Algorithms for clustering data

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Finding Groups in Data: An Introduction to Chster Analysis

Statistics for Spatial Data.

Population stratification has long been recognized as a confounding factor in genetic association studies. Estimated ancestries, derived from multi-locus genotype data, can be used to perform a statistical correction for population stratification. One popular technique for estimation of ancestry is the model-based approach embodied by the widely applied program structure. Another approach, implemented in the program EIGENSTRAT, relies on Principal Component Analysis rather than model-based estimation and does not directly deliver admixture fractions. EIGENSTRAT has gained in popularity in part owing to its remarkable speed in comparison to structure. We present a new algorithm and a program, ADMIXTURE, for model-based estimation of ancestry in unrelated individuals. ADMIXTURE adopts the likelihood model embedded in structure. However, ADMIXTURE runs considerably faster, solving problems in minutes that take structure hours. In many of our experiments, we have found that ADMIXTURE is almost as fast as EIGENSTRAT. The runtime improvements of ADMIXTURE rely on a fast block relaxation scheme using sequential quadratic programming for block updates, coupled with a novel quasi-Newton acceleration of convergence. Our algorithm also runs faster and with greater accuracy than the implementation of an Expectation-Maximization (EM) algorithm incorporated in the program FRAPPE. Our simulations show that ADMIXTURE's maximum likelihood estimates of the underlying admixture coefficients and ancestral allele frequencies are as accurate as structure's Bayesian estimates. On real-world data sets, ADMIXTURE's estimates are directly comparable to those from structure and EIGENSTRAT. Taken together, our results show that ADMIXTURE's computational speed opens up the possibility of using a much larger set of markers in model-based ancestry estimation and that its estimates are suitable for use in correcting for population stratification in association studies.

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Fast model-based estimation of ancestry in unrelated individuals

E. Diday: Symbolic Data Analysis and the SODAS Project: Purpose, History, Perspective.- H.H. Bock: The Classical Data Situation.- H.H. Bock: Symbolic Data.- H.H. Bock, E. Diday: Symbolic Objects.- V. Stephan, G. Hebrail, Y. Lechevallier: Generation of Symbolic Objects from Relational Databases.- P. Bertrand, F. Goupil: Descriptive Statistics for Symbolic Data.- M. Noirhomme-Fraiture, M. Rouard: Visualizing and Editing Symbolic Objects.- Similarity and Dissimilarity: F. Esposito, D. Malerba, V. Tamma, H.H. Bock: Classical Resemblance Measures.- H.H. Bock: Dissimilarity Measures for Probability Distributions.- F. Esposito, D. Malerba, V. Tamma: Dissimilarity Measures for Symbolic Objects.- F. Esposito, D. Malerba, F. Lisi: Matching Symbolic Objects.- Symbolic Factor Analysis: H.H.Bock: Classical Principal Component Analysis.- A. Chouakria, P. Cazes, E. Diday: Symbolic Principal Component Analysis.- N.C. Lauro, F. Palumbo, R. Verde: Factorial Discriminant Analysis on Symbolic Objects.- Discrimination: Assigning Symbolic Objects to Classes: J. Rasson, S. Lissoir: Classical Methods of Discrimination.- J. Rasson, S. Lissoir: Symbolic Kernel Discriminant Analysis.- E. Perinel, Y. Lechevalier: Symbolic Discrimination Rules.- M. Bravo Llatas, J. Garcia-Santesmases: Segmentation Trees for Stratified Data.- Clustering Methods for Symbolic Objects: M. Chavent, H.H. Bock: Clustering Problem, Clustering Methods for Classical Data.- M. Chavent: Criterion-Based Divisive Clustering for Symbolic Data.- P. Brito: Hierarchical and Pyramidal Clustering with Complete Symbolic Objects.- G. Polaillon: Pyramidal Classification for Interval Data Using Galois Lattice Reduction.- M. Gettler-Summa, C. Pardoux: Symbolic Approaches for Three-way Data.-Illustrative Benchmark Analysis: R. Bisdorff: Introduction.- R. Bisdorff: Professional Careers of Retired Working Persons.- A. Iztueta, P. Calvo: Labour Force Survey.- F. Goupil, M. Touati, E. Diday, R. Moult: Census Data from the Office for National Statistics.- A. Morineau: The SODAS Software Package.

Analysis of Symbolic Data: Exploratory Methods for Extracting Statistical Information from Complex Data

Analysis of Symbolic Data

Classification and Related Methods of Data Analysis

In this paper we present a structured overview of methods for two-mode clustering, that is, methods that provide a simultaneous clustering of the rows and columns of a rectangular data matrix. Key structuring principles include the nature of row, column and data clusters and the type of model structure or associated loss function. We illustrate with analyses of symptom data on archetypal psychiatric patients.

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Hans-Hermann Bock

Papers

Analysis of Symbolic Data: Exploratory Methods for Extracting Statistical Information from Complex Data

Analysis of Symbolic Data

Classification and Related Methods of Data Analysis

Two-mode clustering methods: a structured overview.

Probabilistic models in cluster analysis