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104
A New GraphTheoretic Approach to Clustering, with Applications to Computer Vision
, 2004
"... This work applies cluster analysis as a unified approach for a wide range of vision applications, thereby combining the research domain of computer vision and that of machine learning. Cluster analysis is the formal study of algorithms and methods for recovering the inherent structure within a given ..."
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Cited by 59 (6 self)
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This work applies cluster analysis as a unified approach for a wide range of vision applications, thereby combining the research domain of computer vision and that of machine learning. Cluster analysis is the formal study of algorithms and methods for recovering the inherent structure within a given dataset. Many problems of computer vision have precisely this goal, namely to find which visual entities belong to an inherent structure, e.g. in an image or in a database of images. For example, a meaningful structure in the context of image segmentation is a set of pixels which correspond to the same object in a scene. Clustering algorithms can be used to partition the pixels of an image into meaningful parts, which may correspond to different objects. In this work we focus on the problems of image segmentation and image database organization. The visual entities to consider are pixels and images, respectively. Our first contribution in this work is a novel partitional (flat) clustering algorithm. The algorithm uses pairwise representation, where the visual objects (pixels,
Efficient spatiotemporal grouping using the Nyström method
 In Proc. IEEE Conf. Comput. Vision and Pattern Recognition
, 2001
"... Spectral graph theoretic methods have recently shown great promise for the problem of image segmentation, but due to the computational demands, applications of such methods to spatiotemporal data have been slow to appear. For even a short video sequence, the set of all pairwise voxel similarities is ..."
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Cited by 59 (5 self)
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Spectral graph theoretic methods have recently shown great promise for the problem of image segmentation, but due to the computational demands, applications of such methods to spatiotemporal data have been slow to appear. For even a short video sequence, the set of all pairwise voxel similarities is a huge quantity of data: one second of a � � ¢ � � sequence captured at Hz entails on the order of pairwise similarities. The contribution of this paper is a method that substantially reduces the computational requirements of grouping algorithms based on spectral partitioning, making it feasible to apply them to very large spatiotemporal grouping problems. Our approach is based on a technique for the numerical solution of eigenfunction problems known as the Nyström method. This method allows extrapolation of the complete grouping solution using only a small number of “typical ” samples. In doing so, we successfully exploit the fact that there are far fewer coherent groups in an image sequence than pixels. 1
Salient Closed Boundary Extraction with Ratio Contour
 IEEE Trans. on Pattern Analysis and Machine Intelligence
, 2005
"... We present ratio contour, a novel graphbased method for extracting salient closed boundaries from noisy images. This method operates on a set of boundary fragments that are produced by edge detection. Boundary extraction identifies a subset of these fragments and connects them sequentially to for ..."
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Cited by 57 (13 self)
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We present ratio contour, a novel graphbased method for extracting salient closed boundaries from noisy images. This method operates on a set of boundary fragments that are produced by edge detection. Boundary extraction identifies a subset of these fragments and connects them sequentially to form a closed boundary with the largest saliency. We encode the Gestalt laws of proximity and continuity in a novel boundarysaliency measure based on the relative gap length and average curvature when connecting fragments to form a closed boundary. This new measure attempts to remove a possible bias toward short boundaries. We present a polynomialtime algorithm for finding the mostsalient closed boundary. We also present supplementary preprocessing steps that facilitate the application of ratio contour to real images. We compare ratio contour to two closely related methods for extracting closed boundaries: Elder and Zucker's method based on the shortestpath algorithm and Williams and Thornber's method based on spectral analysis and a stronglyconnectedcomponents algorithm. This comparison involves both theoretic analysis and experimental evaluation on both synthesized data and real images.
Feature Selection for Unsupervised and Supervised Inference: the Emergence of Sparsity in a Weightedbased Approach
 School of Eng. and CS, June 2003. Proceedings of the Ninth IEEE International Conference on Computer Vision (ICCV 2003) 2Volume Set 0769519504/03 $17.00 © 2003 IEEE
"... The problem of selecting a subset of relevant features in a potentially overwhelming quantity of data is classic and found in many branches of science including — examples in computer vision, text processing and more recently bioinformatics are abundant. In this work we present a definition of ”rele ..."
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Cited by 53 (3 self)
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The problem of selecting a subset of relevant features in a potentially overwhelming quantity of data is classic and found in many branches of science including — examples in computer vision, text processing and more recently bioinformatics are abundant. In this work we present a definition of ”relevancy ” based on spectral properties of the Affinity (or Laplacian) of the features ’ measurement matrix. The feature selection process is then based on a continuous ranking of the features defined by a leastsquares optimization process. A remarkable property of the feature relevance function is that sparse solutions for the ranking values naturally emerge as a result of a “biased nonnegativity ” of a key matrix in the process. As a result, a simple leastsquares optimization process converges onto a sparse solution, i.e., a selection of a subset of features which form a local maxima over the relevance function. The feature selection algorithm can be embedded in both unsupervised and supervised inference problems and empirical evidence show that the feature selections typically achieve high accuracy even when only a small fraction of the features are relevant. 1.
Clustering and Embedding using Commute Times
 IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
"... This paper exploits the properties of the commute time between nodes of a graph for the purposes of clustering and embedding, and explores its applications to image segmentation and multibody motion tracking. Our starting point is the lazy random walk on the graph, which is determined by the heatke ..."
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Cited by 52 (4 self)
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This paper exploits the properties of the commute time between nodes of a graph for the purposes of clustering and embedding, and explores its applications to image segmentation and multibody motion tracking. Our starting point is the lazy random walk on the graph, which is determined by the heatkernel of the graph and can be computed from the spectrum of the graph Laplacian. We characterize the random walk using the commute time (i.e. the expected time taken for a random walk to travel between two nodes and return) and show how this quantity may be computed from the Laplacian spectrum using the discrete Green’s function. Our motivation is that the commute time can be anticipated to be a more robust measure of the proximity of data than the raw proximity matrix. In this paper, we explore two applications of the commute time. The first is to develop a method for image segmentation using the eigenvector corresponding to the smallest eigenvalue of the commute time matrix. We show that our commute time segmentation method has the property of enhancing the intragroup coherence while weakening intergroup coherence and is superior to the normalized cut. The second application is to develop a robust multibody motion tracking method using an embedding based on the commute time. Our embedding procedure preserves commute time, and is closely akin to kernel PCA, the Laplacian eigenmap and the diffusion map. We illustrate the results both on synthetic image sequences and real world video sequences, and compare our results with several alternative methods.
Eigenspacebased Anomaly Detection in Computer Systems
 Proceedings of the Tenth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD
, 2004
"... We report on an automated runtime anomaly detection method at the application layer of multinode computer systems. Although several network management systems are available in the market, none of them have sufficient capabilities to detect faults in multitier Webbased systems with redundancy. We ..."
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Cited by 49 (4 self)
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We report on an automated runtime anomaly detection method at the application layer of multinode computer systems. Although several network management systems are available in the market, none of them have sufficient capabilities to detect faults in multitier Webbased systems with redundancy. We model a Webbased system as a weighted graph, where each node represents a “service ” and each edge represents a dependency between services. Since the edge weights vary greatly over time, the problem we address is that of anomaly detection from a time sequence of graphs. In our method, we first extract a feature vector from the adjacency matrix that represents the activities of all of the services. The heart of our method is to use the principal eigenvector of the eigenclusters of the graph. Then we derive a probability distribution for an anomaly measure defined for a timeseries of directional data derived from the graph sequence. Given a critical probability, the threshold value is adaptively updated using a novel online algorithm. We demonstrate that a fault in a Web application can be automatically detected and the faulty services are identified without using detailed knowledge of the behavior of the system.
Pattern vectors from algebraic graph theory
 IEEE PAMI
, 2005
"... Graph structures have proved computationally cumbersome for pattern analysis. The reason for this is that before graphs can be converted to pattern vectors, correspondences must be established between the nodes of structures which are potentially of different size. To overcome this problem, in this ..."
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Cited by 34 (3 self)
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Graph structures have proved computationally cumbersome for pattern analysis. The reason for this is that before graphs can be converted to pattern vectors, correspondences must be established between the nodes of structures which are potentially of different size. To overcome this problem, in this paper we turn to the spectral decomposition of the Laplacian matrix. We show how the elements of the spectral matrix for the Laplacian can be used to construct symmetric polynomials that are permutation invariants. The coefficients of these polynomials can be used as graph features which can be encoded in a vectorial manner. We extend this representation to graphs in which there are unary attributes on the nodes and binary attributes on the edges by using the spectral decomposition of a Hermitian property matrix that can be viewed as a complex analogue of the Laplacian. To embed the graphs in a pattern space, we explore whether the vectors of invariants can be embedded in a low dimensional space using a number of alternative strategies including principal components analysis (PCA), multidimensional scaling (MDS) and locality preserving projection (LPP). Experimentally, we demonstrate that the embeddings result in well defined graph clusters. Our experiments with the
A GameTheoretic Approach to Hypergraph Clustering
, 2009
"... Hypergraph clustering refers to the process of extracting maximally coherent groups from a set of objects using highorder (rather than pairwise) similarities. Traditional approaches to this problem are based on the idea of partitioning the input data into a userdefined number of classes, thereby o ..."
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Cited by 27 (2 self)
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Hypergraph clustering refers to the process of extracting maximally coherent groups from a set of objects using highorder (rather than pairwise) similarities. Traditional approaches to this problem are based on the idea of partitioning the input data into a userdefined number of classes, thereby obtaining the clusters as a byproduct of the partitioning process. In this paper, we provide a radically different perspective to the problem. In contrast to the classical approach, we attempt to provide a meaningful formalization of the very notion of a cluster and we show that game theory offers an attractive and unexplored perspective that serves well our purpose. Specifically, we show that the hypergraph clustering problem can be naturally cast into a noncooperative multiplayer “clustering game”, whereby the notion of a cluster is equivalent to a classical gametheoretic equilibrium concept. From the computational viewpoint, we show that the problem of finding the equilibria of our clustering game is equivalent to locally optimizing a polynomial function over the standard simplex, and we provide a discretetime dynamics to perform this optimization. Experiments are presented which show the superiority of our approach over stateoftheart hypergraph clustering techniques.
Retrieval By Classification of Images Containing Large Manmade Objects Using Perceptual Grouping
"... This paper applies perceptual grouping rules to the retrieval by classification of images containing large manmade objects such as buildings, towers, bridges, and other architectural objects. The semantic interrelationships between primitive image features are exploited by perceptual grouping to ext ..."
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Cited by 26 (4 self)
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This paper applies perceptual grouping rules to the retrieval by classification of images containing large manmade objects such as buildings, towers, bridges, and other architectural objects. The semantic interrelationships between primitive image features are exploited by perceptual grouping to extract structure to detect the presence of manmade objects. Segmentation and detailed object representation are not required. The system analyzes each image to extract features that are strong evidence of the presence of these objects. These features are generated by the strong boundaries typical of manmade structures: straight line segments, longer linear lines, coterminations, "L" junctions, "U" junctions, parallel lines, parallel groups, "significant" parallel groups, cotermination graph, and polygons. A Knearest neighbor framework is employed to classify these features and retrieve the images that contain manmade objects. Results are demonstrated for two databases of monocular outdoor images. Keywords: Perceptual grouping, structure, contentbased image retrieval, image databases, multimedia systems, nearest neighbor classifier. # This work was supported in part by the Army Research O#ce under contracts DAAD190010044, DAAG55981 0230 and DAAD199910012 (Johns Hopkins University subcontract agreement 890548168). 1
Probabilistic Models for Combining Diverse Knowledge Sources in Multimedia Retrieval
 In Ph.D Thesis
, 2006
"... In recent years, the multimedia retrieval community is gradually shifting its emphasis from analyzing one media source at a time to exploring the opportunities of combining diverse knowledge sources from correlated media types and context. This thesis presents a conditional probabilistic retrieval m ..."
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Cited by 26 (3 self)
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In recent years, the multimedia retrieval community is gradually shifting its emphasis from analyzing one media source at a time to exploring the opportunities of combining diverse knowledge sources from correlated media types and context. This thesis presents a conditional probabilistic retrieval model as a principled framework to combine diverse knowledge sources. An efficient rankbased learning approach has been developed to explicitly model the ranking relations in the learning process. Under this retrieval framework, we overview and develop a number of stateoftheart approaches for extracting ranking features from multimedia knowledge sources. To incorporate query information in the combination model, this thesis develops a number of query analysis models that can automatically discover mixing structure of the query space based on previous retrieval results. To adapt the combination function on a per query basis, this thesis also presents a probabilistic local context analysis(pLCA) model to automatically leverage additional retrieval sources to improve initial retrieval outputs. All the proposed approaches are evaluated on multimedia retrieval tasks with largescale video collections as well as metasearch tasks with largescale text collections. 1