Markov random fields for image modelling and analysis
Modelling and applications of stochastic processes
An optimal on-line algorithm for metrical task system
Journal of the ACM (JACM)
Evolutionary trees: An integer multicommodity max-flow-min-cut theorem
Advances in Applied Mathematics
The Complexity of Multiterminal Cuts
SIAM Journal on Computing
Markov random field modeling in computer vision
Markov random field modeling in computer vision
Inducing Features of Random Fields
IEEE Transactions on Pattern Analysis and Machine Intelligence
Enhanced hypertext categorization using hyperlinks
SIGMOD '98 Proceedings of the 1998 ACM SIGMOD international conference on Management of data
An improved approximation algorithm for multiway cut
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
On approximating arbitrary metrices by tree metrics
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Minimum 0-extensions of graph metrics
European Journal of Combinatorics
Rounding algorithms for a geometric embedding of minimum multiway cut
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Optimal 3-Terminal Cuts and Linear Programming
Proceedings of the 7th International IPCO Conference on Integer Programming and Combinatorial Optimization
Segmentation by Grouping Junctions
CVPR '98 Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition
Markov Random Fields with Efficient Approximations
CVPR '98 Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition
Probabilistic approximation of metric spaces and its algorithmic applications
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
A Maximum-Flow Formulation of the N-Camera Stereo Correspondence Problem
ICCV '98 Proceedings of the Sixth International Conference on Computer Vision
A constant factor approximation algorithm for a class of classification problems
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Improved classification via connectivity information
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Approximation algorithms for the 0-extension problem
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Approximation algorithms for the metric labeling problem via a new linear programming formulation
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
An efficient algorithm for image segmentation, Markov random fields and related problems
Journal of the ACM (JACM)
Fast Approximate Energy Minimization via Graph Cuts
IEEE Transactions on Pattern Analysis and Machine Intelligence
Similarity estimation techniques from rounding algorithms
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
An improved approximation algorithm for the 0-extension problem
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Optimal Net Surface Problems with Applications
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
Local Similarity Based Point-Pattern Matching
CPM '02 Proceedings of the 13th Annual Symposium on Combinatorial Pattern Matching
A tight bound on approximating arbitrary metrics by tree metrics
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Tree consistency and bounds on the performance of the max-product algorithm and its generalizations
Statistics and Computing
Approximating metrics by tree metrics
ACM SIGACT News
A probabilistic framework for semi-supervised clustering
Proceedings of the tenth ACM SIGKDD international conference on Knowledge discovery and data mining
Integrating constraints and metric learning in semi-supervised clustering
ICML '04 Proceedings of the twenty-first international conference on Machine learning
Learning associative Markov networks
ICML '04 Proceedings of the twenty-first international conference on Machine learning
Recovering articulated object models from 3D range data
UAI '04 Proceedings of the 20th conference on Uncertainty in artificial intelligence
A tight bound on approximating arbitrary metrics by tree metrics
Journal of Computer and System Sciences - Special issue: STOC 2003
Algorithmic detection of semantic similarity
WWW '05 Proceedings of the 14th international conference on World Wide Web
Efficient algorithms for online decision problems
Journal of Computer and System Sciences - Special issue: Learning theory 2003
A Feature-based Approach for Dense Segmentation and Estimation of Large Disparity Motion
International Journal of Computer Vision
Quadratic programming relaxations for metric labeling and Markov random field MAP estimation
ICML '06 Proceedings of the 23rd international conference on Machine learning
Graph-based text classification: learn from your neighbors
SIGIR '06 Proceedings of the 29th annual international ACM SIGIR conference on Research and development in information retrieval
Convergent Tree-Reweighted Message Passing for Energy Minimization
IEEE Transactions on Pattern Analysis and Machine Intelligence
Minimizing bank selection instructions for partitioned memory architecture
CASES '06 Proceedings of the 2006 international conference on Compilers, architecture and synthesis for embedded systems
Journal of Experimental Algorithmics (JEA)
Classification in Networked Data: A Toolkit and a Univariate Case Study
The Journal of Machine Learning Research
Pricing of partially compatible products
Proceedings of the 8th ACM conference on Electronic commerce
Matching by Linear Programming and Successive Convexification
IEEE Transactions on Pattern Analysis and Machine Intelligence
Minimal placement of bank selection instructions for partitioned memory architectures
ACM Transactions on Embedded Computing Systems (TECS)
The Journal of Machine Learning Research
Protein functional class prediction with a combined graph
Expert Systems with Applications: An International Journal
Semi-supervised graph clustering: a kernel approach
Machine Learning
Constrained Local Regularized Transducer for Multi-Component Category Classification
PRICAI '08 Proceedings of the 10th Pacific Rim International Conference on Artificial Intelligence: Trends in Artificial Intelligence
Ontology-Based Service Discovery Front-End Interface for GloServ
ESWC 2009 Heraklion Proceedings of the 6th European Semantic Web Conference on The Semantic Web: Research and Applications
Convex Multi-class Image Labeling by Simplex-Constrained Total Variation
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
Message-passing for Graph-structured Linear Programs: Proximal Methods and Rounding Schemes
The Journal of Machine Learning Research
Improved Moves for Truncated Convex Models
The Journal of Machine Learning Research
CVPR'03 Proceedings of the 2003 IEEE computer society conference on Computer vision and pattern recognition
Metric labeling and semi-metric embedding for protein annotation prediction
RECOMB'11 Proceedings of the 15th Annual international conference on Research in computational molecular biology
Minimizing count-based high order terms in markov random fields
EMMCVPR'11 Proceedings of the 8th international conference on Energy minimization methods in computer vision and pattern recognition
Globally optimal image partitioning by multicuts
EMMCVPR'11 Proceedings of the 8th international conference on Energy minimization methods in computer vision and pattern recognition
Optimality bounds for a variational relaxation of the image partitioning problem
EMMCVPR'11 Proceedings of the 8th international conference on Energy minimization methods in computer vision and pattern recognition
Curvature regularity for multi-label problems - standard and customized linear programming
EMMCVPR'11 Proceedings of the 8th international conference on Energy minimization methods in computer vision and pattern recognition
Ranking sports teams and the inverse equal paths problem
WINE'06 Proceedings of the Second international conference on Internet and Network Economics
An adaptive kernel method for semi-supervised clustering
ECML'06 Proceedings of the 17th European conference on Machine Learning
Linear programming for matching in human body gesture recognition
AMFG'05 Proceedings of the Second international conference on Analysis and Modelling of Faces and Gestures
Mining inter-entity semantic relations using improved transductive learning
IJCNLP'05 Proceedings of the Second international joint conference on Natural Language Processing
Linear programming matching and appearance-adaptive object tracking
EMMCVPR'05 Proceedings of the 5th international conference on Energy Minimization Methods in Computer Vision and Pattern Recognition
Approximating a class of classification problems
Efficient Approximation and Online Algorithms
Mechanisms and allocations with positive network externalities
Proceedings of the 13th ACM Conference on Electronic Commerce
Exact algorithms for a discrete metric labeling problem
Discrete Optimization
New algorithms for convex cost tension problem with application to computer vision
Discrete Optimization
Continuous Multiclass Labeling Approaches and Algorithms
SIAM Journal on Imaging Sciences
Total Cyclic Variation and Generalizations
Journal of Mathematical Imaging and Vision
Optimality Bounds for a Variational Relaxation of the Image Partitioning Problem
Journal of Mathematical Imaging and Vision
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In a traditional classification problem, we wish to assign one of k labels (or classes) to each of n objects, in a way that is consistent with some observed data that we have about the problem. An active line of research in this area is concerned with classification when one has information about pairwise relationships among the objects to be classified; this issue is one of the principal motivations for the framework of Markov random fields, and it arises in areas such as image processing, biometry, and document analysis. In its most basic form, this style of analysis seeks a classification that optimizes a combinatorial function consisting of assignment costs - based on the individual choice of label we make for each object - and separation costs - based on the pair of choices we make for two "related" objects.We formulate a general classification problem of this type, the metric labeling problem; we show that it contains as special cases a number of standard classification frameworks, including several arising from the theory of Markov random fields. From the perspective of combinatorial optimization, our problem can be viewed as a substantial generalization of the multi-way cut problem, and equivalent to a type of uncapacitated quadratic assignment problem.We provide the first non-trivial polynomial-time approximation algorithms for a general family of classification problems of this type. Our main result is an O(log k log log k)-approximation algorithm for the metric labeling problem, with respect to an arbitrary metric on a set of k labels, and an arbitrary weighted graph of relationships on a set of objects. For the special case in which the labels are endowed with the uniform metric - all distances are the same - our methods provide a 2-approximation.