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

Unsupervised multiple kernel learning approaches for integrating molecular cancer patient data

Cancer is the second leading cause of death worldwide. A characteristic of this disease is its complexity leading to a wide variety of genetic and molecular aberrations in the tumors. This heterogeneity necessitates personalized therapies for the patients. However, currently defined cancer subtypes used in clinical practice for treatment decision-making are based on relatively few selected markers and thus provide only a coarse classifcation of tumors. The increased availability in multi-omics data measured for cancer patients now offers the possibility of defining more informed cancer subtypes. Such a more fine-grained characterization of cancer subtypes harbors the potential of substantially expanding treatment options in personalized cancer therapy. In this thesis, we identify comprehensive cancer subtypes using multidimensional data. For this purpose, we apply and extend unsupervised multiple kernel learning methods. Three challenges of unsupervised multiple kernel learning are addressed: robustness, applicability, and interpretability. First, we show that regularization of the multiple kernel graph embedding framework, which enables the implementation of dimensionality reduction techniques, can increase the stability of the resulting patient subgroups. This improvement is especially beneficial for data sets with a small number of samples. Second, we adapt the objective function of kernel principal component analysis to enable the application of multiple kernel learning in combination with this widely used dimensionality reduction technique. Third, we improve the interpretability of kernel learning procedures by performing feature clustering prior to integrating the data via multiple kernel learning. On the basis of these clusters, we derive a score indicating the impact of a feature cluster on a patient cluster, thereby facilitating further analysis of the cluster-specific biological properties. All three procedures are successfully tested on real-world cancer data. Comparing our newly derived methodologies to established methods provides evidence that our work offers novel and beneficial ways of identifying patient subgroups and gaining insights into medically relevant characteristics of cancer subtypes.Krebs ist eine der häufigsten Todesursachen weltweit. Krebs ist gekennzeichnet durch seine Komplexität, die zu vielen verschiedenen genetischen und molekularen Aberrationen im Tumor führt. Die Unterschiede zwischen Tumoren erfordern personalisierte Therapien für die einzelnen Patienten. Die Krebssubtypen, die derzeit zur Behandlungsplanung in der klinischen Praxis verwendet werden, basieren auf relativ wenigen, genetischen oder molekularen Markern und können daher nur eine grobe Unterteilung der Tumoren liefern. Die zunehmende Verfügbarkeit von Multi-Omics-Daten für Krebspatienten ermöglicht die Neudefinition von fundierteren Krebssubtypen, die wiederum zu spezifischeren Behandlungen für Krebspatienten führen könnten. In dieser Dissertation identifizieren wir neue, potentielle Krebssubtypen basierend auf Multi-Omics-Daten. Hierfür verwenden wir unüberwachtes Multiple Kernel Learning, welches in der Lage ist mehrere Datentypen miteinander zu kombinieren. Drei Herausforderungen des unüberwachten Multiple Kernel Learnings werden adressiert: Robustheit, Anwendbarkeit und Interpretierbarkeit. Zunächst zeigen wir, dass die zusätzliche Regularisierung des Multiple Kernel Learning Frameworks zur Implementierung verschiedener Dimensionsreduktionstechniken die Stabilität der identifizierten Patientengruppen erhöht. Diese Robustheit ist besonders vorteilhaft für Datensätze mit einer geringen Anzahl von Proben. Zweitens passen wir die Zielfunktion der kernbasierten Hauptkomponentenanalyse an, um eine integrative Version dieser weit verbreiteten Dimensionsreduktionstechnik zu ermöglichen. Drittens verbessern wir die Interpretierbarkeit von kernbasierten Lernprozeduren, indem wir verwendete Merkmale in homogene Gruppen unterteilen bevor wir die Daten integrieren. Mit Hilfe dieser Gruppen definieren wir eine Bewertungsfunktion, die die weitere Auswertung der biologischen Eigenschaften von Patientengruppen erleichtert. Alle drei Verfahren werden an realen Krebsdaten getestet. Den Vergleich unserer Methodik mit etablierten Methoden weist nach, dass unsere Arbeit neue und nützliche Möglichkeiten bietet, um integrative Patientengruppen zu identifizieren und Einblicke in medizinisch relevante Eigenschaften von Krebssubtypen zu erhalten

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

Integrative Analysis Methods for Biological Problems Using Data Reduction Approaches

The "big data" revolution of the past decade has allowed researchers to procure or access biological data at an unprecedented scale, on the front of both volume (low-cost high-throughput technologies) and variety (multi-platform genomic profiling). This has fueled the development of new integrative methods, which combine and consolidate across multiple sources of data in order to gain generalizability, robustness, and a more comprehensive systems perspective. The key challenges faced by this new class of methods primarily relate to heterogeneity, whether it is across cohorts from independent studies or across the different levels of genomic regulation. While the different perspectives among data sources is invaluable in providing different snapshots of the global system, such diversity also brings forth many analytic difficulties as each source introduces a distinctive element of noise. In recent years, many styles of data integration have appeared to tackle this problem ranging from Bayesian frameworks to graphical models, a wide assortment as diverse as the biology they intend to explain. My focus in this work is dimensionality reduction-based methods of integration, which offer the advantages of efficiency in high-dimensions (an asset among genomic datasets) and simplicity in allowing for elegant mathematical extensions. In the course of these chapters I will describe the biological motivations, the methodological directions, and the applications of three canonical reductionist approaches for relating information across multiple data groups.PHDStatisticsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/138564/1/yangzi_1.pd

A Statistical Approach to the Alignment of fMRI Data

Multi-subject functional Magnetic Resonance Image studies are critical. The anatomical and functional structure varies across subjects, so the image alignment is necessary. We define a probabilistic model to describe functional alignment. Imposing a prior distribution, as the matrix Fisher Von Mises distribution, of the orthogonal transformation parameter, the anatomical information is embedded in the estimation of the parameters, i.e., penalizing the combination of spatially distant voxels. Real applications show an improvement in the classification and interpretability of the results compared to various functional alignment methods

A comparison of the CAR and DAGAR spatial random effects models with an application to diabetics rate estimation in Belgium

When hierarchically modelling an epidemiological phenomenon on a finite collection of sites in space, one must always take a latent spatial effect into account in order to capture the correlation structure that links the phenomenon to the territory. In this work, we compare two autoregressive spatial models that can be used for this purpose: the classical CAR model and the more recent DAGAR model. Differently from the former, the latter has a desirable property: its ρ parameter can be naturally interpreted as the average neighbor pair correlation and, in addition, this parameter can be directly estimated when the effect is modelled using a DAGAR rather than a CAR structure. As an application, we model the diabetics rate in Belgium in 2014 and show the adequacy of these models in predicting the response variable when no covariates are available