In the context of cancer diagnosis and treatment, we consider the problem of constructing an accurate prediction rule on the basis of a relatively small number of tumor tissue samples of known type containing the expression data on very many (possibly thousands) genes. Recently, results have been presented in the literature suggesting that it is possible to construct a prediction rule from only a few genes such that it has a negligible prediction error rate. However, in these results the test error or the leave-one-out cross-validated error is calculated without allowance for the selection bias. There is no allowance because the rule is either tested on tissue samples that were used in the first instance to select the genes being used in the rule or because the cross-validation of the rule is not external to the selection process; that is, gene selection is not performed in training the rule at each stage of the cross-validation process. We describe how in practice the selection bias can be assessed and corrected for by either performing a cross-validation or applying the bootstrap external to the selection process. We recommend using 10-fold rather than leave-one-out cross-validation, and concerning the bootstrap, we suggest using the so-called .632+ bootstrap error estimate designed to handle overfitted prediction rules. Using two published data sets, we demonstrate that when correction is made for the selection bias, the cross-validated error is no longer zero for a subset of only a few genes.

/pdf/selection-bias-in-gene-extraction-on-the-basis-of-microarray-3melvwlrf0.pdf

Selection bias in gene extraction on the basis of microarray gene-expression data.

DNA microarray technology has now made it possible to simultaneously monitor the expression levels of thousands of genes during important biological processes and across collections of related samples. Elucidating the patterns hidden in gene expression data offers a tremendous opportunity for an enhanced understanding of functional genomics. However, the large number of genes and the complexity of biological networks greatly increases the challenges of comprehending and interpreting the resulting mass of data, which often consists of millions of measurements. A first step toward addressing this challenge is the use of clustering techniques, which is essential in the data mining process to reveal natural structures and identify interesting patterns in the underlying data. Cluster analysis seeks to partition a given data set into groups based on specified features so that the data points within a group are more similar to each other than the points in different groups. A very rich literature on cluster analysis has developed over the past three decades. Many conventional clustering algorithms have been adapted or directly applied to gene expression data, and also new algorithms have recently been proposed specifically aiming at gene expression data. These clustering algorithms have been proven useful for identifying biologically relevant groups of genes and samples. In this paper, we first briefly introduce the concepts of microarray technology and discuss the basic elements of clustering on gene expression data. In particular, we divide cluster analysis for gene expression data into three categories. Then, we present specific challenges pertinent to each clustering category and introduce several representative approaches. We also discuss the problem of cluster validation in three aspects and review various methods to assess the quality and reliability of clustering results. Finally, we conclude this paper and suggest the promising trends in this field.

/pdf/cluster-analysis-for-gene-expression-data-a-survey-n507v99tm6.pdf

Cluster analysis for gene expression data: a survey

Data analysis is used as a common method in modern science research, which is across communication science, computer science and biology science. Clustering, as the basic composition of data analysis, plays a significant role. On one hand, many tools for cluster analysis have been created, along with the information increase and subject intersection. On the other hand, each clustering algorithm has its own strengths and weaknesses, due to the complexity of information. In this review paper, we begin at the definition of clustering, take the basic elements involved in the clustering process, such as the distance or similarity measurement and evaluation indicators, into consideration, and analyze the clustering algorithms from two perspectives, the traditional ones and the modern ones. All the discussed clustering algorithms will be compared in detail and comprehensively shown in Appendix Table 22.

/pdf/a-comprehensive-survey-of-clustering-algorithms-2webn4t8if.pdf

A Comprehensive Survey of Clustering Algorithms

Iterative model-building, structure refinement, and density modification with the PHENIX AutoBuild Wizard Thomas C. Terwilliger a* , Ralf W. Grosse-Kunstleve b , Pavel V. Afonine b , Nigel W. Moriarty b , Peter Zwart b , Li-Wei Hung a , Randy J. Read c , Paul D. Adams b* a b Los Alamos National Laboratory, Mailstop M888, Los Alamos, NM 87545, USA Lawrence Berkeley National Laboratory, One Cyclotron Road, Bldg 64R0121, Berkeley, CA 94720, USA. c Department of Haematology, University of Cambridge, Cambridge CB2 0XY, UK. * Email: terwill@lanl.gov or PDAdams@lbl.gov Running title: The PHENIX AutoBuild Wizard Abstract The PHENIX AutoBuild Wizard is a highly automated tool for iterative model- building, structure refinement and density modification using RESOLVE or TEXTAL model- building, RESOLVE statistical density modification, and phenix.refine structure refinement. Recent advances in the AutoBuild Wizard and phenix.refine include automated detection and application of NCS from models as they are built, extensive model completion algorithms, and automated solvent molecule picking. Model completion algorithms in the AutoBuild Wizard include loop-building, crossovers between chains in different models of a structure, and side-chain optimization. The AutoBuild Wizard has been applied to a set of 48 structures at resolutions ranging from 1.1 A to 3.2 A, resulting in a mean R-factor of 0.24 and a mean free R factor of 0.29. The R-factor of the final model is dependent on the quality of the starting electron density, and relatively independent of resolution. Keywords: Model building; model completion; macromolecular models; Protein Data Bank; structure refinement; PHENIX Introduction Iterative model-building and refinement is a powerful approach to obtaining a complete and accurate macromolecular model. The approach consists of cycles of building an atomic model based on an electron density map for a macromolecular structure, refining the structure, using the refined structure as a basis for improving the map, and building a new model. This type of approach has been carried out in a semi-automated fashion for many years, with manual model-building iterating with automated refinement (Jensen, 1997). More recently, with the development first of ARP/wARP (Perrakis et al., 1999), and later other procedures including RESOLVE iterative model-building and refinement (Terwilliger,

Iterative model-building, structure refinement, and density modification with the PHENIX AutoBuild Wizard

Microarray technology is increasingly being applied in biological and medical research to address a wide range of problems, such as the classification of tumors. An important statistical problem associated with tumor classification is the identification of new tumor classes using gene-expression profiles. Two essential aspects of this clustering problem are: to estimate the number of clusters, if any, in a dataset; and to allocate tumor samples to these clusters, and assess the confidence of cluster assignments for individual samples. Here we address the first of these problems. We have developed a new prediction-based resampling method, Clest, to estimate the number of clusters in a dataset. The performance of the new and existing methods were compared using simulated data and gene-expression data from four recently published cancer microarray studies. Clest was generally found to be more accurate and robust than the six existing methods considered in the study. Focusing on prediction accuracy in conjunction with resampling produces accurate and robust estimates of the number of clusters.

/pdf/a-prediction-based-resampling-method-for-estimating-the-19rjx1st6k.pdf

A prediction-based resampling method for estimating the number of clusters in a dataset

Motivation: This paper introduces the software EMMIX-GENE that has been developed for the specific purpose of a model-based approach to the clustering of microarray expression data, in particular, of tissue samples on a very large number of genes. The latter is a nonstandard problem in parametric cluster analysis because the dimension of the feature space (the number of genes) is typically much greater than the number of tissues. A feasible approach is provided by first selecting a subset of the genes relevant for the clustering of the tissue samples by fitting mixtures of t distributions to rank the genes in order of increasing size of the likelihood ratio statistic for the test of one versus two components in the mixture model. The imposition of a threshold on the likelihood ratio statistic used in conjunction with a threshold on the size of a cluster allows the selection of a relevant set of genes. However, even this reduced set of genes will usually be too large for a normal mixture model to be fitted directly to the tissues, and so the use of mixtures of factor analyzers is exploited to reduce effectively the dimension of the feature space of genes. Results: The usefulness of the EMMIX-GENE approach for the clustering of tissue samples is demonstrated on two well-known data sets on colon and leukaemia tissues. For both data sets, relevant subsets of the genes are able to be selected that reveal interesting clusterings of the tissues that are either consistent with the external classification of the tissues or with background and biological knowledge of these sets.

/pdf/a-mixture-model-based-approach-to-the-clustering-of-1y6qqbebk5.pdf

A mixture model-based approach to the clustering of microarray expression data

https://people.smp.uq.edu.au/GeoffMcLachlan/mpb_csda03.pdf

Modelling high-dimensional data by mixtures of factor analyzers

Motivation: An important problem in microarray experiments is the detection of genes that are differentially expressed in a given number of classes. We provide a straightforward and easily implemented method for estimating the posterior probability that an individual gene is null. The problem can be expressed in a two-component mixture framework, using an empirical Bayes approach. Current methods of implementing this approach either have some limitations due to the minimal assumptions made or with more specific assumptions are computationally intensive.

Results: By converting to a z-score the value of the test statistic used to test the significance of each gene, we propose a simple two-component normal mixture that models adequately the distribution of this score. The usefulness of our approach is demonstrated on three real datasets.

Availability: An R-program for implementing the approach is freely available at http://www.maths.uq.edu.au/~gjm/

Contact: gjm@maths.uq.edu.au

Supplementary information: http://www.maths.uq.edu.au/~gjm/bioinf061supp_data.pdf

A simple implementation of a normal mixture approach to differential gene expression in multiclass microarrays

This paper proposes a peer-to-peer (P2P) energy trading scheme that can help a centralized power system to reduce the total electricity demand of its customers at the peak hour. To do so, a cooperative Stackelberg game is formulated, in which the centralized power system acts as the leader that needs to decide on a price at the peak demand period to incentivize prosumers to not seek any energy from it. The prosumers, on the other hand, act as followers and respond to the leader’s decision by forming suitable coalitions with neighboring prosumers in order to participate in P2P energy trading to meet their energy demand. The properties of the proposed Stackelberg game are studied. It is shown that the game has a unique and stable Stackelberg equilibrium, as a result of the stability of prosumers’ coalitions. At the equilibrium, the leader chooses its strategy using a derived closed-form expression, while the prosumers choose their equilibrium coalition structure. An algorithm is proposed that enables the centralized power system and the prosumers to reach the equilibrium solution. Numerical case studies demonstrate the beneficial properties of the proposed scheme.

Richard Bean

Papers

A mixture model-based approach to the clustering of microarray expression data

Modelling high-dimensional data by mixtures of factor analyzers

A simple implementation of a normal mixture approach to differential gene expression in multiclass microarrays

Grid Influenced Peer-to-Peer Energy Trading

Extension of the mixture of factor analyzers model to incorporate the multivariate t-distribution