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Author Kleinberg, Jon ♦ Tardos, va
Source ACM Digital Library
Content type Text
Publisher Association for Computing Machinery (ACM)
File Format PDF
Copyright Year ©2002
Language English
Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Subject Keyword Approximation algorithms ♦ Markov random fields ♦ Classification ♦ Metric labeling
Abstract 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 to find 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 $\textit{pair}$ 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 multiway cut problem, and equivalent to a type of uncapacitated quadratic assignment problem.We provide the first nontrivial polynomial-time approximation algorithms for a general family of classification problems of this type. Our main result is an $\textit{O}(log$ $\textit{k}$ log log $\textit{k})-approximation$ algorithm for the metric labeling problem, with respect to an arbitrary metric on a set of $\textit{k}$ 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 algorithm.
ISSN 00045411
Age Range 18 to 22 years ♦ above 22 year
Educational Use Research
Education Level UG and PG
Learning Resource Type Article
Publisher Date 2002-09-01
Publisher Place New York
e-ISSN 1557735X
Journal Journal of the ACM (JACM)
Volume Number 49
Issue Number 5
Page Count 24
Starting Page 616
Ending Page 639

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Source: ACM Digital Library