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clustering algorithms and other exploratory methods for microarray data analysis

METHODS OF INFORMATION IN MEDICINE 2005年第3期44卷 444-448页

作者： Rahnenführer, J Max Planck Inst Informat D-66123 Saarbrucken Germany

Objectives. We introduce methods for the exploratory analysis of microarray data, especially focusing on cluster algorithms. Benefits and problems are discussed. Methods. We describe application and suitability of unsupervised learning methods for the classification of gene expression data. cluster algorithms are treated in more detail, including assessment of cluster quality. Results: When dealing with microarray data, most cluster algorithms must be applied with caution. As long as the structure of the true generating models of such data is not fully understood, the use of simple algorithms seems to be more appropriate than the application of complex block-box algorithms. New methods explicitly targeted to the analysis of microarray data are increasingly being developed in order to increase the amount of useful information extracted from the experiments. Conclusions: Unsupervised methods can be a helpful tool for the analysis of microarray data, but a critical choice of the algorithm and a careful interpretation of the results are required in order to avoid false conclusions.

关键词： unsupervised learning cluster algorithms biclustering assessment of cluster quality

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From spin ladders to the 2D O(3) model at non-zero density

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COMPUTER PHYSICS COMMUNICATIONS 2002年第1-2期147卷 388-393页

作者： Chandrasekharan, S Scarlet, B Wiese, UJ MIT Ctr Theoret Phys Nucl Sci Lab Cambridge MA 02139 USA MIT Dept Phys Cambridge MA 02139 USA Duke Univ Dept Phys Durham NC 27708 USA Univ Bern Inst Theoret Phys CH-3012 Bern Switzerland

The numerical simulation of various field theories at non-zero chemical potential suffers from severe complex action problems. In particular, QCD at non-zero quark density can presently not be simulated for that reason. A similar complex action problem arises in the 2D O(3) model-a toy model for QCD. Here we construct the 2D 0(3) model at non-zero density via dimensional reduction of an antiferromagnetic quantum spin ladder in a magnetic field. The complex action problem of the 2D 0(3) model manifests itself as a sign problem of the ladder system. This sign problem is solved completely with a meron cluster algorithm. (C) 2002 Elsevier Science B.V. All rights reserved.

关键词： field theory with chemical potential sign problem cluster algorithms

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From spin ladders to the 2D O(3) model at non-zero density

From spin ladders to the 2D O(3) model at non-zero density

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Europhysics Conference on Computational Physics (CCP 2001)

关键词： field theory with chemical potential sign problem cluster algorithms

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cluster analysis: a further approach based on density estimation

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COMPUTATIONAL STATISTICS & DATA ANALYSIS 2001年第4期36卷 441-459页

作者： Cuevas, A Febrero, M Fraiman, R Univ Autonoma Madrid Dept Math E-28049 Madrid Spain Univ Santiago de Compostela Dept Stat Santiago De Compostela 15771 Spain Univ San Andres Dept Math Buenos Aires DF Argentina

A cluster methodology, motivated via density estimation, is proposed. It is based on the idea of estimating the population clusters, which, following Hartigan (1975), are defined as the connected parts of the "substantial" support of the underlying density. The empirical clusters are defined by analogy in terms of the substantial support of a convolution (kemel-type) density estimator. The sample observations are grouped into data clusters, according to the empirical cluster they belong. An algorithm to implement the method, based on resampling ideas, is proposed. It allows either to automatically choose the number of clusters or to give this number as an input. Some theoretical and practical aspects are briefly discussed and a simulation study is given. The results show a good performance of our method, in terms of efficiency and robustness, when compared with two classical cluster algorithms: k-means and single linkage. Finally, a real-data example is discussed. (C) 2001 Elsevier Science B.V. All rights reserved.

关键词： cluster algorithms density estimates smoothed bootstrap level set estimation

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Graphical representations and cluster algorithms II

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PHYSICA A 1998年第3-4期254卷 477-516页

作者： Chayes, L Machta, J Univ Calif Los Angeles Dept Math Los Angeles CA 90095 USA Univ Massachusetts Dept Phys & Astron Amherst MA 01003 USA

We continue the study, initiated in Part I, of graphical representations and cluster algorithms for various models in (or related to) statistical mechanics. For certain models, e.g. the Blume-Emery-Griffths model and various generalizations, we develop Fortuin Kasteleyn-type representations which lead immediately to Swendsen Wang-type algorithms. For other models, e.g. the random cluster model, that are defined by a graphical representation, we develop cluster algorithms without reference to an underlying spin system. In all cases, phase transitions are related to percolation (or incipient percolation) in the graphical representation which, via the IC algorithm, allows for the rapid simulation of these systems at the transition point. Pertinent examples include the (continuum) Widom-Rowlinson model, the restricted 1-step solid-on-solid model and the XY model. (C) 1998 Published by Elsevier Science B.V. All rights reserved.

关键词： cluster algorithms random cluster models

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Nonlocal Monte Carlo algorithms for statistical physics applications

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MATHEMATICS AND COMPUTERS IN SIMULATION 1998年第2-5期47卷 329-346页

作者： Janke, W Johannes Gutenberg Univ Mainz Inst Phys D-55099 Mainz Germany

After a brief general overview of Monte Carlo computer simulations in statistical physics, special emphasis is placed on applications to phase transitions and critical phenomena. Here, standard simulations employing local update algorithms are severely hampered by the problem of critical slowing down, that is by strong correlations between successively generated data It is shown that this problem can be greatly reduced by using nonlocal update techniques such as cluster and multigrid algorithms. The general ideas are illustrated for simple lattice spin models and Euclidean path integrals. (C) 1998 IMACS/ Elsevier Science B.V.

关键词： Monte Carlo simulations importance sampling cluster algorithms multigrid techniques phase transitions critical phenomena

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Damage spreading in a 2D Ising model with Swendsen-Wang dynamics

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JOURNAL OF STATISTICAL PHYSICS 1998年第3-4期91卷 807-814页

作者： Hinrichsen, H Domany, E Stauffer, D Weizmann Inst Sci Dept Phys Complex Syst IL-76100 Rehovot Israel Max Planck Inst Phys Komplexer Syst D-01187 Dresden Germany Tel Aviv Univ Sch Phys & Astron Raymond & Beverly Sackler Fac Exact Sci IL-69978 Tel Aviv Israel Univ Cologne Inst Theoret Phys D-50923 Cologne Germany

Damage spreading for Ising cluster dynamics :is investigated numerically by using random numbers in a way that conforms with the notion of submitting the two evolving replicas to the same thermal noise. Two damage spreading transitions are found;damage does not spread either at low or high temperatures. We determine some critical exponents at the high-temperature transition point, which seem consistent with directed percolation.

关键词： damage spreading cluster algorithms

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PARALLEL WOLFF cluster algorithms

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INTERNATIONAL JOURNAL OF MODERN PHYSICS C 1995年第2期6卷 197-210页

作者： BAE, S KO, SH CODDINGTON, PD SYRACUSE UNIV CTR NE PARALLEL ARCHITECTURE SYRACUSE NY 13244 USA

The Wolff single-cluster algorithm is the most efficient method known for Monte Carlo simulation of many spin models. Due to the irregular size, shape and position of the Wolff clusters, this method does not easily lend itself to efficient parallel implementation, so that simulations using this method have thus far been confined to workstations and vector machines. Here we present two parallel implementations of this algorithm, and show that one gives fairly good performance on a MIMD parallel computer.

关键词： MONTE CARLO SPIN MODELS cluster algorithms WOLFF algorithms PARALLEL algorithms

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The computational complexity of generating random fractals

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JOURNAL OF STATISTICAL PHYSICS 1996年第5-6期82卷 1299-1326页

作者： Machta, J Greenlaw, R UNIV NEW HAMPSHIRE DEPT COMP SCIDURHAMNH 03824

We examine a number of models that generate random fractals. The models are studied using the tools of computational complexity theory from the perspective of parallel computation. Diffusion-limited aggregation and several widely used algorithms for equilibrating the Ising model are shown to be highly sequential;it is unlikely they can be simulated efficiently in parallel. This is in contrast to Mandelbrot percolation, which can be simulated in constant parallel time. Our research helps shed light on the intrinsic complexity of these models relative to each other and to different growth processes that have been recently studied using complexity theory. In addition, the results may serve as a guide to simulation physics.

关键词： cluster algorithms computational complexity diffusion-limited aggregation Ising model Metropolis algorithm P-completeness

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cluster concept dynamics leading to creative ideas without critical slowing down

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INTERNATIONAL JOURNAL OF MODERN PHYSICS C-PHYSICS AND COMPUTERS 1996年第5期7卷 655-673页

作者： Goldenberg, Y Solomon, S Mazursky, D HEBREW UNIV JERUSALEM SCH BUSINESS ADMIL-91904 JERUSALEMISRAEL

We present algorithmic procedures for generating systematically ideas and solutions to problems which are perceived as creative. Our method consists of identifying and characterizing the most creative ideas among a vast pool. We show that they fall within a few large classes (archetypes) which share the same conceptual structure (Macros). We prescribe well defined abstract algorithms which can act deterministically on arbitrary given objects. Each algorithm generates ideas with the same conceptual structure characteristic to one of the Macros. The resulting new ideas turn out to be perceived as highly creative. We support our claims by experiments in which senior advertising professionals graded advertisement ideas produced by our method according to their creativity. The marks (grade 4.6 +/- 0.2 on a 1-7 scale) obtained by laymen applying our algorithms (after being instructed for only two hours) were significantly better than the marks obtained by advertising professionals using standard methods (grade 3.6 +/- 0.2)). The method, which is currently taught in USA, Europe, and Israel and used by advertising agencies in Britain and Israel has received formal international recognition.

关键词： creativity advertising complex systems reductionism cluster algorithms artificial intelligence accelerated dynamics connectionist modeling

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