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In Honor of Boris Mirkin's 70th Birthday

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The cover of “Clusters, Orders, and Trees : Methods and Applications” - Open Library.

"Clusters, Orders, and Trees : Methods and Applications" was published by Springer in Jun 12, 2014 - New York, NY and it has 404 pages.


“Clusters, Orders, and Trees : Methods and Applications” Metadata:

  • Title: ➤  Clusters, Orders, and Trees : Methods and Applications
  • Authors:
  • Number of Pages: 404
  • Publisher: Springer
  • Publish Date:
  • Publish Location: New York, NY
  • Library of Congress Classification: QA1-939QA76.9.M35

“Clusters, Orders, and Trees : Methods and Applications” Subjects and Themes:

Edition Specifications:

  • Format: hardcover

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"Clusters, Orders, and Trees : Methods and Applications" Description:

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Intro -- Preface -- Contents -- Three and One Questions to Dr. B. Mirkin About Complexity Statistics -- 1 Three Constants in Boris Mirkin's Life -- 2 Questions About Clustering and More -- References -- Part I Classification and Cluster -- A Polynomial Algorithm for a Class of 0-1 Fractional Programming Problems Involving Composite Functions, with an Application to Additive Clustering -- 1 Introduction -- 2 Definitions and Related Works -- 2.1 Supermodularity -- 2.1.1 Definitions -- 2.1.2 Mathematical Results -- 2.1.3 Supermodular Maximization -- 2.1.4 Parametric Supermodular Maximization: The Notion of Monotone Optimal Solutions -- 2.2 The Minimum Cut Problem -- 2.2.1 Definition -- 2.2.2 The Selection Problem -- 2.2.3 The Parametric Minimum Cut Problem -- 2.3 Single-Ratio Fractional Programming -- 2.3.1 The Parametric Approach -- 3 A New Algorithm -- 3.1 Description -- 3.2 Computing the Breakpoint Vertex Set -- 3.2.1 Properties -- 3.2.2 The Eisner and Severance Algorithm -- 3.2.3 Complexity -- 3.3 Correctness of the New Algorithm -- 3.4 Polynomial Solvable Instances -- 4 Application to an Additive Clustering Problem -- 4.1 Additive Clustering -- 4.2 The Additive Clustering Problem with One Cluster -- 4.3 A Polynomial Algorithm -- 5 Discussions: Limitations and Extensions -- 5.1 Limitations -- 5.2 Minimization Problems -- 5.3 Maximization of the Product of Two Composed Functions -- 5.4 Constrained Problems -- 6 Conclusion -- References -- Experiments with a Non-convex Variance-Based Clustering Criterion -- 1 Introduction -- 2 Variance-Based Clustering: Criteria and an Optimization Heuristic -- 2.1 Notation -- 2.2 Variance-Based Clustering Criteria -- 2.2.1 Non-convexity of J3 -- 2.3 Algorithms -- 2.3.1 An Iterative Heuristic for Variance-Based Clustering Criteria -- 3 Experimental Results -- 3.1 Clustering Quality Analysis

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