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46
Beyond pairwise clustering
 in IEEE Computer Society Conference on Computer Vision and Pattern Recognition
"... We consider the problem of clustering in domains where the affinity relations are not dyadic (pairwise), but rather triadic, tetradic or higher. The problem is an instance of the hypergraph partitioning problem. We propose a twostep algorithm for solving this problem. In the first step we use a nove ..."
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Cited by 42 (2 self)
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We consider the problem of clustering in domains where the affinity relations are not dyadic (pairwise), but rather triadic, tetradic or higher. The problem is an instance of the hypergraph partitioning problem. We propose a twostep algorithm for solving this problem. In the first step we use a novel scheme to approximate the hypergraph using a weighted graph. In the second step a spectral partitioning algorithm is used to partition the vertices of this graph. The algorithm is capable of handling hyperedges of all orders including order two, thus incorporating information of all orders simultaneously. We present a theoretical analysis that relates our algorithm to an existing hypergraph partitioning algorithm and explain the reasons for its superior performance. We report the performance of our algorithm on a variety of computer vision problems and compare it to several existing hypergraph partitioning algorithms. 1.
Detection and explanation of anomalous activities: representing activities as bags of event ngrams
 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR
, 2005
"... We present a novel representation and method for detecting and explaining anomalous activities in a video stream. Drawing from natural language processing, we introduce a representation of activities as bags of event ngrams, where we analyze the global structural information of activities using the ..."
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Cited by 36 (6 self)
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We present a novel representation and method for detecting and explaining anomalous activities in a video stream. Drawing from natural language processing, we introduce a representation of activities as bags of event ngrams, where we analyze the global structural information of activities using their local event statistics. We demonstrate how maximal cliques in an undirected edgeweighted graph of activities, can be used in an unsupervised manner, to discover regular subclasses of an activity class. Based on these discovered subclasses, we formulate a definition of anomalous activities and present a way to detect them. Finally, we characterize each discovered subclass in terms of its “most representative member, ” and present an informationtheoretic method to explain the detected anomalies in a humaninterpretable form. 1. Introduction and Previous
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 34 (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.
Dominant sets and pairwise clustering
 IEEE Trans. on Pattern Anal. and Mach. Intell
, 2007
"... ..."
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 30 (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.
PolynomialTime Metrics for Attributed Trees
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 2005
"... We address the problem of comparing attributed trees and propose four novel distance measures centered around the notion of a maximal similarity common subtree. The proposed measures are general and defined on trees endowed with either symbolic or continuousvalued attributes, and can be equally app ..."
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Cited by 28 (1 self)
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We address the problem of comparing attributed trees and propose four novel distance measures centered around the notion of a maximal similarity common subtree. The proposed measures are general and defined on trees endowed with either symbolic or continuousvalued attributes, and can be equally applied to ordered and unordered, rooted and unrooted trees. We prove that our measures satisfy the metric constraints and provide a polynomialtime algorithm to compute them. This is a remarkable and attractive property, since the computation of traditional editdistancebased metrics is NPcomplete, except for ordered structures. We experimentally validate the usefulness of our metrics on shape matching tasks, and compare them with editdistance measures. ∗ Submitted to IEEE Transactions on Pattern Analysis and Machine Intelligence 1
Structure from statistics  unsupervised activity analysis using suffix trees
 In IEEE ICCV
, 2007
"... Models of activity structure for unconstrained environments are generally not available a priori. Recent representational approaches to this end are limited by their computational complexity, and ability to capture activity structure only up to some fixed temporal scale. In this work, we propose Suf ..."
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Cited by 16 (2 self)
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Models of activity structure for unconstrained environments are generally not available a priori. Recent representational approaches to this end are limited by their computational complexity, and ability to capture activity structure only up to some fixed temporal scale. In this work, we propose Suffix Trees as an activity representation to efficiently extract structure of activities by analyzing their constituent eventsubsequences over multiple temporal scales. We empirically compare Suffix Trees with some of the previous approaches in terms of feature cardinality, discriminative prowess, noise sensitivity and activityclass discovery. Finally, exploiting properties of Suffix Trees, we present a novel perspective on anomalous subsequences of activities, and propose an algorithm to detect them in lineartime. We present comparative results over experimental data, collected from a kitchen environment to demonstrate the competence of our proposed framework. 1. Introduction & Previous
Image segmentation using commute times
 In BMVC
, 2005
"... This paper exploits the properties of the commute time to develop a graphspectral method for image segmentation. 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 characterise ..."
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Cited by 15 (2 self)
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This paper exploits the properties of the commute time to develop a graphspectral method for image segmentation. 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 characterise the random walk using the commute time between nodes, and show how this quantity may be computed from the Laplacian spectrum using the discrete Green’s function. We explore the application of the commute time for image segmentation using the eigenvector corresponding to the smallest eigenvalue of the commute time matrix. 1
Dominant Sets and Hierarchical Clustering
"... Dominant sets are a new graphtheoretic concept that has proven to be relevant in partitional (flat) clustering as well as image segmentation problems. However, in many computer vision applications, such as the organization of an image database, it is important to provide the data to be clustered wi ..."
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Cited by 14 (2 self)
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Dominant sets are a new graphtheoretic concept that has proven to be relevant in partitional (flat) clustering as well as image segmentation problems. However, in many computer vision applications, such as the organization of an image database, it is important to provide the data to be clustered with a hierarchical organization, and it is not clear how to do this within the dominant set framework. In this paper we address precisely this problem, and present a simple and elegant solution to it. To this end, we consider a family of (continuous) quadratic programs which contain a parameterized regularization term that controls the global shape of the energy landscape. When the regularization parameter is zero the local solutions are known to be in onetoone correspondence with dominant sets, but when it is positive an interesting picture emerges. We determine bounds for the regularization parameter that allow us to exclude from the set of local solutions those inducing clusters of size smaller than a prescribed threshold. This suggests a new (divisive) hierarchical approach to clustering, which is based on the idea of properly varying the regularization parameter during the clustering process. Straightforward dynamics from evolutionary game theory are used to locate the solutions of the quadratic programs at each level of the hierarchy. We apply the proposed framework to the problem of organizing a shape database. Experiments with three different similarity matrices (and databases) reported in the literature have been conducted, and the results confirm the effectiveness of our approach.