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

New approaches for unsupervised transcriptomic data analysis based on Dictionary learning

The era of high-throughput data generation enables new access to biomolecular profiles and exploitation thereof. However, the analysis of such biomolecular data, for example, transcriptomic data, suffers from the so-called "curse of dimensionality". This occurs in the analysis of datasets with a significantly larger number of variables than data points. As a consequence, overfitting and unintentional learning of process-independent patterns can appear. This can lead to insignificant results in the application. A common way of counteracting this problem is the application of dimension reduction methods and subsequent analysis of the resulting low-dimensional representation that has a smaller number of variables. In this thesis, two new methods for the analysis of transcriptomic datasets are introduced and evaluated. Our methods are based on the concepts of Dictionary learning, which is an unsupervised dimension reduction approach. Unlike many dimension reduction approaches that are widely applied for transcriptomic data analysis, Dictionary learning does not impose constraints on the components that are to be derived. This allows for great flexibility when adjusting the representation to the data. Further, Dictionary learning belongs to the class of sparse methods. The result of sparse methods is a model with few non-zero coefficients, which is often preferred for its simplicity and ease of interpretation. Sparse methods exploit the fact that the analysed datasets are highly structured. Indeed, a characteristic of transcriptomic data is particularly their structuredness, which appears due to the connection of genes and pathways, for example. Nonetheless, the application of Dictionary learning in medical data analysis is mainly restricted to image analysis. Another advantage of Dictionary learning is that it is an interpretable approach. Interpretability is a necessity in biomolecular data analysis to gain a holistic understanding of the investigated processes. Our two new transcriptomic data analysis methods are each designed for one main task: (1) identification of subgroups for samples from mixed populations, and (2) temporal ordering of samples from dynamic datasets, also referred to as "pseudotime estimation". Both methods are evaluated on simulated and real-world data and compared to other methods that are widely applied in transcriptomic data analysis. Our methods convince through high performance and overall outperform the comparison methods

Four algorithms to solve symmetric multi-type non-negative matrix tri-factorization problem

In this paper, we consider the symmetric multi-type non-negative matrix tri-factorization problem (SNMTF), which attempts to factorize several symmetric non-negative matrices simultaneously. This can be considered as a generalization of the classical non-negative matrix tri-factorization problem and includes a non-convex objective function which is a multivariate sixth degree polynomial and a has convex feasibility set. It has a special importance in data science, since it serves as a mathematical model for the fusion of different data sources in data clustering. We develop four methods to solve the SNMTF. They are based on four theoretical approaches known from the literature: the fixed point method (FPM), the block-coordinate descent with projected gradient (BCD), the gradient method with exact line search (GM-ELS) and the adaptive moment estimation method (ADAM). For each of these methods we offer a software implementation: for the former two methods we use Matlab and for the latter Python with the TensorFlow library. We test these methods on three data-sets: the synthetic data-set we generated, while the others represent real-life similarities between different objects. Extensive numerical results show that with sufficient computing time all four methods perform satisfactorily and ADAM most often yields the best mean square error ($\mathrm{MSE}$). However, if the computation time is limited, FPM gives the best $\mathrm{MSE}$ because it shows the fastest convergence at the beginning. All data-sets and codes are publicly available on our GitLab profile

Integration of multi-scale protein interactions for biomedical data analysis

With the advancement of modern technologies, we observe an increasing accumulation of biomedical data about diseases. There is a need for computational methods to sift through and extract knowledge from the diverse data available in order to improve our mechanistic understanding of diseases and improve patient care. Biomedical data come in various forms as exemplified by the various omics data. Existing studies have shown that each form of omics data gives only partial information on cells state and motivated jointly mining multi-omics, multi-modal data to extract integrated system knowledge. The interactome is of particular importance as it enables the modelling of dependencies arising from molecular interactions. This Thesis takes a special interest in the multi-scale protein interactome and its integration with computational models to extract relevant information from biomedical data. We define multi-scale interactions at different omics scale that involve proteins: pairwise protein-protein interactions, multi-protein complexes, and biological pathways. Using hypergraph representations, we motivate considering higher-order protein interactions, highlighting the complementary biological information contained in the multi-scale interactome. Based on those results, we further investigate how those multi-scale protein interactions can be used as either prior knowledge, or auxiliary data to develop machine learning algorithms. First, we design a neural network using the multi-scale organization of proteins in a cell into biological pathways as prior knowledge and train it to predict a patient's diagnosis based on transcriptomics data. From the trained models, we develop a strategy to extract biomedical knowledge pertaining to the diseases investigated. Second, we propose a general framework based on Non-negative Matrix Factorization to integrate the multi-scale protein interactome with multi-omics data. We show that our approach outperforms the existing methods, provide biomedical insights and relevant hypotheses for specific cancer types

Proteogenomic landscape of breast cancer tumorigenesis and targeted therapy

The integration of mass spectrometry-based proteomics with next-generation DNA and RNA sequencing profiles tumors more comprehensively. Here this "proteogenomics" approach was applied to 122 treatment-naive primary breast cancers accrued to preserve post-translational modifications, including protein phosphorylation and acetylation. Proteogenomics challenged standard breast cancer diagnoses, provided detailed analysis of the ERBB2 amplicon, defined tumor subsets that could benefit from immune checkpoint therapy, and allowed more accurate assessment of Rb status for prediction of CDK4/6 inhibitor responsiveness. Phosphoproteomics profiles uncovered novel associations between tumor suppressor loss and targetable kinases. Acetylproteome analysis highlighted acetylation on key nuclear proteins involved in the DNA damage response and revealed cross-talk between cytoplasmic and mitochondrial acetylation and metabolism. Our results underscore the potential of proteogenomics for clinical investigation of breast cancer through more accurate annotation of targetable pathways and biological features of this remarkably heterogeneous malignancy

Consistent community detection in uni-layer and multi-layer networks

Over the last two decades, we have witnessed a massive explosion of our data collection abilities and the birth of a "big data" age. This has led to an enormous interest in statistical inference of a new type of complex data structure, a graph or network. The surge in interdisciplinary interest on statistical analysis of network data has been driven by applications in Neuroscience, Genetics, Social sciences, Computer science, Economics and Marketing. A network consists of a set of nodes or vertices, representing a set of entities, and a set of edges, representing the relations or interactions among the entities. Networks are flexible frameworks that can model many complex systems. In the majority of the network examples dealt with in the literature, the relations between nodes are assumed to be of the same type such as web page linkage, friendship, co-authorship or protein-protein interaction. However, the complex networks in many modern applications are often multi-layered in the sense that they consist of multiple types of edges/relations among a group of entities. Each of those different types of relations can be viewed as creating its own network, called a layer of the multi-layer network. Multi-layer networks are a more accurate representation of many complex systems since many entities in those systems are involved simultaneously in multiple interactions. In this dissertation we view multi-layer networks in the broad sense that includes multiple types of relations as well as multiple information sources on the same set of nodes (e.g., multiple trials or multiple subjects). The problem of detecting communities or clusters of nodes in a network has received considerable attention in literature. As with uni-layer networks, community detection is an important task in multi-layer networks. This dissertation aims to develop new methods and theory for community detection in both uni-layer and multi-layer networks that can be used to answer scientific questions from experimental data. For community detection in uni and multi-layer graphs, we take three approaches - (1) based on statistical random graph models, (2) based on maximizing quality functions, e.g., the modularity score and (3) based on spectral and matrix factorization methods. In Chapter 2 we consider two random graph models for community detection in multi-layer networks, the multi-layer stochastic block model (MLSBM) and a model with a restricted parameter space, the restricted multi-layer stochastic block model (RMLSBM). We derive consistency results for community assignments of the maximum likelihood estimators (MLEs) in both models where MLSBM is assumed to be the true model, and either the number of nodes or the number of types of edges or both grow. We compared MLEs in the two models among themselves and with other baseline approaches both theoretically and through simulations. We also derived minimax error rates and thresholds for achieving consistency of community detection in MLSBM, which were then used to show the advantage of the multi-layer model over a traditional alternative, the aggregate stochastic block model. In simulations RMLSBM is shown to have advantage over MLSBM when either the growth rate of the number of communities is high or the growth rate of the average degree of the component graphs in the multi-graph is low. A popular method of community detection in uni-layer networks is maximization of a partition quality function called modularity. In Chapter 3 we introduce several multi-layer network modularity measures based on different random graph null models, motivated by empirical observations from a diverse field of applications. In particular, we derived different modularities by defining the multi-layer configuration model, the multi-layer expected degree model and their various modifications as null models for multi-layer networks. These measures are then optimized to detect the optimal community assignment of nodes. We apply the methods to five real multi-layer networks - three social networks from the website Twitter, a complete neuronal network of a nematode, C-elegans and a classroom friendship network of 7th-grade students. In Chapter 4 we present a method based on the orthogonal symmetric non-negative matrix tri-factorization of the normalized Laplacian matrix for community detection in complex networks. While the exact factorization of a given order may not exist and is NP hard to compute, we obtain an approximate factorization by solving an optimization problem. We establish the connection of the factors obtained through the factorization to a non-negative basis of an invariant subspace of the estimated matrix, drawing parallel with the spectral clustering. Using such factorization for clustering in networks is motivated by analyzing a block-diagonal Laplacian matrix with the blocks representing the connected components of a graph. The method is shown to be consistent for community detection in graphs generated from the stochastic block model and the degree corrected stochastic block model. Simulation results and real data analysis show the effectiveness of these methods under a wide variety of situations, including sparse and highly heterogeneous graphs where the usual spectral clustering is known to fail. Our method also performs better than the state of the art in popular benchmark network datasets, e.g., the political web blogs and the karate club data. In Chapter 5 we once again consider the problem of estimating a consensus community structure by combining information from multiple layers of a multi-layer network or multiple snapshots of a time-varying network. Numerous methods have been proposed in the literature for the more general problem of multi-view clustering in the past decade based on the spectral clustering or a low-rank matrix factorization. As a general theme, these "intermediate fusion" methods involve obtaining a low column rank matrix by optimizing an objective function and then using the columns of the matrix for clustering. Such methods can be adapted for community detection in multi-layer networks with minimal modifications. However, the theoretical properties of these methods remain largely unexplored and most authors have relied on performance in synthetic and real data to assess the goodness of the procedures. In the absence of statistical guarantees on the objective functions, it is difficult to determine if the algorithms optimizing the objective will return a good community structure. We apply some of these methods for consensus community detection in multi-layer networks and investigate the consistency properties of the global optimizer of the objective functions under the multi-layer stochastic block model. We derive several new asymptotic results showing consistency of the intermediate fusion techniques along with the spectral clustering of mean adjacency matrix under a high dimensional setup where both the number of nodes and the number of layers of the multi-layer graph grow. We complement the asymptotic analysis with a thorough numerical study to compare the finite sample performance of the methods. Motivated by multi-subject and multi-trial experiments in neuroimaging studies, in Chapter 6 we develop a modeling framework for joint community detection in a group of related networks. The proposed model, which we call the random effects stochastic block model facilitates the study of group differences and subject specific variations in the community structure. In contrast to the previously proposed multi-layer stochastic block models, our model allows community memberships of nodes to vary in each component network or layer with a transition probability matrix, thus modeling the variation in community structure across a group of subjects or trials. We propose two methods to estimate the parameters of the model, a variational-EM algorithm and two non-parametric "two-step" methods based on spectral and matrix factorization respectively. We also develop several hypothesis tests with p-values obtained through resampling (permutation test) for differences in community structure in two groups of subjects both at the whole network level and node level. The methodology is applied to publicly available fMRI datasets from multi-subject experiments involving schizophrenia patients along with healthy controls. Our methods reveal an overall putative community structure representative of the groups as well as subject-specific variations within each group. Using our network level hypothesis tests we are able to ascertain statistically significant difference in community structure between the two groups, while our node level tests help determine the nodes that are driving the difference

Summer 2008 Research Symposium Abstract Book

Summer 2008 volume of abstracts for science research projects conducted by Trinity College students

Identifying protein complexes and disease genes from biomolecular networks

With advances in high-throughput measurement techniques, large-scale biological data, such as protein-protein interaction (PPI) data, gene expression data, gene-disease association data, cellular pathway data, and so on, have been and will continue to be produced. Those data contain insightful information for understanding the mechanisms of biological systems and have been proved useful for developing new methods in disease diagnosis, disease treatment and drug design. This study focuses on two main research topics: (1) identifying protein complexes and (2) identifying disease genes from biomolecular networks. Firstly, protein complexes are groups of proteins that interact with each other at the same time and place within living cells. They are molecular entities that carry out cellular processes. The identification of protein complexes plays a primary role for understanding the organization of proteins and the mechanisms of biological systems. Many previous algorithms are designed based on the assumption that protein complexes are densely connected sub-graphs in PPI networks. In this research, a dense sub-graph detection algorithm is first developed following this assumption by using clique seeds and graph entropy. Although the proposed algorithm generates a large number of reasonable predictions and its f-score is better than many previous algorithms, it still cannot identify many known protein complexes. After that, we analyze characteristics of known yeast protein complexes and find that not all of the complexes exhibit dense structures in PPI networks. Many of them have a star-like structure, which is a very special case of the core-attachment structure and it cannot be identified by many previous core-attachment-structure-based algorithms. To increase the prediction accuracy of protein complex identification, a multiple-topological-structure-based algorithm is proposed to identify protein complexes from PPI networks. Four single-topological-structure-based algorithms are first employed to detect raw predictions with clique, dense, core-attachment and star-like structures, respectively. A merging and trimming step is then adopted to generate final predictions based on topological information or GO annotations of predictions. A comprehensive review about the identification of protein complexes from static PPI networks to dynamic PPI networks is also given in this study. Secondly, genetic diseases often involve the dysfunction of multiple genes. Various types of evidence have shown that similar disease genes tend to lie close to one another in various biomolecular networks. The identification of disease genes via multiple data integration is indispensable towards the understanding of the genetic mechanisms of many genetic diseases. However, the number of known disease genes related to similar genetic diseases is often small. It is not easy to capture the intricate gene-disease associations from such a small number of known samples. Moreover, different kinds of biological data are heterogeneous and no widely acceptable criterion is available to standardize them to the same scale. In this study, a flexible and reliable multiple data integration algorithm is first proposed to identify disease genes based on the theory of Markov random fields (MRF) and the method of Bayesian analysis. A novel global-characteristic-based parameter estimation method and an improved Gibbs sampling strategy are introduced, such that the proposed algorithm has the capability to tune parameters of different data sources automatically. However, the Markovianity characteristic of the proposed algorithm means it only considers information of direct neighbors to formulate the relationship among genes, ignoring the contribution of indirect neighbors in biomolecular networks. To overcome this drawback, a kernel-based MRF algorithm is further proposed to take advantage of the global characteristics of biological data via graph kernels. The kernel-based MRF algorithm generates predictions better than many previous disease gene identification algorithms in terms of the area under the receiver operating characteristic curve (AUC score). However, it is very time-consuming, since the Gibbs sampling process of the algorithm has to maintain a long Markov chain for every single gene. Finally, to reduce the computational time of the MRF-based algorithm, a fast and high performance logistic-regression-based algorithm is developed for identifying disease genes from biomolecular networks. Numerical experiments show that the proposed algorithm outperforms many existing methods in terms of the AUC score and running time. To summarize, this study has developed several computational algorithms for identifying protein complexes and disease genes from biomolecular networks, respectively. These proposed algorithms are better than many other existing algorithms in the literature