Dimensionality reduction of clustered data sets

We present a novel probabilistic latent variable model to perform linear dimensionality reduction on data sets which contain clusters. We prove that the maximum likelihood solution of the model is an unsupervised generalisation of linear discriminant analysis. This provides a completely new approach to one of the most established and widely used classification algorithms. The performance of the model is then demonstrated on a number of real and artificial data sets

bioNMF: a versatile tool for non-negative matrix factorization in biology

BACKGROUND: In the Bioinformatics field, a great deal of interest has been given to Non-negative matrix factorization technique (NMF), due to its capability of providing new insights and relevant information about the complex latent relationships in experimental data sets. This method, and some of its variants, has been successfully applied to gene expression, sequence analysis, functional characterization of genes and text mining. Even if the interest on this technique by the bioinformatics community has been increased during the last few years, there are not many available simple standalone tools to specifically perform these types of data analysis in an integrated environment. RESULTS: In this work we propose a versatile and user-friendly tool that implements the NMF methodology in different analysis contexts to support some of the most important reported applications of this new methodology. This includes clustering and biclustering gene expression data, protein sequence analysis, text mining of biomedical literature and sample classification using gene expression. The tool, which is named bioNMF, also contains a user-friendly graphical interface to explore results in an interactive manner and facilitate in this way the exploratory data analysis process. CONCLUSION: bioNMF is a standalone versatile application which does not require any special installation or libraries. It can be used for most of the multiple applications proposed in the bioinformatics field or to support new research using this method. This tool is publicly available at

Computational, Integrative, and Comparative Methods for the Elucidation of Genetic Coexpression Networks

Gene expression microarray data can be used for the assembly of genetic coexpression network graphs. Using mRNA samples obtained from recombinant inbred Mus musculus strains, it is possible to integrate allelic variation with molecular and higher-order phenotypes. The depth of quantitative genetic analysis of microarray data can be vastly enhanced utilizing this mouse resource in combination with powerful computational algorithms, platforms, and data repositories. The resulting network graphs transect many levels of biological scale. This approach is illustrated with the extraction of cliques of putatively coregulated genes and their annotation using gene ontology analysis and cis-regulatory element discovery. The causal basis for coregulation is detected through the use of quantitative trait locus mapping

Sample phenotype clusters in high-density oligonucleotide microarray data sets are revealed using Isomap, a nonlinear algorithm

BACKGROUND: Life processes are determined by the organism's genetic profile and multiple environmental variables. However the interaction between these factors is inherently non-linear [1]. Microarray data is one representation of the nonlinear interactions among genes and genes and environmental factors. Still most microarray studies use linear methods for the interpretation of nonlinear data. In this study, we apply Isomap, a nonlinear method of dimensionality reduction, to analyze three independent large Affymetrix high-density oligonucleotide microarray data sets. RESULTS: Isomap discovered low-dimensional structures embedded in the Affymetrix microarray data sets. These structures correspond to and help to interpret biological phenomena present in the data. This analysis provides examples of temporal, spatial, and functional processes revealed by the Isomap algorithm. In a spinal cord injury data set, Isomap discovers the three main modalities of the experiment – location and severity of the injury and the time elapsed after the injury. In a multiple tissue data set, Isomap discovers a low-dimensional structure that corresponds to anatomical locations of the source tissues. This model is capable of describing low- and high-resolution differences in the same model, such as kidney-vs.-brain and differences between the nuclei of the amygdala, respectively. In a high-throughput drug screening data set, Isomap discovers the monocytic and granulocytic differentiation of myeloid cells and maps several chemical compounds on the two-dimensional model. CONCLUSION: Visualization of Isomap models provides useful tools for exploratory analysis of microarray data sets. In most instances, Isomap models explain more of the variance present in the microarray data than PCA or MDS. Finally, Isomap is a promising new algorithm for class discovery and class prediction in high-density oligonucleotide data sets

A mixture model with a reference-based automatic selection of components for disease classification from protein and/or gene expression levels

Background Bioinformatics data analysis is often using linear mixture model representing samples as additive mixture of components. Properly constrained blind matrix factorization methods extract those components using mixture samples only. However, automatic selection of extracted components to be retained for classification analysis remains an open issue. Results The method proposed here is applied to well-studied protein and genomic datasets of ovarian, prostate and colon cancers to extract components for disease prediction. It achieves average sensitivities of: 96.2 (sd=2.7%), 97.6% (sd=2.8%) and 90.8% (sd=5.5%) and average specificities of: 93.6% (sd=4.1%), 99% (sd=2.2%) and 79.4% (sd=9.8%) in 100 independent two-fold cross-validations. Conclusions We propose an additive mixture model of a sample for feature extraction using, in principle, sparseness constrained factorization on a sample-by-sample basis. As opposed to that, existing methods factorize complete dataset simultaneously. The sample model is composed of a reference sample representing control and/or case (disease) groups and a test sample. Each sample is decomposed into two or more components that are selected automatically (without using label information) as control specific, case specific and not differentially expressed (neutral). The number of components is determined by cross-validation. Automatic assignment of features (m/z ratios or genes) to particular component is based on thresholds estimated from each sample directly. Due to the locality of decomposition, the strength of the expression of each feature across the samples can vary. Yet, they will still be allocated to the related disease and/or control specific component. Since label information is not used in the selection process, case and control specific components can be used for classification. That is not the case with standard factorization methods. Moreover, the component selected by proposed method as disease specific can be interpreted as a sub-mode and retained for further analysis to identify potential biomarkers. As opposed to standard matrix factorization methods this can be achieved on a sample (experiment)-by-sample basis. Postulating one or more components with indifferent features enables their removal from disease and control specific components on a sample-by-sample basis. This yields selected components with reduced complexity and generally, it increases prediction accuracy

Comparative Analysis of Thresholding Algorithms for Microarray-derived Gene Correlation Matrices

The thresholding problem is important in today’s data-rich research scenario. A threshold is a well-defined point in the data distribution beyond which the data is highly likely to have scientific meaning. The selection of threshold is crucial since it heavily influences any downstream analysis and inferences made there from. A legitimate threshold is one that is not arbitrary but scientifically well grounded, data-dependent and best segregates the information-rich and noisy sections of data. Although the thresholding problem is not restricted to any particular field of study, little research has been done. This study investigates the problem in context of network-based analysis of transcriptomic data. Six conceptually diverse algorithms – based on number of maximal cliques, correlations of control spots with genes, top 1% of correlations, spectral graph clustering, Bonferroni correction of p-values and statistical power – are used to threshold the gene correlation matrices of three time-series microarray datasets and tested for stability and validity. Stability or reliability of the first four algorithms towards thresholding is tested upon block bootstrapping of arrays in the datasets and comparing the estimated thresholds against the bootstrap threshold distributions. Validity of thresholding algorithms is tested by comparison of the estimated thresholds against threshold based on biological information. Thresholds based on the modular basis of gene networks are concluded to perform better both in terms of stability as well as validity. Future challenges to research the problem have been identified. Although the study utilizes transcriptomic data for analysis, we assert its applicability to thresholding across various fields

Report of the Regional Ecosystem Study Group of the North Sea (REGNS) [15-19 May 2006 ICES Headquarters, Copenhagen]

Contributors: Hein Rune Skjolda