Biclustering via optimal re-ordering of data matrices in systems biology: rigorous methods and comparative studies

<p>Abstract</p> <p>Background</p> <p>The analysis of large-scale data sets via clustering techniques is utilized in a number of applications. Biclustering in particular has emerged as an important problem in the analysis of gene expression data since genes may only jointly respond over a subset of conditions. Biclustering algorithms also have important applications in sample classification where, for instance, tissue samples can be classified as cancerous or normal. Many of the methods for biclustering, and clustering algorithms in general, utilize simplified models or heuristic strategies for identifying the "best" grouping of elements according to some metric and cluster definition and thus result in suboptimal clusters.</p> <p>Results</p> <p>In this article, we present a rigorous approach to biclustering, OREO, which is based on the Optimal RE-Ordering of the rows and columns of a data matrix so as to globally minimize the dissimilarity metric. The physical permutations of the rows and columns of the data matrix can be modeled as either a network flow problem or a traveling salesman problem. Cluster boundaries in one dimension are used to partition and re-order the other dimensions of the corresponding submatrices to generate biclusters. The performance of OREO is tested on (a) metabolite concentration data, (b) an image reconstruction matrix, (c) synthetic data with implanted biclusters, and gene expression data for (d) colon cancer data, (e) breast cancer data, as well as (f) yeast segregant data to validate the ability of the proposed method and compare it to existing biclustering and clustering methods.</p> <p>Conclusion</p> <p>We demonstrate that this rigorous global optimization method for biclustering produces clusters with more insightful groupings of similar entities, such as genes or metabolites sharing common functions, than other clustering and biclustering algorithms and can reconstruct underlying fundamental patterns in the data for several distinct sets of data matrices arising in important biological applications.</p

On Solving Selected Nonlinear Integer Programming Problems in Data Mining, Computational Biology, and Sustainability

This thesis consists of three essays concerning the use of optimization techniques to solve four problems in the fields of data mining, computational biology, and sustainable energy devices. To the best of our knowledge, the particular problems we discuss have not been previously addressed using optimization, which is a specific contribution of this dissertation. In particular, we analyze each of the problems to capture their underlying essence, subsequently demonstrating that each problem can be modeled as a nonlinear (mixed) integer program. We then discuss the design and implementation of solution techniques to locate optimal solutions to the aforementioned problems. Running throughout this dissertation is the theme of using mixed-integer programming techniques in conjunction with context-dependent algorithms to identify optimal and previously undiscovered underlying structure

Collective analysis of multiple high-throughput gene expression datasets

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University LondonModern technologies have resulted in the production of numerous high-throughput biological datasets. However, the pace of development of capable computational methods does not cope with the pace of generation of new high-throughput datasets. Amongst the most popular biological high-throughput datasets are gene expression datasets (e.g. microarray datasets). This work targets this aspect by proposing a suite of computational methods which can analyse multiple gene expression datasets collectively. The focal method in this suite is the unification of clustering results from multiple datasets using external specifications (UNCLES). This method applies clustering to multiple heterogeneous datasets which measure the expression of the same set of genes separately and then combines the resulting partitions in accordance to one of two types of external specifications; type A identifies the subsets of genes that are consistently co-expressed in all of the given datasets while type B identifies the subsets of genes that are consistently co-expressed in a subset of datasets while being poorly co-expressed in another subset of datasets. This contributes to the types of questions which can addressed by computational methods because existing clustering, consensus clustering, and biclustering methods are inapplicable to address the aforementioned objectives. Moreover, in order to assist in setting some of the parameters required by UNCLES, the M-N scatter plots technique is proposed. These methods, and less mature versions of them, have been validated and applied to numerous real datasets from the biological contexts of budding yeast, bacteria, human red blood cells, and malaria. While collaborating with biologists, these applications have led to various biological insights. In yeast, the role of the poorly-understood gene CMR1 in the yeast cell-cycle has been further elucidated. Also, a novel subset of poorly understood yeast genes has been discovered with an expression profile consistently negatively correlated with the well-known ribosome biogenesis genes. Bacterial data analysis has identified two clusters of negatively correlated genes. Analysis of data from human red blood cells has produced some hypotheses regarding the regulation of the pathways producing such cells. On the other hand, malarial data analysis is still at a preliminary stage. Taken together, this thesis provides an original integrative suite of computational methods which scrutinise multiple gene expression datasets collectively to address previously unresolved questions, and provides the results and findings of many applications of these methods to real biological datasets from multiple contexts.National Institute for Health Research (NIHR) and the Brunel College of Engineering, Design and Physical Science

Neuroengineering of Clustering Algorithms

Cluster analysis can be broadly divided into multivariate data visualization, clustering algorithms, and cluster validation. This dissertation contributes neural network-based techniques to perform all three unsupervised learning tasks. Particularly, the first paper provides a comprehensive review on adaptive resonance theory (ART) models for engineering applications and provides context for the four subsequent papers. These papers are devoted to enhancements of ART-based clustering algorithms from (a) a practical perspective by exploiting the visual assessment of cluster tendency (VAT) sorting algorithm as a preprocessor for ART offline training, thus mitigating ordering effects; and (b) an engineering perspective by designing a family of multi-criteria ART models: dual vigilance fuzzy ART and distributed dual vigilance fuzzy ART (both of which are capable of detecting complex cluster structures), merge ART (aggregates partitions and lessens ordering effects in online learning), and cluster validity index vigilance in fuzzy ART (features a robust vigilance parameter selection and alleviates ordering effects in offline learning). The sixth paper consists of enhancements to data visualization using self-organizing maps (SOMs) by depicting in the reduced dimension and topology-preserving SOM grid information-theoretic similarity measures between neighboring neurons. This visualization\u27s parameters are estimated using samples selected via a single-linkage procedure, thereby generating heatmaps that portray more homogeneous within-cluster similarities and crisper between-cluster boundaries. The seventh paper presents incremental cluster validity indices (iCVIs) realized by (a) incorporating existing formulations of online computations for clusters\u27 descriptors, or (b) modifying an existing ART-based model and incrementally updating local density counts between prototypes. Moreover, this last paper provides the first comprehensive comparison of iCVIs in the computational intelligence literature --Abstract, page iv

Vertical integration of multiple high-dimensional datasets

Research in genomics and related fields now often requires the analysis of emph{multi-block} data, in which multiple high-dimensional types of data are available for a common set of objects. We introduce Joint and Individual Variation Explained (JIVE), a general decomposition of variation for the integrated analysis of multi-block datasets. The decomposition consists of three terms: a low-rank approximation capturing joint variation across datatypes, low-rank approximations for structured variation individual to each datatype, and residual noise. JIVE quantifies the amount of joint variation between datatypes, reduces the dimensionality of the data, and allows for the visual exploration of joint and individual structure. JIVE is an extension of Principal Components Analysis and has clear advantages over popular two-block methods such as Canonical Correlation and Partial Least Squares. Research in a number of fields also requires the analysis of emph{multi-way data}. Multi-way data take the form of a three (or higher) dimensional array. We compare several existing factorization methods for multi-way data, and we show that these methods belong to the same unified framework. The final portion of this dissertation concerns biclustering. We introduce an approach to biclustering a binary data matrix, and discuss the application of biclustering to classification problems

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