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Proximity Graphs for Nearest Neighbor Decision Rules: Recent Progress
 Progress”, Proceedings of the 34 th Symposium on the INTERFACE
, 2002
"... In the typical nonparametric approach to pattern classification, random data (the training set of patterns) are collected and used to design a decision rule (classifier). One of the most well known such rules is the knearestneighbor decision rule (also known as instancebased learning, and lazy le ..."
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In the typical nonparametric approach to pattern classification, random data (the training set of patterns) are collected and used to design a decision rule (classifier). One of the most well known such rules is the knearestneighbor decision rule (also known as instancebased learning, and lazy learning) in which an unknown pattern is classified into the majority class among its k nearest neighbors in the training set. Several questions related to this rule have received considerable attention over the years. Such questions include the following. How can the storage of the training set be reduced without degrading the performance of the decision rule? How should the reduced training set be selected to represent the different classes? How large should k be? How should the value of k be chosen? Should all k neighbors be equally weighted when used to decide the class of an unknown pattern? If not, how should the weights be chosen? Should all the features (attributes) we weighted equally and if not how should the feature weights be chosen? What distance metric should be used? How can the rule be made robust to overlapping classes or noise present in the training data? How can the rule be made invariant to scaling of the measurements? Geometric proximity graphs such as Voronoi diagrams and their many relatives provide elegant solutions to most of these problems. After a brief and nonexhaustive review of some of the classical canonical approaches to solving these problems, the methods that use proximity graphs are discussed, some new observations are made, and avenues for further research are proposed.
On the History of Combinatorial Optimization (till 1960)
"... Introduction As a coherent mathematical discipline, combinatorial optimization is relatively young. When studying the history of the field, one observes a number of independent lines of research, separately considering problems like optimum assignment, shortest spanning tree, transportation, and the ..."
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Introduction As a coherent mathematical discipline, combinatorial optimization is relatively young. When studying the history of the field, one observes a number of independent lines of research, separately considering problems like optimum assignment, shortest spanning tree, transportation, and the traveling salesman problem. Only in the 1950's, when the unifying tool of linear and integer programming became available and the area of operations research got intensive attention, these problems were put into one framework, and relations between them were laid. Indeed, linear programming forms the hinge in the history of combinatorial optimization. Its initial conception by Kantorovich and Koopmans was motivated by combinatorial applications, in particular in transportation and transshipment. After the formulation of linear programming as generic problem, and the development in 1947 by Dantzig of the simplex method as a tool, one has tried to attack about all combinatorial opti
Estimating And Depicting The Structure Of A Distribution Of Random Functions
, 2000
"... . We suggest a nonparametric approach to making inference about the structure of distributions in a potentially infinitedimensional space, for example a function space, and displaying information about that structure. Our methodology is based on nonparametric density estimation, and draws inference ..."
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. We suggest a nonparametric approach to making inference about the structure of distributions in a potentially infinitedimensional space, for example a function space, and displaying information about that structure. Our methodology is based on nonparametric density estimation, and draws inference about the slope of the density. The latter step is implemented in a purely iterative way, using only elementary operations of addition and multiplication, and does not require any differentiation or dimensionreduction. Nevertheless it leads in a very simple and reliable manner to "curves" of steepest ascent up the "surface" defined by an estimate of the density of a potentially infinitedimensional distribution. The projections of these curves into the sample space are always onedimensional, or more properly oneparameter, structures, and so can be displayed visually even when the sample space is a class of functions. Also, the modes to which the sample space projections lead are themselv...
Evidence for a Relationship Between Algorithmic Scheme And Shape Of Inferred Trees
"... Agglomeration and addition are the two main algorithmic schemes for constructing a tree distance from a dissimilarity matrix. The former scheme iteratively agglomerates pairs of leaves to form larger and larger clusters, while the latter proceeds by stepwise addition of objects to a growing tree. A ..."
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Agglomeration and addition are the two main algorithmic schemes for constructing a tree distance from a dissimilarity matrix. The former scheme iteratively agglomerates pairs of leaves to form larger and larger clusters, while the latter proceeds by stepwise addition of objects to a growing tree. A third approach involves improving the global fitness of an initial tree by exchanging subtrees. This article suggests that the shape of inferred trees partly depends on the chosen algorithmic scheme: agglomeration tends to produce compact and bushy tree shapes, while addition and exchange have a preference for sparse and chainlike trees. This phenomenon is explained by the difference between the a priori probability distributions induced by each scheme. An illustration is provided with the Mitochondrial Eve data set (Vigilant et al. 1991), and the practical impacts are discussed.
On the complexity of minimum sumofsquares clustering. Cahiers du GERAD
"... Les textes publiés dans la série des rapports de recherche HEC n’engagent que la responsabilité de leurs auteurs. La publication de ces rapports de recherche bénéficie d’une subvention du Fonds québécois de la recherche sur la nature et les technologies. A BranchandCut SDPBased Algorithm for ..."
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Les textes publiés dans la série des rapports de recherche HEC n’engagent que la responsabilité de leurs auteurs. La publication de ces rapports de recherche bénéficie d’une subvention du Fonds québécois de la recherche sur la nature et les technologies. A BranchandCut SDPBased Algorithm for
SAS/STAT ® 12.3 User’s Guide The CLUSTER Procedure
, 1924
"... For a Web download or ebook: Your use of this publication shall be governed by the terms established by the vendor at the time you acquire this publication. The scanning, uploading, and distribution of this book via the Internet or any other means without the permission of the publisher is illegal ..."
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For a Web download or ebook: Your use of this publication shall be governed by the terms established by the vendor at the time you acquire this publication. The scanning, uploading, and distribution of this book via the Internet or any other means without the permission of the publisher is illegal and punishable by law. Please purchase only authorized electronic editions and do not participate in or encourage electronic piracy of copyrighted materials. Your support of others ’ rights is appreciated. U.S. Government Restricted Rights Notice: Use, duplication, or disclosure of this software and related documentation by the U.S.
SAS/STAT ® 9.2 User’s Guide The CLUSTER Procedure (Book Excerpt)
, 1247
"... For a Web download or ebook: Your use of this publication shall be governed by the terms established by the vendor at the time you acquire this publication. U.S. Government Restricted Rights Notice: Use, duplication, or disclosure of this software and related documentation by the U.S. government is ..."
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For a Web download or ebook: Your use of this publication shall be governed by the terms established by the vendor at the time you acquire this publication. U.S. Government Restricted Rights Notice: Use, duplication, or disclosure of this software and related documentation by the U.S. government is subject to the Agreement with SAS Institute and the restrictions set forth in FAR 52.22719, Commercial Computer SoftwareRestricted Rights (June 1987).
SAS/STAT ® 9.3 User’s Guide The CLUSTER Procedure (Chapter)
, 1838
"... For a Web download or ebook: Your use of this publication shall be governed by the terms established by the vendor at the time you acquire this publication. The scanning, uploading, and distribution of this book via the Internet or any other means without the permission of the publisher is illegal ..."
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For a Web download or ebook: Your use of this publication shall be governed by the terms established by the vendor at the time you acquire this publication. The scanning, uploading, and distribution of this book via the Internet or any other means without the permission of the publisher is illegal and punishable by law. Please purchase only authorized electronic editions and do not participate in or encourage electronic piracy of copyrighted materials. Your support of others ’ rights is appreciated. U.S. Government Restricted Rights Notice: Use, duplication, or disclosure of this software and related documentation by the