A survey of kernel and spectral methods for clustering

Clustering algorithms are a useful tool to explore data structures and have been employed in many disciplines. The focus of this paper is the partitioning clustering problem with a special interest in two recent approaches: kernel and spectral methods. The aim of this paper is to present a survey of kernel and spectral clustering methods, two approaches able to produce nonlinear separating hypersurfaces between clusters. The presented kernel clustering methods are the kernel version of many classical clustering algorithms, e.g., K-means, SOM and neural gas. Spectral clustering arise from concepts in spectral graph theory and the clustering problem is configured as a graph cut problem where an appropriate objective function has to be optimized. An explicit proof of the fact that these two paradigms have the same objective is reported since it has been proven that these two seemingly different approaches have the same mathematical foundation. Besides, fuzzy kernel clustering methods are presented as extensions of kernel K-means clustering algorithm. (C) 2007 Pattem Recognition Society. Published by Elsevier Ltd. All rights reserved

Expression cartography of human tissues using self organizing maps

Background: The availability of parallel, high-throughput microarray and sequencing experiments poses a challenge how to best arrange and to analyze the obtained heap of multidimensional data in a concerted way. Self organizing maps (SOM), a machine learning method, enables the parallel sample- and gene-centered view on the data combined with strong visualization and second-level analysis capabilities. The paper addresses aspects of the method with practical impact in the context of expression analysis of complex data sets.
Results: The method was applied to generate a SOM characterizing the whole genome expression profiles of 67 healthy human tissues selected from ten tissue categories (adipose, endocrine, homeostasis, digestion, exocrine, epithelium, sexual reproduction, muscle, immune system and nervous tissues). SOM mapping reduces the dimension of expression data from ten thousands of genes to a few thousands of metagenes where each metagene acts as representative of a minicluster of co-regulated single genes. Tissue-specific and common properties shared between groups of tissues emerge as a handful of localized spots in the tissue maps collecting groups of co-regulated and co-expressed metagenes. The functional context of the spots was discovered using overrepresentation analysis with respect to pre-defined gene sets of known functional impact. We found that tissue related spots typically contain enriched populations of gene sets well corresponding to molecular processes in the respective tissues. Analysis techniques normally used at the gene-level such as two-way hierarchical clustering provide a better signal-to-noise ratio and a better representativeness of the method if applied to the metagenes. Metagene-based clustering analyses aggregate the tissues into essentially three clusters containing nervous, immune system and the remaining tissues. 
Conclusions: The global view on the behavior of a few well-defined modules of correlated and differentially expressed genes is more intuitive and more informative than the separate discovery of the expression levels of hundreds or thousands of individual genes. The metagene approach is less sensitive to a priori selection of genes. It can detect a coordinated expression pattern whose components would not pass single-gene significance thresholds and it is able to extract context-dependent patterns of gene expression in complex data sets.
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Expression cartography of human tissues using self organizing maps

Background: The availability of parallel, high-throughput microarray and sequencing experiments poses a challenge how to best arrange and to analyze the obtained heap of multidimensional data in a concerted way. Self organizing maps (SOM), a machine learning method, enables the parallel sample- and gene-centered view on the data combined with strong visualization and second-level analysis capabilities. The paper addresses aspects of the method with practical impact in the context of expression analysis of complex data sets.
Results: The method was applied to generate a SOM characterizing the whole genome expression profiles of 67 healthy human tissues selected from ten tissue categories (adipose, endocrine, homeostasis, digestion, exocrine, epithelium, sexual reproduction, muscle, immune system and nervous tissues). SOM mapping reduces the dimension of expression data from ten thousands of genes to a few thousands of metagenes where each metagene acts as representative of a minicluster of co-regulated single genes. Tissue-specific and common properties shared between groups of tissues emerge as a handful of localized spots in the tissue maps collecting groups of co-regulated and co-expressed metagenes. The functional context of the spots was discovered using overrepresentation analysis with respect to pre-defined gene sets of known functional impact. We found that tissue related spots typically contain enriched populations of gene sets well corresponding to molecular processes in the respective tissues. Analysis techniques normally used at the gene-level such as two-way hierarchical clustering provide a better signal-to-noise ratio and a better representativeness of the method if applied to the metagenes. Metagene-based clustering analyses aggregate the tissues into essentially three clusters containing nervous, immune system and the remaining tissues. 
Conclusions: The global view on the behavior of a few well-defined modules of correlated and differentially expressed genes is more intuitive and more informative than the separate discovery of the expression levels of hundreds or thousands of individual genes. The metagene approach is less sensitive to a priori selection of genes. It can detect a coordinated expression pattern whose components would not pass single-gene significance thresholds and it is able to extract context-dependent patterns of gene expression in complex data sets.
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Establishment of a integrative multi-omics expression database CKDdb in the context of chronic kidney disease (CKD)

Complex human traits such as chronic kidney disease (CKD) are a major health and financial burden in modern societies. Currently, the description of the CKD onset and progression at the molecular level is still not fully understood. Meanwhile, the prolific use of high-throughput omic technologies in disease biomarker discovery studies yielded a vast amount of disjointed data that cannot be easily collated. Therefore, we aimed to develop a molecule-centric database featuring CKD-related experiments from available literature publications. We established the Chronic Kidney Disease database CKDdb, an integrated and clustered information resource that covers multi-omic studies (microRNAs, genomics, peptidomics, proteomics and metabolomics) of CKD and related disorders by performing literature data mining and manual curation. The CKDdb database contains differential expression data from 49395 molecule entries (redundant), of which 16885 are unique molecules (non-redundant) from 377 manually curated studies of 230 publications. This database was intentionally built to allow disease pathway analysis through a systems approach in order to yield biological meaning by integrating all existing information and therefore has the potential to unravel and gain an in-depth understanding of the key molecular events that modulate CKD pathogenesis

UNCLES: Method for the identification of genes differentially consistently co-expressed in a specific subset of datasets

Background: Collective analysis of the increasingly emerging gene expression datasets are required. The recently proposed binarisation of consensus partition matrices (Bi-CoPaM) method can combine clustering results from multiple datasets to identify the subsets of genes which are consistently co-expressed in all of the provided datasets in a tuneable manner. However, results validation and parameter setting are issues that complicate the design of such methods. Moreover, although it is a common practice to test methods by application to synthetic datasets, the mathematical models used to synthesise such datasets are usually based on approximations which may not always be sufficiently representative of real datasets. Results: Here, we propose an unsupervised method for the unification of clustering results from multiple datasets using external specifications (UNCLES). This method has the ability to identify the subsets of genes consistently co-expressed in a subset of datasets while being poorly co-expressed in another subset of datasets, and to identify the subsets of genes consistently co-expressed in all given datasets. We also propose the M-N scatter plots validation technique and adopt it to set the parameters of UNCLES, such as the number of clusters, automatically. Additionally, we propose an approach for the synthesis of gene expression datasets using real data profiles in a way which combines the ground-truth-knowledge of synthetic data and the realistic expression values of real data, and therefore overcomes the problem of faithfulness of synthetic expression data modelling. By application to those datasets, we validate UNCLES while comparing it with other conventional clustering methods, and of particular relevance, biclustering methods. We further validate UNCLES by application to a set of 14 real genome-wide yeast datasets as it produces focused clusters that conform well to known biological facts. Furthermore, in-silico-based hypotheses regarding the function of a few previously unknown genes in those focused clusters are drawn. Conclusions: The UNCLES method, the M-N scatter plots technique, and the expression data synthesis approach will have wide application for the comprehensive analysis of genomic and other sources of multiple complex biological datasets. Moreover, the derived in-silico-based biological hypotheses represent subjects for future functional studies.The National Institute for Health Research (NIHR) under its Programme Grants for Applied Research Programme (Grant Reference Number RP-PG-0310-1004)

Swarm-Organized Topographic Mapping

Topographieerhaltende Abbildungen versuchen, hochdimensionale oder komplexe Datenbestände auf einen niederdimensionalen Ausgaberaum abzubilden, wobei die Topographie der Daten hinreichend gut wiedergegeben werden soll. Die Qualität solcher Abbildung hängt gewöhnlich vom eingesetzten Nachbarschaftskonzept des konstruierenden Algorithmus ab. Die Schwarm-Organisierte Projektion ermöglicht eine Lösung dieses Parametrisierungsproblems durch die Verwendung von Techniken der Schwarmintelligenz. Die praktische Verwendbarkeit dieser Methodik wurde durch zwei Anwendungen auf dem Feld der Molekularbiologie sowie der Finanzanalytik demonstriert

Analysis of large-scale molecular biological data using self-organizing maps

Modern high-throughput technologies such as microarrays, next generation sequencing and mass spectrometry provide huge amounts of data per measurement and challenge traditional analyses. New strategies of data processing, visualization and functional analysis are inevitable. This thesis presents an approach which applies a machine learning technique known as self organizing maps (SOMs). SOMs enable the parallel sample- and feature-centered view of molecular phenotypes combined with strong visualization and second-level analysis capabilities. We developed a comprehensive analysis and visualization pipeline based on SOMs. The unsupervised SOM mapping projects the initially high number of features, such as gene expression profiles, to meta-feature clusters of similar and hence potentially co-regulated single features. This reduction of dimension is attained by the re-weighting of primary information and does not entail a loss of primary information in contrast to simple filtering approaches. The meta-data provided by the SOM algorithm is visualized in terms of intuitive mosaic portraits. Sample-specific and common properties shared between samples emerge as a handful of localized spots in the portraits collecting groups of co-regulated and co-expressed meta-features. This characteristic color patterns reflect the data landscape of each sample and promote immediate identification of (meta-)features of interest. It will be demonstrated that SOM portraits transform large and heterogeneous sets of molecular biological data into an atlas of sample-specific texture maps which can be directly compared in terms of similarities and dissimilarities. Spot-clusters of correlated meta-features can be extracted from the SOM portraits in a subsequent step of aggregation. This spot-clustering effectively enables reduction of the dimensionality of the data in two subsequent steps towards a handful of signature modules in an unsupervised fashion. Furthermore we demonstrate that analysis techniques provide enhanced resolution if applied to the meta-features. The improved discrimination power of meta-features in downstream analyses such as hierarchical clustering, independent component analysis or pairwise correlation analysis is ascribed to essentially two facts: Firstly, the set of meta-features better represents the diversity of patterns and modes inherent in the data and secondly, it also possesses the better signal-to-noise characteristics as a comparable collection of single features. Additionally to the pattern-driven feature selection in the SOM portraits, we apply statistical measures to detect significantly differential features between sample classes. Implementation of scoring measurements supplements the basal SOM algorithm. Further, two variants of functional enrichment analyses are introduced which link sample specific patterns of the meta-feature landscape with biological knowledge and support functional interpretation of the data based on the ‘guilt by association’ principle. Finally, case studies selected from different ‘OMIC’ realms are presented in this thesis. In particular, molecular phenotype data derived from expression microarrays (mRNA, miRNA), sequencing (DNA methylation, histone modification patterns) or mass spectrometry (proteome), and also genotype data (SNP-microarrays) is analyzed. It is shown that the SOM analysis pipeline implies strong application capabilities and covers a broad range of potential purposes ranging from time series and treatment-vs.-control experiments to discrimination of samples according to genotypic, phenotypic or taxonomic classifications