Download or read book Clustering Via Minimum Volume Ellipsoids written by Tunçel, Levent and published by . This book was released on 2005 with total page 35 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Scale Invariant Clustering Using Minimum Volume Ellipsoids written by Mahesh Kumar and published by . This book was released on 2006 with total page 9 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Minimum volume Ellipsoids written by Michael J. Todd and published by SIAM. This book was released on 2016-07-11 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, the first on these topics, addresses the problem of finding an ellipsoid to represent a large set of points in high-dimensional space, which has applications in computational geometry, data representations, and optimal design in statistics. The book covers the formulation of this and related problems, theoretical properties of their optimal solutions, and algorithms for their solution. Due to the high dimensionality of these problems, first-order methods that require minimal computational work at each iteration are attractive. While algorithms of this kind have been discovered and rediscovered over the past fifty years, their computational complexities and convergence rates have only recently been investigated. The optimization problems in the book have the entries of a symmetric matrix as their variables, so the author's treatment also gives an introduction to recent work in matrix optimization. This book provides historical perspective on the problems studied by optimizers, statisticians, and geometric functional analysts; demonstrates the huge computational savings possible by exploiting simple updates for the determinant and the inverse after a rank-one update, and highlights the difficulties in algorithms when related problems are studied that do not allow simple updates at each iteration; and gives rigorous analyses of the proposed algorithms, MATLAB codes, and computational results.
Download or read book Modern Algorithms of Cluster Analysis written by Slawomir Wierzchoń and published by Springer. This book was released on 2017-12-29 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Data Mining and Mathematical Programming written by Panos M. Pardalos and published by American Mathematical Soc.. This book was released on 2008-04-09 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Advances on Data Mining Applications and Theoretical Aspects written by Petra PErner and published by Springer. This book was released on 2011-08-09 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 11th Industrial Conference on Data Mining, ICDM 2011, held in New York, USA in September 2011. The 22 revised full papers presented were carefully reviewed and selected from 100 submissions. The papers are organized in topical sections on data mining in medicine and agriculture, data mining in marketing, data mining for Industrial processes and in telecommunication, Multimedia Data Mining, theoretical aspects of data mining, Data Warehousing, WebMining and Information Mining.
Download or read book Computation of Minimum Volume Covering Ellipsoids written by Peng Sun and published by . This book was released on 2002 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: We present a practical algorithm for computing the minimum volume n-dimensional ellipsoid that must contain m given points a_1, ..., a_m in R^n. This convex constrained problem arises in a variety of applied computational settings, particularly in data mining and robust statistics. Its structure makes it particularly amenable to solution by interior-point methods, and it has been the subject of much theoretical complexity analysis. Here we focus on computation. We present a combined interior-point and active-set method for solving this problem. Our computational results demonstrate that our method solves very large problem instances (m=30,000 and n=30) to a high degree of accuracy in under 30 seconds on a personal computer.
Download or read book Handbook of Cluster Analysis written by Christian Hennig and published by CRC Press. This book was released on 2015-12-16 with total page 753 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Combinatorial and Computational Geometry written by Jacob E. Goodman and published by Cambridge University Press. This book was released on 2005-08-08 with total page 640 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 2005 book deals with interest topics in Discrete and Algorithmic aspects of Geometry.
Download or read book Statistics and Data Analysis for Microarrays Using R and Bioconductor written by Sorin Draghici and published by CRC Press. This book was released on 2016-04-19 with total page 1036 pages. Available in PDF, EPUB and Kindle. Book excerpt: Richly illustrated in color, Statistics and Data Analysis for Microarrays Using R and Bioconductor, Second Edition provides a clear and rigorous description of powerful analysis techniques and algorithms for mining and interpreting biological information. Omitting tedious details, heavy formalisms, and cryptic notations, the text takes a hands-on,
Download or read book Rock characterization written by John A. Hudson and published by Thomas Telford. This book was released on 1992 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Advances in Regression Survival Analysis Extreme Values Markov Processes and Other Statistical Applications written by João Lita da Silva and published by Springer Science & Business Media. This book was released on 2013-06-14 with total page 465 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Advances in Data Mining Applications and Theoretical Aspects written by Petra Perner and published by Springer. This book was released on 2018-07-04 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume constitutes the proceedings of the 18th Industrial Conference on Adances in Data Mining, ICDM 2018, held in New York, NY, USA, in July 2018. The 24 regular papers presented in this book were carefully reviewed and selected from 146 submissions. The topics range from theoretical aspects of data mining to applications of data mining, such as in multimedia data, in marketing, in medicine and agriculture, and in process control, industry, and society.
Download or read book Innovations in Bio Inspired Computing and Applications written by Ajith Abraham and published by Springer Nature. This book was released on 2021-04-09 with total page 573 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book highlights recent research on bio-inspired computing and its various innovative applications in information and communication technologies. It presents 51 high-quality papers from the 11th International Conference on Innovations in Bio-Inspired Computing and Applications (IBICA 2020) and 10th World Congress on Information and Communication Technologies (WICT 2020), which was held online during December 16–18, 2019. As a premier conference, IBICA–WICT brings together researchers, engineers and practitioners whose work involves bio-inspired computing, computational intelligence and their applications in information security, real-world contexts, etc. Including contributions by authors from 25 countries, the book offers a valuable reference guide for all researchers, students and practitioners in the fields of Computer Science and Engineering.
Download or read book Mathematical Reviews written by and published by . This book was released on 2008 with total page 994 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Real Estate Analysis in the Information Age written by Kimberly Winson-Geideman and published by Routledge. This book was released on 2017-11-09 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: The creation, accumulation, and use of copious amounts of data are driving rapid change across a wide variety of industries and academic disciplines. This ‘Big Data’ phenomenon is the result of recent developments in computational technology and improved data gathering techniques that have led to substantial innovation in the collection, storage, management, and analysis of data. Real Estate Analysis in the Information Age: Techniques for Big Data and Statistical Modeling focuses on the real estate discipline, guiding researchers and practitioners alike on the use of data-centric methods and analysis from applied and theoretical perspectives. In it, the authors detail the integration of Big Data into conventional real estate research and analysis. The book is process-oriented, not only describing Big Data and associated methods, but also showing the reader how to use these methods through case studies supported by supplemental online material. The running theme is the construction of efficient, transparent, and reproducible research through the systematic organization and application of data, both traditional and 'big'. The final chapters investigate legal issues, particularly related to those data that are publicly available, and conclude by speculating on the future of Big Data in real estate.
Download or read book Journal of the American Statistical Association written by and published by . This book was released on 2002 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt:
