You are here
Search results
(1  12 of 12)
 Title
 Machine learning method for authorship attribution
 Creator
 Hu, Xianfeng
 Date
 2015
 Collection
 Electronic Theses & Dissertations
 Description

MACHINE LEARNING METHOD FOR AUTHORSHIP ATTRIBUTIONBy Xianfeng HuBroadly speaking, the authorship identification or authorship attribution problem is to determine the authorship of a given sample such as text, painting and so on. Our main work is to develop an effective and mathesound approach for the analysis of authorship of doubted books.Inspired by various authorship attribution problems in the history of literature and the application of machine learning in the study of literary...
Show moreMACHINE LEARNING METHOD FOR AUTHORSHIP ATTRIBUTIONBy Xianfeng HuBroadly speaking, the authorship identification or authorship attribution problem is to determine the authorship of a given sample such as text, painting and so on. Our main work is to develop an effective and mathesound approach for the analysis of authorship of doubted books.Inspired by various authorship attribution problems in the history of literature and the application of machine learning in the study of literary stylometry, we develop a rigorous new method for the mathematical analysis of authorship by testing for a socalled chronodivide in writing styles. Our method incorporates some of the latest advances in the study of au thorship attribution, particularly techniques from support vector machines. By introducing the notion of relative frequency of word and phrases as feature ranking metrics our method proves to be highly effective and robust.Applying our method to the classical Chinese novel Dream of the Red Chamber has led to convincing if not irrefutable evidence that the first 80 chapters and the last 40 chapters of the book were written by two different authors.Also applying our method to the English novel Micro, we are able to confirm the existence of the chronodivide and identify its location so that we can differentiate the contribution of Michael Crichton and Richard Preston, the authors of the novel.We have also tested our method to the other three Great Classical Novels in Chinese. As expected no chronodivides have been found in these novels. This provides further evidenceof the robustness of our method. We also proposed a new approach to authorship identification to solve the open classproblem where the candidate group is nonexistent or very large, which is reliably scaled from a new method we have developed for the closed class problem in which the candidates author pool is small. This is attained by using support vector machines and by analyzing the relative frequencies of common words in the function words dictionary and most frequently used words. This method scales very nicely to the open class problem through a novel author randomization technique, where an author in question is compared repeatedly to randomly selected authors. The author randomization technique proves to be highly robust and effective. Using our approaches we have found answers to three well known authorship controversies: (1) Did Robert Galbraith write Cuckoo’s Calling? (2) Did Harper Lee write To Kill a Mockingbird or did her friend Truman Capote write it? (3) Did Bill Ayers write Obama’s autobiography Dreams From My Father?
Show less
 Title
 A novel approach to blind source separation and extraction in audio
 Creator
 Wang, Xun
 Date
 2015
 Collection
 Electronic Theses & Dissertations
 Description

In this thesis, the blind source separation (BSS) on digitalaudio signals via background learning by several differentmethodologies is carefully studied. In the daily auditory, acoustic audio signals are usually mixtures of different sources, including foreground andbackground noises. Most of the time, we only want to receive the foregroundsources and get rid of the background ones. Because of the randomness ofvarious situations, it is very difficult to perform this separation without knowing...
Show moreIn this thesis, the blind source separation (BSS) on digitalaudio signals via background learning by several differentmethodologies is carefully studied. In the daily auditory, acoustic audio signals are usually mixtures of different sources, including foreground andbackground noises. Most of the time, we only want to receive the foregroundsources and get rid of the background ones. Because of the randomness ofvarious situations, it is very difficult to perform this separation without knowing the detailed information. Even if the background noises are not dominating the foreground sources, or even much weaker, it is still a difficult problem, especially for the case that there are more than three sources including the noise. This also makes it even more difficult to separate different sources from mixed signals. In this thesis, a novel approach to solve cancellation kernels is provided by using a modified sigular value decomposition method. The main focus is to use this new technique to estimate the cacellation kernels with good results in short computational time.In this work, some background information for blind source separation of audio will be first introduced. Next, the knowledge of four different methods for solving this type of problems is mentioned. Split Bregman has been studied by others in solving cancellation kernels for the separation of speech signals. We apply proximity operator method to solve the cancellation kernels for BSS of audio signal processing. It has been applied to study image processing by other researchers. Quadratic programming method has been applied to solve cancellation kernels by Wang and Zhou. We provide a new approach to bring sparseness to cancellation kernels by using quadratic programming. We developed a modified singular value decomposition (SVD) algorithm based on the numerical experiments. It is a new technique to estimate cancellation kernels for BSS of audio signals. The detailed information and schemes are presented in Chapter 3. Then, in the fouth chapter, there are different numerical simulation examples according to different scenarios. We compare the results of our modified SVD method with others methods, and conclude that our modified SVD is the best approach.
Show less
 Title
 Novel simulation and data processing algorithms for eddy current inspection
 Creator
 Efremov, Anton
 Date
 2020
 Collection
 Electronic Theses & Dissertations
 Description

Eddy Current Testing (ECT) is a widely used technique in the area of Nondestructive Evaluation. It offers a cheap, fast, noncontact way for finding surface and subsurface defects in a conductive material. Due to development of new designs of eddy current probe coils and advance of model based solutions to inverse problems in ECT, there is an emerging need for fast and accurate numerical methods for efficient modeling and processing of the data. This work contributes to the two directions of...
Show moreEddy Current Testing (ECT) is a widely used technique in the area of Nondestructive Evaluation. It offers a cheap, fast, noncontact way for finding surface and subsurface defects in a conductive material. Due to development of new designs of eddy current probe coils and advance of model based solutions to inverse problems in ECT, there is an emerging need for fast and accurate numerical methods for efficient modeling and processing of the data. This work contributes to the two directions of computational ECT: eddy current inspection simulation ("forward problem") and analysis of the measured data for automated defect detection ("inverse problem").A new approach to simulate lowfrequency electromagnetics in 3D is presented, based on a combination of a frequencydomain reduced vector potential formulation with a boundary condition based on DirichlettoNeumann operator. The equations are solved via a Finite Element Method (FEM), and a novel technique for the fast solution of the related linear system is proposed. The performance of the method is analyzed for a few representative ECT problems. The obtained numerical results are validated against analytic solutions, other simulation codes, and experimental data.The inverse problem of interpreting measured ECT data is also a significant challenge in many practical applications. Very often, the defect indication in a measurement is very subtle due to the large contribution from the geometry of the test sample, making defect detection very difficult. This thesis presents a novel approach to address this problem. The developed algorithm is applied to real problems of detecting defects under steel fasteners in aircraft geometry using 2D data obtained from a raster scan of a multilayer structure with a low frequency eddy current excitation and GMR (Giant Magnetoresistive) sensors. The algorithm is also applied to the data obtained from EC inspection of heat exchange tubes in nuclear power plant.
Show less
 Title
 TENSOR LEARNING WITH STRUCTURE, GEOMETRY AND MULTIMODALITY
 Creator
 Sofuoglu, Seyyid Emre
 Date
 2022
 Collection
 Electronic Theses & Dissertations
 Description

With the advances in sensing and data acquisition technology, it is now possible to collect datafrom different modalities and sources simultaneously. Most of these data are multidimensional in nature and can be represented by multiway arrays known as tensors. For instance, a color image is a thirdorder tensor defined by two indices for spatial variables and one index for color mode. Some other examples include color video, medical imaging such as EEG and fMRI, spatiotemporal data...
Show moreWith the advances in sensing and data acquisition technology, it is now possible to collect datafrom different modalities and sources simultaneously. Most of these data are multidimensional in nature and can be represented by multiway arrays known as tensors. For instance, a color image is a thirdorder tensor defined by two indices for spatial variables and one index for color mode. Some other examples include color video, medical imaging such as EEG and fMRI, spatiotemporal data encountered in urban traffic monitoring, etc.In the past two decades, tensors have become ubiquitous in signal processing, statistics andcomputer science. Traditional unsupervised and supervised learning methods developed for one dimensional signals do not translate well to higher order data structures as they get computationally prohibitive with increasing dimensionalities. Vectorizing high dimensional inputs creates problems in nearly all machine learning tasks due to exponentially increasing dimensionality, distortion of data structure and the difficulty of obtaining sufficiently large training sample size.In this thesis, we develop tensorbased approaches to various machine learning tasks. Existingtensor based unsupervised and supervised learning algorithms extend many wellknown algorithms, e.g. 2D component analysis, support vector machines and linear discriminant analysis, with better performance and lower computational and memory costs. Most of these methods rely on Tucker decomposition which has exponential storage complexity requirements; CANDECOMPPARAFAC (CP) based methods which might not have a solution; or Tensor Train (TT) based solutions which suffer from exponentially increasing ranks. Many tensor based methods have quadratic (w.r.t the size of data), or higher computational complexity, and similarly, high memory complexity. Moreover, existing tensor based methods are not always designed with the particular structure of the data in mind. Many of the existing methods use purely algebraic measures as their objective which might not capture the local relations within data. Thus, there is a necessity to develop new models with better computational and memory efficiency, with the particular structure of the data and problem in mind. Finally, as tensors represent the data with more faithfulness to the original structure compared to the vectorization, they also allow coupling of heterogeneous data sources where the underlying physical relationship is known. Still, most of the current work on coupled tensor decompositions does not explore supervised problems.In order to address the issues around computational and storage complexity of tensor basedmachine learning, in Chapter 2, we propose a new tensor train decomposition structure, which is a hybrid between Tucker and Tensor Train decompositions. The proposed structure is used to imple ment Tensor Train based supervised and unsupervised learning frameworks: linear discriminant analysis (LDA) and graph regularized subspace learning. The algorithm is designed to solve ex tremal eigenvalueeigenvector pair computation problems, which can be generalized to many other methods. The supervised framework, Tensor Train Discriminant Analysis (TTDA), is evaluated in a classification task with varying storage complexities with respect to classification accuracy and training time on four different datasets. The unsupervised approach, Graph Regularized TT, is evaluated on a clustering task with respect to clustering quality and training time on various storage complexities. Both frameworks are compared to discriminant analysis algorithms with similar objectives based on Tucker and TT decompositions.In Chapter 3, we present an unsupervised anomaly detection algorithm for spatiotemporaltensor data. The algorithm models the anomaly detection problem as a lowrank plus sparse tensor decomposition problem, where the normal activity is assumed to be lowrank and the anomalies are assumed to be sparse and temporally continuous. We present an extension of this algorithm, where we utilize a graph regularization term in our objective function to preserve the underlying geometry of the original data. Finally, we propose a computationally efficient implementation of this framework by approximating the nuclear norm using graph total variation minimization. The proposed approach is evaluated for both simulated data with varying levels of anomaly strength, length and number of missing entries in the observed tensor as well as urban traffic data. In Chapter 4, we propose a geometric tensor learning framework using product graph structures for tensor completion problem. Instead of purely algebraic measures such as rank, we use graph smoothness constraints that utilize geometric or topological relations within data. We prove the equivalence of a Cartesian graph structure to TTbased graph structure under some conditions. We show empirically, that introducing such relaxations due to the conditions do not deteriorate the recovery performance. We also outline a fully geometric learning method on product graphs for data completion.In Chapter 5, we introduce a supervised learning method for heterogeneous data sources suchas simultaneous EEG and fMRI. The proposed twostage method first extracts features taking the coupling across modalities into account and then introduces kernelized support tensor machines for classification. We illustrate the advantages of the proposed method on simulated and real classification tasks with small number of training data with high dimensionality.
Show less
 Title
 Three Variations on JohnsonLindenstrauss Maps for Submanifolds of Euclidean Space via Reach
 Creator
 Tavakoli, Arman
 Date
 2021
 Collection
 Electronic Theses & Dissertations
 Description

In this thesis we investigate 3 variations of the classical JohnsonLindenstrauss (JL) maps. In one direction we build on the earlier work of Wakin and Eftekhari (2015), by considering generalizations to manifolds with boundary. In a second direction we extend the work of Noga Alon (2003) for lower bounds for the final embedding dimension in JL maps. In the third direction, we consider matrices with fast matrixvector multiply and improve the runtime in the earlier work of Oymak, Recht and...
Show moreIn this thesis we investigate 3 variations of the classical JohnsonLindenstrauss (JL) maps. In one direction we build on the earlier work of Wakin and Eftekhari (2015), by considering generalizations to manifolds with boundary. In a second direction we extend the work of Noga Alon (2003) for lower bounds for the final embedding dimension in JL maps. In the third direction, we consider matrices with fast matrixvector multiply and improve the runtime in the earlier work of Oymak, Recht and Soltanolkotabi (2018), and Ailon and Liberty (2009).This thesis is organized into 6 chapters. The three variations are discussed in chapters 4, 5 and 6. The variation for manifolds with boundary is presented in chapter 4. The lower bound problem is discussed in chapter 5, and chapter 6 is regarding the runtime improvements. The first chapter is an introduction to JohnsonLindenstrauss maps. The second chapter is about a regularity parameter called reach and geometrical estimates for manifolds. The third chapter is regarding two geometry questions about reach that arise from the discussions in chapter 2.
Show less
 Title
 APPLICATIONS OF PERSISTENT COHOMOLOGY TO DIMENSIONALITY REDUCTION AND CLASSIFICATION PROBLEMS
 Creator
 Polanco Contreras, Luis G.
 Date
 2022
 Collection
 Electronic Theses & Dissertations
 Description

Many natural phenomena are characterized by their underlying geometry and topological invariants. Part of understanding such processes is being able to differentiate them and classify them through their topological and geometrical signatures. Many advances have been made which use topological data analysis to such end. In this work we present multiple machine learning tools aided by topological data analysis to classify and understand said phenomena.First, feature extraction from persistence...
Show moreMany natural phenomena are characterized by their underlying geometry and topological invariants. Part of understanding such processes is being able to differentiate them and classify them through their topological and geometrical signatures. Many advances have been made which use topological data analysis to such end. In this work we present multiple machine learning tools aided by topological data analysis to classify and understand said phenomena.First, feature extraction from persistence diagrams, as a tool to enrich machine learning techniques, has received increasing attention in recent years. In this paper we explore an adaptive methodology to localize features in persistent diagrams, which are then used in learning tasks. Specifically, we investigate three algorithms, CDER, GMM and HDBSCAN, to obtain adaptive template functions/features. Said features are evaluated in three classification experiments with persistence diagrams. Namely, manifold, human shapes and protein classification. In this area, our main conclusion is that adaptive template systems, as a feature extraction technique, yield competitive and often superior results in the studied examples. Moreover, from the adaptive algorithms here studied, CDER consistently provides the most reliable and robust adaptive featurization.Furthermore, we introduce a framework to construct coordinates in finite Lens spaces for data with nontrivial 1dimensional $\Z_q := \Z / \Z_q$ persistent cohomology, for $q > 2$ prime. Said coordinates are defined on an open neighborhood of the data, yet constructed with only a small subset of landmarks. We also introduce a dimensionality reduction scheme in $S^{2n−1}/ \Z_q$ (LensPCA: LPCA) and demonstrate the efficacy of the pipeline $\Z_q$ persistent cohomology $\Rightarrow$ $S^{2n−1}/ \Z_q$ coordinates $\Rightarrow$ LPCA, for nonlinear (topological) dimensionality reduction. This methodology allows us to capture and preserve geometrical and topological information through a very efficient dimensionality reduction algorithm.Finally, to make use of some of the most powerful tools in algebraic topology we improve on methodologies that make use of persistent 2dimensional homology to obtain quasiperiodic scores that indicate the degree of periodicity or quasiperiodicity of a signal. There is a significant computational disadvantage in this approach since it requires the often expensive computation of 2dimensional persistent homology.Our contribution in this area uses the algebraic structure of the cohomology ring to obtain classes in the 2dimensional persistent diagram by only using classes in dimension 1, saving valuable computational time in this manner and obtaining more reliable quasiperiodicity scores. We develop an algorithm that allows us to effectively compute the cohomological death and birth of a persistent cup product expression. This allows us to define a quasiperiodic score that reliably separates periodic from quasiperiodic time series.
Show less
 Title
 Efficient Distributed Algorithms : Better Theory and Communication Compression
 Creator
 LI, YAO
 Date
 2022
 Collection
 Electronic Theses & Dissertations
 Description

Largescale machine learning models are often trained by distributed algorithms over either centralized or decentralized networks. The former uses a central server to aggregate the information of local computing agents and broadcast the averaged parameters in a masterslave architecture. The latter considers a connected network formed by all agents. The information can only be exchanged with accessible neighbors with a mixing matrix of communication weights encoding the network's topology....
Show moreLargescale machine learning models are often trained by distributed algorithms over either centralized or decentralized networks. The former uses a central server to aggregate the information of local computing agents and broadcast the averaged parameters in a masterslave architecture. The latter considers a connected network formed by all agents. The information can only be exchanged with accessible neighbors with a mixing matrix of communication weights encoding the network's topology. Compared with centralized optimization, decentralization facilitates data privacy and reduces the communication burden of the single central agent due to model synchronization, but the connectivity of the communication network weakens the theoretical convergence complexity of the decentralized algorithms. Therefore, there are still gaps between decentralized and centralized algorithms in terms of convergence conditions and rates. In the first part of this dissertation, we consider two decentralized algorithms: EXTRA and NIDS, which both converge linearly with strongly convex objective functions and answer two questions regarding them. \textit{What are the optimal upper bounds for their stepsizes?} \textit{Do decentralized algorithms require more properties on the functions for linear convergence than centralized ones?} More specifically, we relax the required conditions for linear convergence of both algorithms. For EXTRA, we show that the stepsize is comparable to that of centralized algorithms. For NIDS, the upper bound of the stepsize is shown to be exactly the same as the centralized ones. In addition, we relax the requirement for the objective functions and the mixing matrices. We provide the linear convergence results for both algorithms under the weakest conditions.As the number of computing agents and the dimension of the model increase, the communication cost of parameter synchronization becomes the major obstacle to efficient learning. Communication compression techniques have exhibited great potential as an antidote to accelerate distributed machine learning by mitigating the communication bottleneck. In the rest of the dissertation, we propose compressed residual communication frameworks for both centralized and decentralized optimization and design different algorithms to achieve efficient communication. For centralized optimization, we propose DORE, a modified parallel stochastic gradient descent method with a bidirectional residual compression, to reduce over $95\%$ of the overall communication. Our theoretical analysis demonstrates that the proposed strategy has superior convergence properties for both strongly convex and nonconvex objective functions. Existing works mainly focus on smooth problems and compressing DGDtype algorithms for decentralized optimization. The class of smooth objective functions and the sublinear convergence rate under relatively strong assumptions limit these algorithms' application and practical performance. Motivated by primaldual algorithms, we propose ProxLEAD, a linear convergent decentralized algorithm with compression, to tackle strongly convex problems with a nonsmooth regularizer. Our theory describes the coupled dynamics of the inexact primal and dual update as well as compression error without assuming bounded gradients. The superiority of the proposed algorithm is demonstrated through the comparison with stateoftheart algorithms in terms of convergence complexities and numerical experiments. Our algorithmic framework also generally enlightens the compressed communication on other primaldual algorithms by reducing the impact of inexact iterations.
Show less
 Title
 GENERATIVE SIGNAL PROCESSING THROUGH MULTILAYER MULTISCALE WAVELET MODELS
 Creator
 He, Jieqian
 Date
 2021
 Collection
 Electronic Theses & Dissertations
 Description

Wavelet analysis and deep learning are two popular fields for signal processing. The scattering transform from wavelet analysis is a recently proposed mathematical model for convolution neural networks. Signals with repeated patterns can be analyzed using the statistics from such models. Specifically, signals from certain classes can be recovered from related statistics. We first focus on recovering 1D deterministic dirac signals from multiscale statistics. We prove a dirac signal can be...
Show moreWavelet analysis and deep learning are two popular fields for signal processing. The scattering transform from wavelet analysis is a recently proposed mathematical model for convolution neural networks. Signals with repeated patterns can be analyzed using the statistics from such models. Specifically, signals from certain classes can be recovered from related statistics. We first focus on recovering 1D deterministic dirac signals from multiscale statistics. We prove a dirac signal can be recovered from multiscale statistics up to a translation and reflection. Then we switch to a stochastic version, modeled using Poisson point processes, and prove wavelet statistics at small scales capture the intensity parameter of Poisson point processes. We also design a scattering generative adversarial network (GAN) to generate new Poisson point samples from statistics of multiple given samples. Next we consider texture images. We successfully synthesize new textures given one sample from the texture class through multiscale, multilayer wavelet models. Finally, we analyze and prove why the multiscale multilayer model is essential for signal recovery, especially natural texture images.
Show less
 Title
 Wavelet Scattering and Graph Representations for Atomic Structures
 Creator
 Brumwell, Xavier
 Date
 2021
 Collection
 Electronic Theses & Dissertations
 Description

Machine learning for quantum chemistry has been gaining much traction in recent years. In this thesis, we address the problem of predicting the ground state energy from a collection of atoms defined by their positions and charges. The ground state energy of an atomic structure is invariant with respect to isometries and permutations. Additionally the energy is multiscale in nature and varies smoothly with movements of the atoms. We develop a wavelet scattering model which encodes all of these...
Show moreMachine learning for quantum chemistry has been gaining much traction in recent years. In this thesis, we address the problem of predicting the ground state energy from a collection of atoms defined by their positions and charges. The ground state energy of an atomic structure is invariant with respect to isometries and permutations. Additionally the energy is multiscale in nature and varies smoothly with movements of the atoms. We develop a wavelet scattering model which encodes all of these properties and scales better than commonly used computational chemistry models. We first demonstrate that this representation has excellent predictive ability on amorphous lithium silicon structures. We extend this model and improve its generalizability as displayed by predictions on several types of lithium silicon systems which are not included in the model training. Finally we take some of the principles from the wavelet scattering approach and apply them to a graph based model to generate a rich representation. This requires developing novel ways to encode the bond angle and multiscale aspects of the atomic structure for the graph. We test this model on a data set of quantum molecular dynamics simulations and get results that are competitive with the state of the art.
Show less
 Title
 AUTOPARAMETRIZED KERNEL METHODS FOR BIOMOLECULAR MODELING
 Creator
 Szocinski, Timothy Andrew
 Date
 2021
 Collection
 Electronic Theses & Dissertations
 Description

Being able to predict various physical quantities of biomolecules is of great importance to biologists, chemists, and pharmaceutical companies. By applying machine learning techniques to develop these predictive models, we find much success in our endeavors. Advanced mathematical techniques involving graph theory, algebraic topology, differential geometry, etc. have been very profitable in generating firstrate biomolecular representations that are used to train a variety of machine learning...
Show moreBeing able to predict various physical quantities of biomolecules is of great importance to biologists, chemists, and pharmaceutical companies. By applying machine learning techniques to develop these predictive models, we find much success in our endeavors. Advanced mathematical techniques involving graph theory, algebraic topology, differential geometry, etc. have been very profitable in generating firstrate biomolecular representations that are used to train a variety of machine learning models. Some of these representations are dependent on a choice of kernel function along with parameters that determine its shape. These kernelbased methods of producing features require careful tuning of the kernel parameters, and the tuning cost increases exponentially as more kernels are involved. This limitation largely restricts us to the use of machine learning models with less hyperparameters, such as random forest (RF) and gradientboosting trees (GBT), thus precluding the use of neural networks for kernelbased representations. To alleviate these concerns, we have developed the autoparametrized weighted elementspecific graph neural network (AweGNN), which uses kernelbased geometric graph features in which the kernel parameters are automatically updated throughout the training to reach an optimal combination of kernel parameters. The AweGNN models have shown to be particularly success in toxicity and solvation predictions, especially when a multitask approach is taken. Although the AweGNN had introduced hundreds of parameters that were automatically tuned, the ability to include multiple kernel types simultaneously was hindered because of the computational expense. In response, the GPUenhanced AweGNN was developed to tackle the issue. Working with GPU architecture, the AweGNN's computation speed was greatly enhanced. To achieve a more comprehensive representation, we suggested a network consisting of fixed topological and spectral auxiliary features to bolster the original AweGNN success. The proposed network was tested on new hydration and solubility datasets, with excellent results. To extend the autoparametrized kernel technique to include features of a different type, we introduced the theoretical foundation for building an autoparametrized spectral layer, which uses kernelbased spectral features to represent biomolecular structures. In this dissertation, we explore some underlying notions of mathematics useful in our models, review important topics in machine learning, discuss techniques and models used in molecular biology, detail the AweGNN architecture and results, and test and expand new concepts pertaining to these autoparametrized kernel methods.
Show less
 Title
 Estimating covariance structure in high dimensions
 Creator
 Maurya, Ashwini
 Date
 2016
 Collection
 Electronic Theses & Dissertations
 Description

"Many of scientific domains rely on extracting knowledge from highdimensional data sets to provide insights into complex mechanisms underlying these data. Statistical modeling has become ubiquitous in the analysis of high dimensional data for exploring the largescale gene regulatory networks in hope of developing better treatments for deadly diseases, in search of better understanding of cognitive systems, and in prediction of volatility in stock market in the hope of averting the potential...
Show more"Many of scientific domains rely on extracting knowledge from highdimensional data sets to provide insights into complex mechanisms underlying these data. Statistical modeling has become ubiquitous in the analysis of high dimensional data for exploring the largescale gene regulatory networks in hope of developing better treatments for deadly diseases, in search of better understanding of cognitive systems, and in prediction of volatility in stock market in the hope of averting the potential risk. Statistical analysis in these highdimensional data sets yields better results only if an estimation procedure exploits hidden structures underlying the data. This thesis develops flexible estimation procedures with provable theoretical guarantees for estimating the unknown covariance structures underlying data generating process. Of particular interest are procedures that can be used on high dimensional data sets where the number of samples n is much smaller than the ambient dimension p. Due to the importance of structure estimation, the methodology is developed for the estimation of both covariance and its inverse in parametric and as well in nonparametric framework."Page ii.
Show less
 Title
 Community detection in temporal multilayer networks
 Creator
 Alsharoa, Esraa Mustafa
 Date
 2019
 Collection
 Electronic Theses & Dissertations
 Description

"Many real world systems and relational data can be modeled as networks or graphs. With the availability of large amounts of network data, it is important to be able to reduce the network's dimensionality and extract useful information from it. A key approach to network data reduction is community detection. The objective of community detection is to summarize the network by a set of modules, where the similarity within the modules is maximized while the similarity between different modules...
Show more"Many real world systems and relational data can be modeled as networks or graphs. With the availability of large amounts of network data, it is important to be able to reduce the network's dimensionality and extract useful information from it. A key approach to network data reduction is community detection. The objective of community detection is to summarize the network by a set of modules, where the similarity within the modules is maximized while the similarity between different modules is minimized. Early work in graph based community detection methods focused on static or single layer networks. This type of networks is usually considered as an oversimplification of many real world complex systems, such as social networks where there may be different types of relationships that evolve with time. Consequently, there is a need for a meaningful representation of such complex systems. Recently, multilayer networks have been used to model complex systems where the objects may interact through different mechanisms. However, there is limited amount of work in community detection methods for dynamic and multilayer networks. In this thesis, we focus on detecting and tracking the community structure in dynamic and multilayer networks. Two particular applications of interest are considered including temporal social networks and dynamic functional connectivity networks (dFCNs) of the brain. In order to detect the community structure in dynamic singlelayer and multilayer networks, we have developed methods that capture the structure of these complex networks. In Chapter 2, a lowrank + sparse estimation based evolutionary spectral clustering approach is proposed to detect and track the community structure in temporal networks. The proposed method tries to decompose the network into lowrank and sparse parts and obtain smooth cluster assignments by minimizing the subspace distance between consecutive time points, simultaneously. Effectiveness of the proposed approach is evaluated on several synthetic and real social temporal networks and compared to the existing stateoftheart algorithms. As the method developed in Chapter 2 is limited to dynamic singlelayer networks and can only take limited amount of historic information into account, a tensorbased approach is developed in Chapter 3 to detect the community structure in dynamic singlelayer and multilayer networks. The proposed framework is used to track the change points as well as identify the community structure across time and multiple subjects of dFCNs constructed from resting state functional magnetic resonance imaging (rsfMRI) data. The dFCNs are summarized into a set of FC states that are consistent over time and subjects. The detected community structures are evaluated using a consistency measure. In Chapter 4, an informationtheoretic approach is introduced to aggregate the dynamic networks and identify the time points that are topologically similar to combine them into a tensor. The community structure of the reduced network is then detected using a tensor based approach similar to the one described in Chapter 3. In Chapter 5, a temporal block spectral clustering framework is introduced to detect and track the community structure of multilayer temporal networks. A set of intra and interadjacency matrices is constructed and combined to create a set of temporal supraadjacency matrices. In particular, both the connections between nodes of the network within a time window, i.e. intralayer adjacency, as well as the connections between nodes across different time windows, i.e. interlayer adjacency are taken into account. The community structure is then detected by applying spectral clustering to these supraadjacency matrices. The proposed approach is evaluated on dFCNs constructed from rsfMRI across time and subjects revealing dynamic connectivity patterns between the resting state networks (RSNs)."Pages iiiii.
Show less