Matching Items (10)
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- All Subjects: Signal Processing
- All Subjects: Statistics
- Creators: Cochran, Douglas
Description
This thesis examines the application of statistical signal processing approaches to data arising from surveys intended to measure psychological and sociological phenomena underpinning human social dynamics. The use of signal processing methods for analysis of signals arising from measurement of social, biological, and other non-traditional phenomena has been an important and growing area of signal processing research over the past decade. Here, we explore the application of statistical modeling and signal processing concepts to data obtained from the Global Group Relations Project, specifically to understand and quantify the effects and interactions of social psychological factors related to intergroup conflicts. We use Bayesian networks to specify prospective models of conditional dependence. Bayesian networks are determined between social psychological factors and conflict variables, and modeled by directed acyclic graphs, while the significant interactions are modeled as conditional probabilities. Since the data are sparse and multi-dimensional, we regress Gaussian mixture models (GMMs) against the data to estimate the conditional probabilities of interest. The parameters of GMMs are estimated using the expectation-maximization (EM) algorithm. However, the EM algorithm may suffer from over-fitting problem due to the high dimensionality and limited observations entailed in this data set. Therefore, the Akaike information criterion (AIC) and the Bayesian information criterion (BIC) are used for GMM order estimation. To assist intuitive understanding of the interactions of social variables and the intergroup conflicts, we introduce a color-based visualization scheme. In this scheme, the intensities of colors are proportional to the conditional probabilities observed.
ContributorsLiu, Hui (Author) / Taylor, Thomas (Thesis advisor) / Cochran, Douglas (Thesis advisor) / Zhang, Junshan (Committee member) / Arizona State University (Publisher)
Created2012
Some topics concerning the singular value decomposition and generalized singular value decomposition
Description
This dissertation involves three problems that are all related by the use of the singular value decomposition (SVD) or generalized singular value decomposition (GSVD). The specific problems are (i) derivation of a generalized singular value expansion (GSVE), (ii) analysis of the properties of the chi-squared method for regularization parameter selection in the case of nonnormal data and (iii) formulation of a partial canonical correlation concept for continuous time stochastic processes. The finite dimensional SVD has an infinite dimensional generalization to compact operators. However, the form of the finite dimensional GSVD developed in, e.g., Van Loan does not extend directly to infinite dimensions as a result of a key step in the proof that is specific to the matrix case. Thus, the first problem of interest is to find an infinite dimensional version of the GSVD. One such GSVE for compact operators on separable Hilbert spaces is developed. The second problem concerns regularization parameter estimation. The chi-squared method for nonnormal data is considered. A form of the optimized regularization criterion that pertains to measured data or signals with nonnormal noise is derived. Large sample theory for phi-mixing processes is used to derive a central limit theorem for the chi-squared criterion that holds under certain conditions. Departures from normality are seen to manifest in the need for a possibly different scale factor in normalization rather than what would be used under the assumption of normality. The consequences of our large sample work are illustrated by empirical experiments. For the third problem, a new approach is examined for studying the relationships between a collection of functional random variables. The idea is based on the work of Sunder that provides mappings to connect the elements of algebraic and orthogonal direct sums of subspaces in a Hilbert space. When combined with a key isometry associated with a particular Hilbert space indexed stochastic process, this leads to a useful formulation for situations that involve the study of several second order processes. In particular, using our approach with two processes provides an independent derivation of the functional canonical correlation analysis (CCA) results of Eubank and Hsing. For more than two processes, a rigorous derivation of the functional partial canonical correlation analysis (PCCA) concept that applies to both finite and infinite dimensional settings is obtained.
ContributorsHuang, Qing (Author) / Eubank, Randall (Thesis advisor) / Renaut, Rosemary (Thesis advisor) / Cochran, Douglas (Committee member) / Gelb, Anne (Committee member) / Young, Dennis (Committee member) / Arizona State University (Publisher)
Created2012
Description
Modern measurement schemes for linear dynamical systems are typically designed so that different sensors can be scheduled to be used at each time step. To determine which sensors to use, various metrics have been suggested. One possible such metric is the observability of the system. Observability is a binary condition determining whether a finite number of measurements suffice to recover the initial state. However to employ observability for sensor scheduling, the binary definition needs to be expanded so that one can measure how observable a system is with a particular measurement scheme, i.e. one needs a metric of observability. Most methods utilizing an observability metric are about sensor selection and not for sensor scheduling. In this dissertation we present a new approach to utilize the observability for sensor scheduling by employing the condition number of the observability matrix as the metric and using column subset selection to create an algorithm to choose which sensors to use at each time step. To this end we use a rank revealing QR factorization algorithm to select sensors. Several numerical experiments are used to demonstrate the performance of the proposed scheme.
ContributorsIlkturk, Utku (Author) / Gelb, Anne (Thesis advisor) / Platte, Rodrigo (Thesis advisor) / Cochran, Douglas (Committee member) / Renaut, Rosemary (Committee member) / Armbruster, Dieter (Committee member) / Arizona State University (Publisher)
Created2015
Description
The detection and characterization of transients in signals is important in many wide-ranging applications from computer vision to audio processing. Edge detection on images is typically realized using small, local, discrete convolution kernels, but this is not possible when samples are measured directly in the frequency domain. The concentration factor edge detection method was therefore developed to realize an edge detector directly from spectral data. This thesis explores the possibilities of detecting edges from the phase of the spectral data, that is, without the magnitude of the sampled spectral data. Prior work has demonstrated that the spectral phase contains particularly important information about underlying features in a signal. Furthermore, the concentration factor method yields some insight into the detection of edges in spectral phase data. An iterative design approach was taken to realize an edge detector using only the spectral phase data, also allowing for the design of an edge detector when phase data are intermittent or corrupted. Problem formulations showing the power of the design approach are given throughout. A post-processing scheme relying on the difference of multiple edge approximations yields a strong edge detector which is shown to be resilient under noisy, intermittent phase data. Lastly, a thresholding technique is applied to give an explicit enhanced edge detector ready to be used. Examples throughout are demonstrate both on signals and images.
ContributorsReynolds, Alexander Bryce (Author) / Gelb, Anne (Thesis director) / Cochran, Douglas (Committee member) / Viswanathan, Adityavikram (Committee member) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2016-05
Description
Deconvolution of noisy data is an ill-posed problem, and requires some form of regularization to stabilize its solution. Tikhonov regularization is the most common method used, but it depends on the choice of a regularization parameter λ which must generally be estimated using one of several common methods. These methods can be computationally intensive, so I consider their behavior when only a portion of the sampled data is used. I show that the results of these methods converge as the sampling resolution increases, and use this to suggest a method of downsampling to estimate λ. I then present numerical results showing that this method can be feasible, and propose future avenues of inquiry.
ContributorsHansen, Jakob Kristian (Author) / Renaut, Rosemary (Thesis director) / Cochran, Douglas (Committee member) / Barrett, The Honors College (Contributor) / School of Music (Contributor) / Economics Program in CLAS (Contributor) / School of Mathematical and Statistical Sciences (Contributor)
Created2015-05
Description
During the inversion of discrete linear systems, noise in data can be amplified and result in meaningless solutions. To combat this effect, characteristics of solutions that are considered desirable are mathematically implemented during inversion. This is a process called regularization. The influence of the provided prior information is controlled by the introduction of non-negative regularization parameter(s). Many methods are available for both the selection of appropriate regularization parame- ters and the inversion of the discrete linear system. Generally, for a single problem there is just one regularization parameter. Here, a learning approach is considered to identify a single regularization parameter based on the use of multiple data sets de- scribed by a linear system with a common model matrix. The situation with multiple regularization parameters that weight different spectral components of the solution is considered as well. To obtain these multiple parameters, standard methods are modified for identifying the optimal regularization parameters. Modifications of the unbiased predictive risk estimation, generalized cross validation, and the discrepancy principle are derived for finding spectral windowing regularization parameters. These estimators are extended for finding the regularization parameters when multiple data sets with common system matrices are available. Statistical analysis of these estima- tors is conducted for real and complex transformations of data. It is demonstrated that spectral windowing regularization parameters can be learned from these new esti- mators applied for multiple data and with multiple windows. Numerical experiments evaluating these new methods demonstrate that these modified methods, which do not require the use of true data for learning regularization parameters, are effective and efficient, and perform comparably to a supervised learning method based on es- timating the parameters using true data. The theoretical developments are validated for one and two dimensional image deblurring. It is verified that the obtained estimates of spectral windowing regularization parameters can be used effectively on validation data sets that are separate from the training data, and do not require known data.
ContributorsByrne, Michael John (Author) / Renaut, Rosemary (Thesis advisor) / Cochran, Douglas (Committee member) / Espanol, Malena (Committee member) / Jackiewicz, Zdzislaw (Committee member) / Platte, Rodrigo (Committee member) / Arizona State University (Publisher)
Created2023
Description
Eigenvalues of the Gram matrix formed from received data frequently appear in sufficient detection statistics for multi-channel detection with Generalized Likelihood Ratio (GLRT) and Bayesian tests. In a frequently presented model for passive radar, in which the null hypothesis is that the channels are independent and contain only complex white Gaussian noise and the alternative hypothesis is that the channels contain a common rank-one signal in the mean, the GLRT statistic is the largest eigenvalue $\lambda_1$ of the Gram matrix formed from data. This Gram matrix has a Wishart distribution. Although exact expressions for the distribution of $\lambda_1$ are known under both hypotheses, numerically calculating values of these distribution functions presents difficulties in cases where the dimension of the data vectors is large. This dissertation presents tractable methods for computing the distribution of $\lambda_1$ under both the null and alternative hypotheses through a technique of expanding known expressions for the distribution of $\lambda_1$ as inner products of orthogonal polynomials. These newly presented expressions for the distribution allow for computation of detection thresholds and receiver operating characteristic curves to arbitrary precision in floating point arithmetic. This represents a significant advancement over the state of the art in a problem that could previously only be addressed by Monte Carlo methods.
ContributorsJones, Scott, Ph.D (Author) / Cochran, Douglas (Thesis advisor) / Berisha, Visar (Committee member) / Bliss, Daniel (Committee member) / Kosut, Oliver (Committee member) / Richmond, Christ (Committee member) / Arizona State University (Publisher)
Created2019
Description
The availability of data for monitoring and controlling the electrical grid has increased exponentially over the years in both resolution and quantity leaving a large data footprint. This dissertation is motivated by the need for equivalent representations of grid data in lower-dimensional feature spaces so that machine learning algorithms can be employed for a variety of purposes. To achieve that, without sacrificing the interpretation of the results, the dissertation leverages the physics behind power systems, well-known laws that underlie this man-made infrastructure, and the nature of the underlying stochastic phenomena that define the system operating conditions as the backbone for modeling data from the grid.
The first part of the dissertation introduces a new framework of graph signal processing (GSP) for the power grid, Grid-GSP, and applies it to voltage phasor measurements that characterize the overall system state of the power grid. Concepts from GSP are used in conjunction with known power system models in order to highlight the low-dimensional structure in data and present generative models for voltage phasors measurements. Applications such as identification of graphical communities, network inference, interpolation of missing data, detection of false data injection attacks and data compression are explored wherein Grid-GSP based generative models are used.
The second part of the dissertation develops a model for a joint statistical description of solar photo-voltaic (PV) power and the outdoor temperature which can lead to better management of power generation resources so that electricity demand such as air conditioning and supply from solar power are always matched in the face of stochasticity. The low-rank structure inherent in solar PV power data is used for forecasting and to detect partial-shading type of faults in solar panels.
The first part of the dissertation introduces a new framework of graph signal processing (GSP) for the power grid, Grid-GSP, and applies it to voltage phasor measurements that characterize the overall system state of the power grid. Concepts from GSP are used in conjunction with known power system models in order to highlight the low-dimensional structure in data and present generative models for voltage phasors measurements. Applications such as identification of graphical communities, network inference, interpolation of missing data, detection of false data injection attacks and data compression are explored wherein Grid-GSP based generative models are used.
The second part of the dissertation develops a model for a joint statistical description of solar photo-voltaic (PV) power and the outdoor temperature which can lead to better management of power generation resources so that electricity demand such as air conditioning and supply from solar power are always matched in the face of stochasticity. The low-rank structure inherent in solar PV power data is used for forecasting and to detect partial-shading type of faults in solar panels.
ContributorsRamakrishna, Raksha (Author) / Scaglione, Anna (Thesis advisor) / Cochran, Douglas (Committee member) / Spanias, Andreas (Committee member) / Vittal, Vijay (Committee member) / Zhang, Junshan (Committee member) / Arizona State University (Publisher)
Created2020
Description
The idea for this thesis emerged from my senior design capstone project, A Wearable Threat Awareness System. A TFmini-S LiDAR sensor is used as one component of this system; the functionality of and signal processing behind this type of sensor are elucidated in this document. Conceptual implementations of the optical and digital stages of the signal processing is described in some detail. Following an introduction in which some general background knowledge about LiDAR is set forth, the body of the thesis is organized into two main sections. The first section focuses on optical processing to demodulate the received signal backscattered from the target object. This section describes the key steps in demodulation and illustrates them with computer simulation. A series of graphs capture the mathematical form of the signal as it progresses through the optical processing stages, ultimately yielding the baseband envelope which is converted to digital form for estimation of the leading edge of the pulse waveform using a digital algorithm. The next section is on range estimation. It describes the digital algorithm designed to estimate the arrival time of the leading edge of the optical pulse signal. This enables the pulse’s time of flight to be estimated, thus determining the distance between the LiDAR and the target. Performance of this algorithm is assessed with four different levels of noise. A calculation of the error in the leading-edge detection in terms of distance is also included to provide more insight into the algorithm’s accuracy.
ContributorsRidgway, Megan (Author) / Cochran, Douglas (Thesis director) / Aberle, James (Committee member) / Barrett, The Honors College (Contributor) / Electrical Engineering Program (Contributor)
Created2022-05
Description
In this work, the author analyzes quantitative and structural aspects of Bayesian inference using Markov kernels, Wasserstein metrics, and Kantorovich monads. In particular, the author shows the following main results: first, that Markov kernels can be viewed as Borel measurable maps with values in a Wasserstein space; second, that the Disintegration Theorem can be interpreted as a literal equality of integrals using an original theory of integration for Markov kernels; third, that the Kantorovich monad can be defined for Wasserstein metrics of any order; and finally, that, under certain assumptions, a generalized Bayes’s Law for Markov kernels provably leads to convergence of the expected posterior distribution in the Wasserstein metric. These contributions provide a basis for studying further convergence, approximation, and stability properties of Bayesian inverse maps and inference processes using a unified theoretical framework that bridges between statistical inference, machine learning, and probabilistic programming semantics.
ContributorsEikenberry, Keenan (Author) / Cochran, Douglas (Thesis advisor) / Lan, Shiwei (Thesis advisor) / Dasarathy, Gautam (Committee member) / Kotschwar, Brett (Committee member) / Shahbaba, Babak (Committee member) / Arizona State University (Publisher)
Created2023