and Data Engineering
, 2010
"... Abstract—Gaussian Mixture Models (GMMs) are among the most statistically mature methods for clustering. Each cluster is represented by a Gaussian distribution. The clustering process thereby turns to estimate the parameters of the Gaussian mixture, usually by the ExpectationMaximization algorithm. ..."
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Cited by 8 (2 self)
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Abstract—Gaussian Mixture Models (GMMs) are among the most statistically mature methods for clustering. Each cluster is represented by a Gaussian distribution. The clustering process thereby turns to estimate the parameters of the Gaussian mixture, usually by the ExpectationMaximization algorithm. In this paper, we consider the case where the probability distribution that generates the data is supported on a submanifold of the ambient space. It is natural to assume that if two points are close in the intrinsic geometry of the probability distribution, then their conditional probability distributions are similar. Specifically, we introduce a regularized probabilistic model based on manifold structure for data clustering, called Laplacian regularized Gaussian Mixture Model (LapGMM). The data manifold is modeled by a nearest neighbor graph, and the graph structure is incorporated in the maximum likelihood objective function. As a result, the obtained conditional probability distribution varies smoothly along the geodesics of the data manifold. Experimental results on real data sets demonstrate the effectiveness of the proposed approach. Index Terms—Gaussian mixture model, clustering, graph laplacian, manifold structure. Ç 1