[PDF] A Scale Invariant Clustering Using Minimum Volume Ellipsoids eBook

Author : Mahesh Kumar
Publisher :
Page : 9 pages
File Size : 48,44 MB
Release : 2006
Category :
ISBN :

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This paper develops theory and algorithms concerning a new metric for clustering data. The metric minimizes the total volume of clusters, where volume of a cluster is defined as the volume of the minimum volume ellipsoid (MVE) enclosing all data points in the cluster. This metric has the scale-invariant property, that is, the optimal clusters are invariant under an affine transformation of the data space. We introduce the concept of outliers in the new metric and show that the proposed method of treating outliers asymptotically recovers the data distribution when the data comes from a single multivariate Gaussian distribution. Two heuristical algorithm are presented that attempt to optimize the new metric. On a series of empirical studies on real and simulated data sets, we show that volume-based clustering out-performs the k-means algorithm.

Author : Panos M. Pardalos
Publisher : American Mathematical Soc.
Page : 252 pages
File Size : 21,34 MB
Release : 2008-04-09
Category : Computers
ISBN : 9780821870402

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Data mining aims at finding interesting, useful or profitable information in very large databases. The enormous increase in the size of available scientific and commercial databases (data avalanche) as well as the continuing and exponential growth in performance of present day computers make data mining a very active field. In many cases, the burgeoning volume of data sets has grown so large that it threatens to overwhelm rather than enlighten scientists. Therefore, traditional methods are revised and streamlined, complemented by many new methods to address challenging new problems. Mathematical Programming plays a key role in this endeavor. It helps us to formulate precise objectives (e.g., a clustering criterion or a measure of discrimination) as well as the constraints imposed on the solution (e.g., find a partition, a covering or a hierarchy in clustering). It also provides powerful mathematical tools to build highly performing exact or approximate algorithms. This book is based on lectures presented at the workshop on "Data Mining and Mathematical Programming" (October 10-13, 2006, Montreal) and will be a valuable scientific source of information to faculty, students, and researchers in optimization, data analysis and data mining, as well as people working in computer science, engineering and applied mathematics.

Author : Christian Hennig
Publisher : CRC Press
Page : 753 pages
File Size : 28,4 MB
Release : 2015-12-16
Category : Business & Economics
ISBN : 1466551895

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Handbook of Cluster Analysis provides a comprehensive and unified account of the main research developments in cluster analysis. Written by active, distinguished researchers in this area, the book helps readers make informed choices of the most suitable clustering approach for their problem and make better use of existing cluster analysis tools.The

Author : Slawomir Wierzchoń
Publisher : Springer
Page : 433 pages
File Size : 18,86 MB
Release : 2017-12-29
Category : Technology & Engineering
ISBN : 3319693085

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This book provides the reader with a basic understanding of the formal concepts of the cluster, clustering, partition, cluster analysis etc. The book explains feature-based, graph-based and spectral clustering methods and discusses their formal similarities and differences. Understanding the related formal concepts is particularly vital in the epoch of Big Data; due to the volume and characteristics of the data, it is no longer feasible to predominantly rely on merely viewing the data when facing a clustering problem. Usually clustering involves choosing similar objects and grouping them together. To facilitate the choice of similarity measures for complex and big data, various measures of object similarity, based on quantitative (like numerical measurement results) and qualitative features (like text), as well as combinations of the two, are described, as well as graph-based similarity measures for (hyper) linked objects and measures for multilayered graphs. Numerous variants demonstrating how such similarity measures can be exploited when defining clustering cost functions are also presented. In addition, the book provides an overview of approaches to handling large collections of objects in a reasonable time. In particular, it addresses grid-based methods, sampling methods, parallelization via Map-Reduce, usage of tree-structures, random projections and various heuristic approaches, especially those used for community detection.

Author : João Lita da Silva
Publisher : Springer Science & Business Media
Page : 465 pages
File Size : 17,34 MB
Release : 2013-06-14
Category : Mathematics
ISBN : 3642349048

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This volume of the Selected Papers from Portugal is a product of the Seventeenth Congress of the Portuguese Statistical Society, held at the beautiful resort seaside city of Sesimbra, Portugal, from September 30 to October 3, 2009. It covers a broad scope of theoretical, methodological as well as application-oriented articles in domains such as: Linear Models and Regression, Survival Analysis, Extreme Value Theory, Statistics of Diffusions, Markov Processes and other Statistical Applications.

Author : Dietmar Plenz
Publisher : John Wiley & Sons
Page : 734 pages
File Size : 18,55 MB
Release : 2014-04-14
Category : Computers
ISBN : 3527651020

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Neurowissenschaftler suchen nach Antworten auf die Fragen, wie wir lernen und Information speichern, welche Prozesse im Gehirn verantwortlich sind und in welchem Zeitrahmen diese ablaufen. Die Konzepte, die aus der Physik kommen und weiterentwickelt werden, können in Medizin und Soziologie, aber auch in Robotik und Bildanalyse Anwendung finden. Zentrales Thema dieses Buches sind die sogenannten kritischen Phänomene im Gehirn. Diese werden mithilfe mathematischer und physikalischer Modelle beschrieben, mit denen man auch Erdbeben, Waldbrände oder die Ausbreitung von Epidemien modellieren kann. Neuere Erkenntnisse haben ergeben, dass diese selbstgeordneten Instabilitäten auch im Nervensystem auftreten. Dieses Referenzwerk stellt theoretische und experimentelle Befunde internationaler Gehirnforschung vor zeichnet die Perspektiven dieses neuen Forschungsfeldes auf.

Author : Wolfgang A. Gaul
Publisher : Springer Science & Business Media
Page : 472 pages
File Size : 11,35 MB
Release : 2013-03-12
Category : Mathematics
ISBN : 364279999X

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The subject of this book is the incorporation and integration of mathematical and statistical techniques and information science topics into the field of classification, data analysis, and knowledge organization. Readers will find survey papers as well as research papers and reports on newest results. The papers are a combination of theoretical issues and applications in special fields: Spatial Data Analysis, Economics, Medicine, Biology, and Linguistics.

Author : R. Paul Young
Publisher : CRC Press
Page : 472 pages
File Size : 49,50 MB
Release : 1993-01-01
Category : Science
ISBN : 9054103205

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These proceedings include the latest developments in research and practice in the area of mining-induced seismicity. Three themes are explored: strong ground motion and rockburst hazard; mechanics of seismic events and stochastic methods; and monitoring of seismicity and geomechanical modelling.