Graphical Model approaches for Biclustering

In many scientific areas, it is crucial to group (cluster) a set of objects, based on a set of observed features. Such operation is widely known as Clustering and it has been exploited in the most different scenarios ranging from Economics to Biology passing through Psychology. Making a step forward, there exist contexts where it is crucial to group objects and simultaneously identify the features that allow to recognize such objects from the others. In gene expression analysis, for instance, the identification of subsets of genes showing a coherent pattern of expression in subsets of objects/samples can provide crucial information about active biological processes. Such information, which cannot be retrieved by classical clustering approaches, can be extracted with the so called Biclustering, a class of approaches which aim at simultaneously clustering both rows and columns of a given data matrix (where each row corresponds to a different object/sample and each column to a different feature). The problem of biclustering, also known as co-clustering, has been recently exploited in a wide range of scenarios such as Bioinformatics, market segmentation, data mining, text analysis and recommender systems. Many approaches have been proposed to address the biclustering problem, each one characterized by different properties such as interpretability, effectiveness or computational complexity. A recent trend involves the exploitation of sophisticated computational models (Graphical Models) to face the intrinsic complexity of biclustering, and to retrieve very accurate solutions. Graphical Models represent the decomposition of a global objective function to analyse in a set of smaller/local functions defined over a subset of variables. The advantages in using Graphical Models relies in the fact that the graphical representation can highlight useful hidden properties of the considered objective function, plus, the analysis of smaller local problems can be dealt with less computational effort. Due to the difficulties in obtaining a representative and solvable model, and since biclustering is a complex and challenging problem, there exist few promising approaches in literature based on Graphical models facing biclustering. 3 This thesis is inserted in the above mentioned scenario and it investigates the exploitation of Graphical Models to face the biclustering problem. We explored different type of Graphical Models, in particular: Factor Graphs and Bayesian Networks. We present three novel algorithms (with extensions) and evaluate such techniques using available benchmark datasets. All the models have been compared with the state-of-the-art competitors and the results show that Factor Graph approaches lead to solid and efficient solutions for dataset of contained dimensions, whereas Bayesian Networks can manage huge datasets, with the overcome that setting the parameters can be not trivial. As another contribution of the thesis, we widen the range of biclustering applications by studying the suitability of these approaches in some Computer Vision problems where biclustering has been never adopted before. Summarizing, with this thesis we provide evidence that Graphical Model techniques can have a significant impact in the biclustering scenario. Moreover, we demonstrate that biclustering techniques are ductile and can produce effective solutions in the most different fields of applications

Co-clustering algorithm for the identification of cancer subtypes from gene expression data

Cancer has been classified as a heterogeneous genetic disease comprising various different subtypes based on gene expression data. Early stages of diagnosis and prognosis for cancer type have become an essential requirement in cancer informatics research because it is helpful for the clinical treatment of patients. Besides this, gene network interaction which is the significant in order to understand the cellular and progressive mechanisms of cancer has been barely considered in current research. Hence, applications of machine learning methods become an important area for researchers to explore in order to categorize cancer genes into high and low risk groups or subtypes. Presently co-clustering is an extensively used data mining technique for analyzing gene expression data. This paper presents an improved network assisted co-clustering for the identification of cancer subtypes (iNCIS) where it combines gene network information with gene expression data to obtain co-clusters. The effectiveness of iNCIS was evaluated on large-scale Breast Cancer (BRCA) and Glioblastoma Multiforme (GBM). This weighted co-clustering approach in iNCIS delivers a distinctive result to integrate gene network into the clustering procedure

Bi-(N-) cluster editing and its biomedical applications

The extremely fast advances in wet-lab techniques lead to an exponential growth of heterogeneous and unstructured biological data, posing a great challenge to data integration in nowadays system biology. The traditional clustering approach, although widely used to divide the data into groups sharing common features, is less powerful in the analysis of heterogeneous data from n different sources (n _ 2). The co-clustering approach has been widely used for combined analyses of multiple networks to address the challenge of heterogeneity. In this thesis, novel methods for the co-clustering of large scale heterogeneous data sets are presented in the software package n-CluE: one exact algorithm and two heuristic algorithms based on the model of bi-/n-cluster editing by modeling the input as n-partite graphs and solving the clustering problem with various strategies. In the first part of the thesis, the complexity and the fixed-parameter tractability of the extended bicluster editing model with relaxed constraints are investigated, namely the ?-bicluster editing model and its NP-hardness is proven. Based on the results of this analysis, three strategies within the n-CluE software package are then established and discussed, together with the evaluations on performances and the systematic comparisons against other algorithms of the same type in solving bi-/n-cluster editing problem. To demonstrate the practical impact, three real-world analyses using n-CluE are performed, including (a) prediction of novel genotype-phenotype associations by clustering the data from Genome-Wide Association Studies; (b) comparison between n-CluE and eight other biclustering tools on GEO Omnibus microarray data sets; (c) drug repositioning predictions by co-clustering on drug, gene and disease networks. The outstanding performance of n-CluE in the real-world applications shows its strength and flexibility in integrating heterogeneous data and extracting biological relevant information in bioinformatic analyses.Die enormen Fortschritte im Bereich Labortechnik haben in jüngster Zeit zu einer exponentiell wachsenden Menge an heterogenen und unstrukturierten Daten geführt. Dies stellt eine große Herausforderung für systembiologische Forschung dar, innerhalb derer diese Datenmengen durch Datenintegration und Datamining zusammengefasst und in Kombination analysiert werden. Traditionelles Clustering ist eine vielseitig eingesetzte Methode, um Entitäten innerhalb grosser Datenmengen bezüglich ihrer Ähnlichkeit bestimmter Attribute zu gruppieren (“clustern„). Beim Clustern von heterogenen Daten aus n (n > 2) unterschiedlichen Quellen zeigen traditionelle Clusteringmethoden jedoch Schwächen. In solchen Fällen bieten Co-clusteringmethoden dadurch Vorteile, dass sie Datensätze gleichzeitig partitionieren können. In dieser Dissertation stelle ich neue Clusteringmethoden vor, die in der Software n-CluE zusammengeführt sind. Diese neuen Methoden wurden aus dem bi-/n-cluster editing heraus entwickelt und lösen durch Transformation der Eingangsdatensätze in n-partite Graphen mit verschiedenen Strategien das zugrundeliegende Clusteringproblem. Diese Dissertation ist in zwei verschiedene Teile gegliedert. Der erste Teil befasst sich eingehend mit der Komplexitätanalyse verschiedener erweiterter bicluster editing Modelle, die sog. ?-bicluster editing Modelle und es wird der Beweis der NP-Schwere erbracht. Basierend auf diesen theoretischen Gesichtspunkten präsentiere ich im zweiten Teil drei unterschiedliche Algorithmen, einen exakten Algorithmus und zwei Heuristiken und demonstriere ihre Leistungsfähigkeit und Robustheit im Vergleich mit anderen algorithmischen Herangehensweisen. Die Stärken von n-CluE werden anhand von drei realen Anwendungsbeispielen untermauert: (a) Die Vorhersage neuartiger Genotyp-Phänotyp-Assoziationen durch Biclustering-Analyse von Daten aus genomweiten Assoziationsstudien (GWAS);(b) Der Vergleich zwischen n-CluE und acht weiteren Softwarepaketen anhand von Bicluster-Analysen von Microarraydaten aus den Gene Expression Omnibus (GEO); (c) Die Vorhersage von Medikamenten-Repositionierung durch integrierte Analyse von Medikamenten-, Gen- und Krankeitsnetzwerken. Die Resultate zeigen eindrucksvoll die Stärken der n-CluE Software. Das Ergebnis ist eine leistungsstarke, robuste und flexibel erweiterbare Implementierung des Biclustering-Theorems zur Integration grosser heterogener Datenmengen für das Extrahieren biologisch relevanter Ergebnisse im Rahmen von bioinformatischen Studien

G-Tric: enhancing triclustering evaluation using three-way synthetic datasets with ground truth

Tese de mestrado, Ciência de Dados, Universidade de Lisboa, Faculdade de Ciências, 2020Three-dimensional datasets, or three-way data, started to gain popularity due to their increasing capacity to describe inherently multivariate and temporal events, such as biological responses, social interactions along time, urban dynamics, or complex geophysical phenomena. Triclustering, subspace clustering of three-way data, enables the discovery of patterns corresponding to data subspaces (triclusters) with values correlated across the three dimensions (observations _ features _ contexts). With an increasing number of algorithms being proposed, effectively comparing them with state-of-the-art algorithms is paramount.These comparisons are usually performed using real data, without a known ground-truth, thus limiting the assessments. In this context, we propose a synthetic data generator, G-Tric, allowing the creation of synthetic datasets with configurable properties and the possibility to plant triclusters. The generator is prepared to create datasets resembling real three-way data from biomedical and social data domains, with the additional advantage of further providing the ground truth (triclustering solution) as output. G-Tric can replicate real-world datasets and create new ones that match researchers’ needs across several properties, including data type (numeric or symbolic), dimension, and background distribution. Users can tune the patterns and structure that characterize the planted triclusters (subspaces) and how they interact (overlapping). Data quality can also be controlled by defining the number of missing values, noise, and errors. Furthermore, a benchmark of datasets resembling real data is made available, together with the corresponding triclustering solutions (planted triclusters) and generating parameters. Triclustering evaluation using G-Tric provides the possibility to combine both intrinsic and extrinsic metrics to compare solutions that produce more reliable analyses. A set of predefined datasets, mimicking widely used three-way data and exploring crucial properties was generated and made available, highlighting G-Tric’s potential to advance triclustering state-of-the-art by easing the process of evaluating the quality of new triclustering approaches. Besides reviewing the current state-of-the-art regarding triclustering approaches, comparison studies and evaluation metrics, this work also analyzes how the lack of frameworks to generate synthetic data influences existent evaluation methodologies, limiting the scope of performance insights that can be extracted from each algorithm. As well as exemplifying how the set of decisions made on these evaluations can impact the quality and validity of those results. Alternatively, a different methodology that takes advantage of synthetic data with ground truth is presented. This approach, combined with the proposal of an extension to an existing clustering extrinsic measure, enables to assess solutions’ quality under new perspectives

Gene expression data analysis using novel methods: Predicting time delayed correlations and evolutionarily conserved functional modules

Microarray technology enables the study of gene expression on a large scale. One of the main challenges has been to devise methods to cluster genes that share similar expression profiles. In gene expression time courses, a particular gene may encode transcription factor and thus controlling several genes downstream; in this case, the gene expression profiles may be staggered, indicating a time-delayed response in transcription of the later genes. The standard clustering algorithms consider gene expression profiles in a global way, thus often ignoring such local time-delayed correlations. We have developed novel methods to capture time-delayed correlations between expression profiles: (1) A method using dynamic programming and (2) CLARITY, an algorithm that uses a local shape based similarity measure to predict time-delayed correlations and local correlations. We used CLARITY on a dataset describing the change in gene expression during the mitotic cell cycle in Saccharomyces cerevisiae. The obtained clusters were significantly enriched with genes that share similar functions, reflecting the fact that genes with a similar function are often co-regulated and thus co-expressed. Time-shifted as well as local correlations could also be predicted using CLARITY. In datasets, where the expression profiles of independent experiments are compared, the standard clustering algorithms often cluster according to all conditions, considering all genes. This increases the background noise and can lead to the missing of genes that change the expression only under particular conditions. We have employed a genetic algorithm based module predictor that is capable to identify group of genes that change their expression only in a subset of conditions. With the aim of supplementing the Ustilago maydis genome annotation, we have used the module prediction algorithm on various independent datasets from Ustilago maydis. The predicted modules were cross-referenced in various Saccharomyces cerevisiae datasets to check its evolutionarily conservation between these two organisms. The key contributions of this thesis are novel methods that explore biological information from DNA microarray data

Gene expression data analysis using novel methods: Predicting time delayed correlations and evolutionarily conserved functional modules

Microarray technology enables the study of gene expression on a large scale. One of the main challenges has been to devise methods to cluster genes that share similar expression profiles. In gene expression time courses, a particular gene may encode transcription factor and thus controlling several genes downstream; in this case, the gene expression profiles may be staggered, indicating a time-delayed response in transcription of the later genes. The standard clustering algorithms consider gene expression profiles in a global way, thus often ignoring such local time-delayed correlations. We have developed novel methods to capture time-delayed correlations between expression profiles: (1) A method using dynamic programming and (2) CLARITY, an algorithm that uses a local shape based similarity measure to predict time-delayed correlations and local correlations. We used CLARITY on a dataset describing the change in gene expression during the mitotic cell cycle in Saccharomyces cerevisiae. The obtained clusters were significantly enriched with genes that share similar functions, reflecting the fact that genes with a similar function are often co-regulated and thus co-expressed. Time-shifted as well as local correlations could also be predicted using CLARITY. In datasets, where the expression profiles of independent experiments are compared, the standard clustering algorithms often cluster according to all conditions, considering all genes. This increases the background noise and can lead to the missing of genes that change the expression only under particular conditions. We have employed a genetic algorithm based module predictor that is capable to identify group of genes that change their expression only in a subset of conditions. With the aim of supplementing the Ustilago maydis genome annotation, we have used the module prediction algorithm on various independent datasets from Ustilago maydis. The predicted modules were cross-referenced in various Saccharomyces cerevisiae datasets to check its evolutionarily conservation between these two organisms. The key contributions of this thesis are novel methods that explore biological information from DNA microarray data

Statistical Techniques for Exploratory Analysis of Structured Three-Way and Dynamic Network Data.

In this thesis, I develop different techniques for the pattern extraction and visual exploration of a collection of data matrices. Specifically, I present methods to help home in on and visualize an underlying structure and its evolution over ordered (e.g., time) or unordered (e.g., experimental conditions) index sets. The first part of the thesis introduces a biclustering technique for such three dimensional data arrays. This technique is capable of discovering potentially overlapping groups of samples and variables that evolve similarly with respect to a subset of conditions. To facilitate and enhance visual exploration, I introduce a framework that utilizes kernel smoothing to guide the estimation of bicluster responses over the array. In the second part of the thesis, I introduce two matrix factorization models. The first is a data integration model that decomposes the data into two factors: a basis common to all data matrices, and a coefficient matrix that varies for each data matrix. The second model is meant for visual clustering of nodes in dynamic network data, which often contains complex evolving structure. Hence, this approach is more flexible and additionally lets the basis evolve for each matrix in the array. Both models utilize a regularization within the framework of non-negative matrix factorization to encourage local smoothness of the basis and coefficient matrices, which improves interpretability and highlights the structural patterns underlying the data, while mitigating noise effects. I also address computational aspects of applying regularized non-negative matrix factorization models to large data arrays by presenting multiple algorithms, including an approximation algorithm based on alternating least squares.PhDStatisticsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/99838/1/smankad_1.pd

Reconstruction of Kauffman networks applying trees

AbstractAccording to Kauffman’s theory [S. Kauffman, The Origins of Order, Self-Organization and Selection in Evolution, Oxford University Press, New York, 1993], enzymes in living organisms form a dynamic network, which governs their activity. For each enzyme the network contains:•a collection of enzymes affecting the enzyme and•a Boolean function prescribing next activity of the enzyme as a function of the present activity of the affecting enzymes.Kauffman’s original pure random structure of the connections was criticized by Barabasi and Albert [A.-L. Barabasi, R. Albert, Emergence of scaling in random networks, Science 286 (1999) 509–512]. Their model was unified with Kauffman’s network by Aldana and Cluzel [M. Aldana, P. Cluzel, A natural class of robust networks, Proc. Natl. Acad. Sci. USA 100 (2003) 8710–8714]. Kauffman postulated that the dynamic character of the network determines the fitness of the organism. If the network is either convergent or chaotic, the chance of survival is lessened. If, however, the network is stable and critical, the organism will proliferate. Kauffman originally proposed a special type of Boolean functions to promote stability, which he called the property canalyzing. This property was extended by Shmulevich et al. [I. Shmulevich, H. Lähdesmäki, E.R. Dougherty, J. Astola, W. Zhang, The role of certain Post classes in Boolean network models of genetic networks, Proc. Natl. Acad. Sci. USA 100 (2003) 10734–10739] using Post classes. Following their ideas, we propose decision tree functions for enzymatic interactions. The model is fitted to microarray data of Cogburn et al. [L.A. Cogburn, W. Wang, W. Carre, L. Rejtő, T.E. Porter, S.E. Aggrey, J. Simon, System-wide chicken DNA microarrays, gene expression profiling, and discovery of functional genes, Poult. Sci. Assoc. 82 (2003) 939–951; L.A. Cogburn, X. Wang, W. Carre, L. Rejtő, S.E. Aggrey, M.J. Duclos, J. Simon, T.E. Porter, Functional genomics in chickens: development of integrated-systems microarrays for transcriptional profiling and discovery of regulatory pathways, Comp. Funct. Genom. 5 (2004) 253–261]. In microarray measurements the activity of clones is measured. The problem here is the reconstruction of the structure of enzymatic interactions of the living organism using microarray data. The task resembles summing up the whole story of a film from unordered and perhaps incomplete collections of its pieces. Two basic ingredients will be used in tackling the problem. In our earlier works [L. Rejtő, G. Tusnády, Evolution of random Boolean NK-models in Tierra environment, in: I. Berkes, E. Csaki, M. Csörgő (Eds.), Limit Theorems in Probability an Statistics, Budapest, vol. II, 2002, pp. 499–526] we used an evolutionary strategy called Tierra, which was proposed by Ray [T.S. Ray, Evolution, complexity, entropy and artificial reality, Physica D 75 (1994) 239–263] for investigating complex systems. Here we apply this method together with the tree–structure of clones found in our earlier statistical analysis of microarray measurements [L. Rejtő, G. Tusnády, Clustering methods in microarrays, Period. Math. Hungar. 50 (2005) 199–221]