Graduation Semester and Year
Fall 2025
Language
English
Document Type
Dissertation
Degree Name
Doctor of Philosophy in Mathematics
Department
Mathematics
First Advisor
Pedro Maia
Abstract
Large-scale electrophysiology experiments produce high-dimensional local field potential (LFP) datasets whose size and heterogeneity challenge classical analysis methods. This thesis develops a unified and scalable computational framework for comparing multichannel rodent LFP recordings collected under formalin injection and electrical stimulation.
We begin by outlining the biological context and formalizing the core research questions in precise mathematical terms. Building on this foundation, we introduce three complementary methodological contributions. First, a window-based fusion framework enables scalable column-wise comparison of large matrices by replacing quadratic-distance computations with segmented, statistically fused evidence. Second, a landmark-based clustering approach provides efficient approximations to pairwise Euclidean distances, with explicit operation-count models and a practical scaling rule that generalizes across synthetic and real data. Third, a row-wise analysis framework based on Elastic-Net PCA and CCA yields low-variance geometric embeddings that support reliable statistical comparison between baseline and post-treatment recordings.
To detect perturbation-induced anomalies, we develop the Combined Outlier Score (COS), an ensemble of nine unsupervised detectors that integrates geometric, probabilistic, and density-based signals into a unified anomaly measure.
Applied to the rodent migraine recovery dataset, the full framework identifies rest intervals that statistically match baseline structure, quantifies deviations following stimulation, and reveals interpretable temporal recovery patterns. The results demonstrate that segmentation-based fusion, landmark approximation, row-wise embeddings, and ensemble outlier detection together form a robust and computationally efficient toolkit for analyzing high-dimensional neural data.
This thesis provides a coherent methodological foundation for scalable similarity assessment and anomaly detection in large electrophysiology datasets, with applicability to a broad range of big-data time-series domains.
Keywords
Electrophysiology Local Field Potentials (LFP) Distance-Based Analysis Column-Wise Fusion Landmark Sampling Clustering-Based Approximation Euclidean Distance Approximation Elastic-Net PCA Canonical Correlation Analysis (CCA) Row-Wise Embeddings Outlier Detection Combined Outlier Score (COS) High-Dimensional Neural Data Rodent Formalin/Stimulation Dataset Temporal Recovery Patterns Big-Data Time Series
License
This work is licensed under a Creative Commons Attribution 4.0 International License.
Recommended Citation
Asiri, Zahra, "Distance-Based Statistical Methods and Outlier Detection in Large-Scale Electrophysiology Data" (2025). Mathematics Dissertations. 270.
https://mavmatrix.uta.edu/math_dissertations/270