Algorithms for internal validation clustering measures in the post genomic era.

Inferring cluster structure in microarray datasets is a fundamental task for the -omic sciences. A fundamental question in Statistics, Data Analysis and Classification, is the prediction of the number of clusters in a dataset, usually established via internal validation measures. Despite the wealth of internal measures available in the literature, new ones have been recently proposed, some of them specifically for microarray data. In this dissertation, a study of internal validation measures is given, paying particular attention to the stability based ones. Indeed, this class of measures is particularly prominent and promising in order to have a reliable estimate the number of clusters in a dataset. For those measures, a new general algorithmic paradigm is proposed here that highlights the richness of measures in this class and accounts for the ones already available in the literature. Moreover, some of the most representative validation measures are also considered. Experiments on 12 benchmark datasets are performed in order to assess both the intrinsic ability of a measure to predict the correct number of clusters in a dataset and its merit relative to the other measures. The main result is a hierarchy of internal validation measures in terms of precision and speed, highlighting some of their merits and limitations not reported before in the literature. This hierarchy shows that the faster the measure, the less accurate it is. In order to reduce the time performance gap between the fastest and the most precise measures, the technique of designing fast approximation algorithms is systematically applied. The end result is a speed-up of many of the measures studied here that brings the gap between the fastest and the most precise within one order of magnitude in time, with no degradation in their prediction power. Prior to this work, the time gap was at least two orders of magnitude

Algorithmic paradigms for stability-based cluster validity and model selection statistical methods, with applications to microarray data analysis

AbstractThe advent of high throughput technologies, in particular microarrays, for biological research has revived interest in clustering, resulting in a plethora of new clustering algorithms. However, model selection, i.e., the identification of the correct number of clusters in a dataset, has received relatively little attention. Indeed, although central for statistics, its difficulty is also well known. Fortunately, a few novel techniques for model selection, representing a sharp departure from previous ones in statistics, have been proposed and gained prominence for microarray data analysis. Among those, the stability-based methods are the most robust and best performing in terms of prediction, but the slowest in terms of time. It is very unfortunate that as fascinating and classic an area of statistics as model selection, with important practical applications, has received very little attention in terms of algorithmic design and engineering. In this paper, in order to partially fill this gap, we make the following contributions: (A) the first general algorithmic paradigm for stability-based methods for model selection; (B) reductions showing that all of the known methods in this class are an instance of the proposed paradigm; (C) a novel algorithmic paradigm for the class of stability-based methods for cluster validity, i.e., methods assessing how statistically significant is a given clustering solution; (D) a general algorithmic paradigm that describes heuristic and very effective speed-ups known in the literature for stability-based model selection methods.Since the performance evaluation of model selection algorithms is mainly experimental, we offer, for completeness and without even attempting to be exhaustive, a representative synopsis of known experimental benchmarking results that highlight the ability of stability-based methods for model selection and the computational resources that they require for the task. As a whole, the contributions of this paper generalize in several respects reference methodologies in statistics and show that algorithmic approaches can yield deep methodological insights into this area, in addition to practical computational procedures

A methodology to assess the intrinsic discriminative ability of a distance function and its interplay with clustering algorithms for microarray data analysis

Background: Clustering is one of the most well known activities in scientific investigation and the object of research in many disciplines, ranging from statistics to computer science. Following Handl et al., it can be summarized as a three step process: (1) choice of a distance function; (2) choice of a clustering algorithm; (3) choice of a validation method. Although such a purist approach to clustering is hardly seen in many areas of science, genomic data require that level of attention, if inferences made from cluster analysis have to be of some relevance to biomedical research. Results: A procedure is proposed for the assessment of the discriminative ability of a distance function. That is, the evaluation of the ability of a distance function to capture structure in a dataset. It is based on the introduction of a new external validation index, referred to as Balanced Misclassification Index (BMI, for short) and of a nontrivial modification of the well known Receiver Operating Curve (ROC, for short), which we refer to as Corrected ROC (CROC, for short). The main results are: (a) a quantitative and qualitative method to describe the intrinsic separation ability of a distance; (b) a quantitative method to assess the performance of a clustering algorithm in conjunction with the intrinsic separation ability of a distance function. The proposed procedure is more informative than the ones available in the literature due to the adopted tools. Indeed, the first one allows to map distances and clustering solutions as graphical objects on a plane, and gives information about the bias of the clustering algorithm with respect to a distance. The second tool is a new external validity index which shows similar performances with respect to the state of the art, but with more flexibility, allowing for a broader spectrum of applications. In fact, it allows not only to quantify the merit of each clustering solution but also to quantify the agglomerative or divisive errors due to the algorithm. Conclusions: The new methodology has been used to experimentally study three popular distance functions, namely, Euclidean distance d2, Pearson correlation dr and mutual information dMI. Based on the results of the experiments, we have that the Euclidean and Pearson correlation distances have a good intrinsic discrimination ability. Conversely, the mutual information distance does not seem to offer the same flexibility and versatility as the other two distances. Apparently, that is due to well known problems in its estimation. since it requires that a dataset must have a substantial number of features to be reliable. Nevertheless, taking into account such a fact, together with results presented in Priness et al., one receives an indication that dMI may be superior to the other distances considered in this study only in conjunction with clustering algorithms specifically designed for its use. In addition, it results that K-means, Average Link, and Complete link clustering algorithms are in most cases able to improve the discriminative ability of the distances considered in this study with respect to clustering. The methodology has a range of applicability that goes well beyond microarray data since it is independent of the nature of the input data. The only requirement is that the input data must have the same format of a "feature matrix". In particular it can be used to cluster ChIP-seq data

Global gene expression profiling of healthy human brain and its application in studying neurological disorders

The human brain is the most complex structure known to mankind and one of the greatest challenges in modern biology is to understand how it is built and organized. The power of the brain arises from its variety of cells and structures, and ultimately where and when different genes are switched on and off throughout the brain tissue. In other words, brain function depends on the precise regulation of gene expression in its sub-anatomical structures. But, our understanding of the complexity and dynamics of the transcriptome of the human brain is still incomplete. To fill in the need, we designed a gene expression model that accurately defines the consistent blueprint of the brain transcriptome; thereby, identifying the core brain specific transcriptional processes conserved across individuals. Functionally characterizing this model would provide profound insights into the transcriptional landscape, biological pathways and the expression distribution of neurotransmitter systems. Here, in this dissertation we developed an expression model by capturing the similarly expressed gene patterns across congruently annotated brain structures in six individual brains by using data from the Allen Brain Atlas (ABA). We found that 84% of genes are expressed in at least one of the 190 brain structures. By employing hierarchical clustering we were able to show that distinct structures of a bigger brain region can cluster together while still retaining their expression identity. Further, weighted correlation network analysis identified 19 robust modules of coexpressing genes in the brain that demonstrated a wide range of functional associations. Since signatures of local phenomena can be masked by larger signatures, we performed local analysis on each distinct brain structure. Pathway and gene ontology enrichment analysis on these structures showed, striking enrichment for brain region specific processes. Besides, we also mapped the structural distribution of the gene expression profiles of genes associated with major neurotransmission systems in the human. We also postulated the utility of healthy brain tissue gene expression to predict potential genes involved in a neurological disorder, in the absence of data from diseased tissues. To this end, we developed a supervised classification model, which achieved an accuracy of 84% and an AUC (Area Under the Curve) of 0.81 from ROC plots, for predicting autism-implicated genes using the healthy expression model as the baseline. This study represents the first use of healthy brain gene expression to predict the scope of genes in autism implication and this generic methodology can be applied to predict genes involved in other neurological disorders

Large-scale methods in computational genomics

The explosive growth in biological sequence data coupled with the design and deployment of increasingly high throughput sequencing technologies has created a need for methods capable of processing large-scale sequence data in a time and cost effective manner. In this dissertation, we address this need through the development of faster algorithms, space-efficient methods, and high-performance parallel computing techniques for some key problems in computational genomics;The first problem addressed is the clustering of DNA sequences based on a measure of sequence similarity. Our clustering method: (i) guarantees linear space complexity, in contrast to the quadratic memory requirements of previously developed methods; (ii) identifies sequence pairs containing long maximal matches in the decreasing order of their maximal match lengths in run-time proportional to the sum of input and output sizes; (iii) provides heuristics to significantly reduce the number of pairs evaluated for checking sequence similarity without affecting quality; and (iv) has parallel strategies that provide linear speedup and a proportionate reduction in space per processor. Our approach has significantly enhanced the problem size reach while also drastically reducing the time to solution;The next problem we address is the de novo detection of genomic repeats called Long Terminal Repeat (LTR) retrotransposons. Our algorithm guarantees linear space complexity and produces high quality candidates for prediction in run-time proportional to the sum of input and output sizes. Validation of our approach on the yeast genome demonstrates both superior quality and performance results when compared to previously developed software;In a genome assembly project, fragments sequenced from a target genome are computationally assembled into numerous supersequences called contigs , which are then ordered and oriented into scaffolds . In this dissertation, we introduce a new problem called retroscaffolding for scaffolding contigs based on the knowledge of their LTR retrotransposon content. Through identification of sequencing gaps that span LTR retrotransposons, retroscaffolding provides a mechanism for prioritizing sequencing gaps for finishing purposes;While most of the problems addressed here have been studied previously, the main contribution in this dissertation is the development of methods that can scale to the largest available sequence collections

Probabilistic analysis of the human transcriptome with side information

Understanding functional organization of genetic information is a major challenge in modern biology. Following the initial publication of the human genome sequence in 2001, advances in high-throughput measurement technologies and efficient sharing of research material through community databases have opened up new views to the study of living organisms and the structure of life. In this thesis, novel computational strategies have been developed to investigate a key functional layer of genetic information, the human transcriptome, which regulates the function of living cells through protein synthesis. The key contributions of the thesis are general exploratory tools for high-throughput data analysis that have provided new insights to cell-biological networks, cancer mechanisms and other aspects of genome function. A central challenge in functional genomics is that high-dimensional genomic observations are associated with high levels of complex and largely unknown sources of variation. By combining statistical evidence across multiple measurement sources and the wealth of background information in genomic data repositories it has been possible to solve some the uncertainties associated with individual observations and to identify functional mechanisms that could not be detected based on individual measurement sources. Statistical learning and probabilistic models provide a natural framework for such modeling tasks. Open source implementations of the key methodological contributions have been released to facilitate further adoption of the developed methods by the research community.Comment: Doctoral thesis. 103 pages, 11 figure

Combining Molecular, Imaging, and Clinical Data Analysis for Predicting Cancer Prognosis

Cancer is one of the most detrimental diseases globally. Accordingly, the prognosis prediction of cancer patients has become a field of interest. In this review, we have gathered 43 stateof- the-art scientific papers published in the last 6 years that built cancer prognosis predictive models using multimodal data. We have defined the multimodality of data as four main types: clinical, anatomopathological, molecular, and medical imaging; and we have expanded on the information that each modality provides. The 43 studies were divided into three categories based on the modelling approach taken, and their characteristics were further discussed together with current issues and future trends. Research in this area has evolved from survival analysis through statistical modelling using mainly clinical and anatomopathological data to the prediction of cancer prognosis through a multi-faceted data-driven approach by the integration of complex, multimodal, and high-dimensional data containing multi-omics and medical imaging information and by applying Machine Learning and, more recently, Deep Learning techniques. This review concludes that cancer prognosis predictive multimodal models are capable of better stratifying patients, which can improve clinical management and contribute to the implementation of personalised medicine as well as provide new and valuable knowledge on cancer biology and its progression

Statistical inference from large-scale genomic data

This thesis explores the potential of statistical inference methodologies in their applications in functional genomics. In essence, it summarises algorithmic findings in this field, providing step-by-step analytical methodologies for deciphering biological knowledge from large-scale genomic data, mainly microarray gene expression time series. This thesis covers a range of topics in the investigation of complex multivariate genomic data. One focus involves using clustering as a method of inference and another is cluster validation to extract meaningful biological information from the data. Information gained from the application of these various techniques can then be used conjointly in the elucidation of gene regulatory networks, the ultimate goal of this type of analysis. First, a new tight clustering method for gene expression data is proposed to obtain tighter and potentially more informative gene clusters. Next, to fully utilise biological knowledge in clustering validation, a validity index is defined based on one of the most important ontologies within the Bioinformatics community, Gene Ontology. The method bridges a gap in current literature, in the sense that it takes into account not only the variations of Gene Ontology categories in biological specificities and their significance to the gene clusters, but also the complex structure of the Gene Ontology. Finally, Bayesian probability is applied to making inference from heterogeneous genomic data, integrated with previous efforts in this thesis, for the aim of large-scale gene network inference. The proposed system comes with a stochastic process to achieve robustness to noise, yet remains efficient enough for large-scale analysis. Ultimately, the solutions presented in this thesis serve as building blocks of an intelligent system for interpreting large-scale genomic data and understanding the functional organisation of the genome

A primer on machine learning techniques for genomic applications

High throughput sequencing technologies have enabled the study of complex biological aspects at single nucleotide resolution, opening the big data era. The analysis of large volumes of heterogeneous “omic” data, however, requires novel and efficient computational algorithms based on the paradigm of Artificial Intelligence. In the present review, we introduce and describe the most common machine learning methodologies, and lately deep learning, applied to a variety of genomics tasks, trying to emphasize capabilities, strengths and limitations through a simple and intuitive language. We highlight the power of the machine learning approach in handling big data by means of a real life example, and underline how described methods could be relevant in all cases in which large amounts of multimodal genomic data are available