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19
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 44 (4 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,
Relaxation Labeling Networks for the Maximum Clique Problem
 J. Artif. Neural Networks
, 1995
"... this paper, it is shown how to take advantage of the properties of these models to approximately solve the maximum clique problem, a wellknown intractable optimization problem which has practical applications in various fields. The approach is based on a result by Motzkin and Straus which naturally ..."
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Cited by 28 (17 self)
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this paper, it is shown how to take advantage of the properties of these models to approximately solve the maximum clique problem, a wellknown intractable optimization problem which has practical applications in various fields. The approach is based on a result by Motzkin and Straus which naturally leads to formulate the problem in a manner that is readily mapped onto a relaxation labeling network. Extensive simulations have demonstrated the validity of the proposed model, both in terms of quality of solutions and speed. Maximum clique problem, relaxation labeling processes, neural networks, optimization. 1 INTRODUCTION
Approximating the Maximum Weight Clique Using Replicator Dynamics
, 2000
"... Given an undirected graph with weights on the vertices, the maximum weight clique problem (MWCP) is to find a subset of mutually adjacent vertices (i.e., a clique) having largest total weight. This is a generalization of the classical problem of finding the maximum cardinality clique of an unweig ..."
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Cited by 26 (9 self)
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Given an undirected graph with weights on the vertices, the maximum weight clique problem (MWCP) is to find a subset of mutually adjacent vertices (i.e., a clique) having largest total weight. This is a generalization of the classical problem of finding the maximum cardinality clique of an unweighted graph, which arises as a special case of the MWCP when all the weights associated to the vertices are equal. The problem is known to be NP hard for arbitrary graphs and, according to recent theoretical results, so is the problem of approximating it within a constant factor. Although there has recently been much interest around neural network algorithms for the unweighted maximum clique problem, no effort has been directed so far towards its weighted counterpart. In this paper, we present a parallel, distributed heuristic for approximating the MWCP based on dynamics principles developed and studied in various branches of mathematical biology. The proposed framework centers aroun...
On Copositive Programming and Standard Quadratic Optimization Problems
 Journal of Global Optimization
, 2000
"... A standard quadratic problem consists of finding global maximizers of a quadratic form over the standard simplex. In this paper, the usual semidefinite programming relaxation is strengthened by replacing the cone of positive semidefinite matrices by the cone of completely positive matrices (the posi ..."
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Cited by 22 (5 self)
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A standard quadratic problem consists of finding global maximizers of a quadratic form over the standard simplex. In this paper, the usual semidefinite programming relaxation is strengthened by replacing the cone of positive semidefinite matrices by the cone of completely positive matrices (the positive semidefinite matrices which allow a factorization FF^T where F is some nonnegative matrix). The dual of this cone is the cone of copositive matrices (i.e., those matrices which yield a nonnegative quadratic form on the positive orthant). This conic formulation allows us to employ primaldual affinescaling directions. Furthermore, these approaches are combined with an evolutionary dynamics algorithm which generates primalfeasible paths along which the objective is monotonically improved until a local solution is reached. In particular, the primaldual affine scaling directions are used to escape from local maxima encountered during the evolutionary dynamics phase.
Annealed Replication: A New Heuristic for the Maximum Clique Problem
 Discr. Appl. Math
, 2000
"... In this paper, a new heuristic for approximating the maximum clique problem is proposed, based on a detailed analysis of a class of continuous optimization models which yield a complete solution to this NPhard combinatorial problem. The idea is to alter a regularization parameter iteratively in suc ..."
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Cited by 20 (11 self)
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In this paper, a new heuristic for approximating the maximum clique problem is proposed, based on a detailed analysis of a class of continuous optimization models which yield a complete solution to this NPhard combinatorial problem. The idea is to alter a regularization parameter iteratively in such a way that an iterative procedure with the updated parameter value would avoid unwanted, inefficient local solutions, i.e., maximal cliques which contain less than the maximum possible number of vertices. The local search procedure is performed with the help of the replicator dynamics, and the regularization parameter is chosen deliberately as to render dynamical instability of the (formerly) stable solutions which we want to discard in order to get an improvement. In this respect, the proposed procedure differs from usual simulated annealing approaches which mostly use a "blackbox" cooling schedule. To demonstrate the validity of this approach, we report on the performance applied to sel...
A Competitive Layer Model for Feature Binding and Sensory Segmentation
 NEURAL COMPUTATION
, 2001
"... We present a recurrent neural network for feature binding and sensory segmentation, the competitive layer model (CLM). The CLM uses topographically structured competitive and cooperative interactions in a layered network to partition a set of input features into salient groups. The dynamics is fo ..."
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Cited by 19 (11 self)
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We present a recurrent neural network for feature binding and sensory segmentation, the competitive layer model (CLM). The CLM uses topographically structured competitive and cooperative interactions in a layered network to partition a set of input features into salient groups. The dynamics is formulated within a standard additive recurrent network with linear threshold neurons. Contextual relations among features are coded by pairwise compatibilities which define an energy function to be minimized by the neural dynamics. Due to the usage of dynamical winnertakeall circuits the model gains more flexible response properties than spin models of segmentation by exploiting amplitude information in the grouping process. We prove analytic results on the convergence and stable attractors of the CLM, which generalize earlier results on winnertakeall networks, and incorporate deterministic annealing for robustness against local minima. The piecewise linear dynamics of the CLM allows a linear eigensubspace analysis which we use to analyze the dynamics of binding in conjunction with annealing. For the example of contour detection we show how the CLM can integrate figureground segmentation and grouping into a unified model.
Self Annealing: Unifying deterministic annealing and relaxation labeling
 In Energy Minimization Methods in Computer Vision and Pattern Recognition (EMMCVPR '97
, 1997
"... . Deterministic annealing and relaxation labeling algorithms for classification and matching are presented and discussed. A new approach self annealingis introduced to bring deterministic annealing and relaxation labeling into accord. Self annealing results in an emergent linear schedule for w ..."
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Cited by 4 (1 self)
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. Deterministic annealing and relaxation labeling algorithms for classification and matching are presented and discussed. A new approach self annealingis introduced to bring deterministic annealing and relaxation labeling into accord. Self annealing results in an emergent linear schedule for winnertakeall and assignment problems. Also, the relaxation labeling algorithm can be seen as an approximation to the self annealing algorithm for matching and labeling problems. 1 Introduction Labeling and matching problems abound in computer vision and pattern recognition (CVPR). It is not an exaggeration to state that some form or the other of the basic problems of template matching or data clustering has remained central to the CVPR and neural networks communities for about three decades. Due to the somewhat disparate natures of these communities, different frameworks for formulating and solving these two problems have emerged and it is not immediately obvious how to go about reconcili...
Self annealing and self annihilation: Unifying deterministic annealing and relaxation labeling
 In Pattern Recognition
, 2000
"... Deterministic annealing and relaxation labeling algorithms for classification and matching are presented and discussed. A new approachself annealingis introduced to bring deterministic annealing and relaxation labeling into accord. Self annealing results in an emergent linear schedule for winn ..."
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Cited by 3 (1 self)
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Deterministic annealing and relaxation labeling algorithms for classification and matching are presented and discussed. A new approachself annealingis introduced to bring deterministic annealing and relaxation labeling into accord. Self annealing results in an emergent linear schedule for winnertakeall and linear assignment problems. Self annihilation, a generalization of self annealing is capable of performing the useful function of symmetry breaking. The original relaxation labeling algorithm is then shown to arise from an approximation to either the self annealing energy function or the corresponding dynamical system. With this relationship in place, self annihilation can be introduced into the relaxation labeling framework. Experimental results on synthetic matching and labeling problems clearly demonstrate the threeway relationship between deterministic annealing, relaxation labeling and self annealing. Keywords: Deterministic annealing, relaxation labeling, self anneal...
Matching Hierarchical Structures for Shape Recognition
, 2004
"... In this thesis we aim to develop a framework for clustering trees and representing and learning a generative model of graph structures from a set of training samples. The approach is applied to the problem of the recognition and classification of shape abstracted in terms of its morphological skelet ..."
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Cited by 2 (0 self)
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In this thesis we aim to develop a framework for clustering trees and representing and learning a generative model of graph structures from a set of training samples. The approach is applied to the problem of the recognition and classification of shape abstracted in terms of its morphological skeleton. We make five contributions. The first is an algorithm to approximate tree editdistance using relaxation labeling. The second is the introduction of the tree union, a representation capable of representing the modes of structural variation present in a set of trees. The third is an information theoretic approach to learning a generative model of tree structures from a training set. While the skeletal...