Localization is a fundamental operation for many wireless networks. While GPS is widely used for location determination, it is unavailable in many environments either due to its high cost or the lack of line of sight to the satellites (e.g., indoors, under the ground, or in a downtown canyon). The limitations of GPS have motivated researchers to develop many localization schemes to infer locations based on measured wireless signals. However, most of these existing schemes focus on localization in static wireless networks. As many wireless networks are mobile (e.g., mobile sensor networks, disaster recovery networks, and vehicular networks), we focus on localization in mobile networks in this thesis. We analyze real mobility traces and find that they exhibit temporal stability and low-rank structure. Motivated by this observation, we develop three novel localization schemes to accurately determine locations in mobile networks: 1. Low Rank based Localization (LRL), which exploits the low-rank structure in mobility. 2. Temporal Stability based Localization (TSL), which leverages the temporal stability. 3. Temporal Stability and Low Rank based Localization (TSLRL), which incorporates both the temporal stability and the low-rank structure. These localization schemes are general and can leverage either mere connectivity (i.e., range-free localization) or distance estimation between neighbors (i.e., range-based localization). Using extensive simulations and testbed experiments, we show that our new schemes significantly outperform state-of-the-art localization schemes under a wide range of scenarios and are robust to measurement errors. / text

Indiana University-Purdue University Indianapolis (IUPUI) / The successful treatment and potential eradication of many complex diseases, such as cancer, begins with elucidating the convoluted mapping of molecular profiles to phenotypical manifestation. Our observed molecular profiles (e.g., genomics, transcriptomics, epigenomics) are often high-dimensional and are collected from patient samples falling into heterogeneous disease subtypes. Interpretable learning from such data calls for sparsity-driven models. This dissertation addresses the high dimensionality, sparsity, and heterogeneity issues when analyzing multiple-omics data, where each method is implemented with a concomitant R package. First, we examine challenges in submatrix identification, which aims to find subgroups of samples that behave similarly across a subset of features. We resolve issues such as two-way sparsity, non-orthogonality, and parameter tuning with an adaptive thresholding procedure on the singular vectors computed via orthogonal iteration. We validate the method with simulation analysis and apply it to an Alzheimer’s disease dataset. The second project focuses on modeling relationships between large, matched datasets. Exploring regressional structures between large data sets can provide insights such as the effect of long-range epigenetic influences on gene expression. We present a high-dimensional version of mixture multivariate regression to detect patient clusters, each with different correlation structures of matched-omics datasets. Results are validated via simulation and applied to matched-omics data sets. In the third project, we introduce a novel approach to modeling spatial transcriptomics (ST) data with a spatially penalized multinomial model of the expression counts. This method solves the low-rank structures of zero-inflated ST data with spatial smoothness constraints. We validate the model using manual cell structure annotations of human brain samples. We then applied this technique to additional ST datasets. / 2025-05-22