Advisory Committee Chair
Abidin Yildirim
Document Type
Dissertation
Date of Award
2024
Degree Name by School
Doctor of Philosophy (PhD) School of Engineering
Abstract
In graph theory, a fundamental problem arises when signals or images are transformed into graphs where they are subsequently represented in the form of matrices, typically as Adjacency or Laplacian matrices. As the number of the samples increases, the dimensionality of these matrices also increases, leading to the "curse of dimensionality." This increase in dimensionality poses significant computational challenges, particularly in biomedical signal analysis or computer vision applications, where the computational efficiency of large-scale data is crucial. Traditional methods of feature extraction and then clustering become computationally intensive and less effective in handling of high-dimensional data, underscoring the need for innovative approaches. These approaches should be capable of extracting dominant features that encapsulate the unique characteristics of the data, thereby improving accuracy and enhancing computational efficiency. This dissertation is addressing these drawbacks by leveraging the Gershgorin Circle theorem (GC) to introduce an innovative approach for enhanced feature extraction and clustering; specifically designed to overcome the hurdles of increased dimensionality in graph-based data representation. The Gershgorin Circle Feature Extraction (GCFE) method is presented here as an innovative approach for biosignal processing. By modifying the Weighted Laplacian Matrix and then utilizing visibility graphs, GCFE not only achieves superior classification accuracy but also reduces significantly computational time across various datasets. The GCFE method outperforms existing techniques, offering a scalable and robust solution for real-time biomedical signal classification. Additionally, the application of GC theorem is expanded into computer vision, demonstrating a dimensionality reduction technique for the Weighted Laplacian Matrix that showcases remarkable accuracy and consistency across different image patch sizes and graph types. Despite its irreversible feature reduction, GCFE efficiently preserves essential features through precise eigenvalue inclusion, highlighting its potential in resource-constrained environments and expanding its applicability beyond biomedical signals to include computer vision applications. Also, the dissertation introduces a novel clustering algorithm, G-NMS (Gershgorin–Non-Maximum Suppression), which combines the geometric principles of the GC theorem with a deep learning post-processing technique, Non-Maximum Suppression. Tested on synthetic neural datasets, G-NMS demonstrates exceptional accuracy and reliability, outperforming established clustering algorithms. This innovative approach not only offers a new perspective on spike clustering applications but also opens avenues for future research in optimizing clustering algorithms through advanced mathematical theorems and deep learning techniques. In conclusion, by taking advantage of the Gershgorin Circle theorem, this research contributes significantly to biomedical signal analysis, computer vision, and clustering algorithms, presenting efficient, accurate, and innovative methods that promise further advancements in data analysis and interpretation. Future research will explore alternative eigenvalue inclusion theorems and enhance algorithmic robustness.
Recommended Citation
Patel, Sahaj Anilbhai, "The Efficiency Impact Of Gershgorin Circle Theorem For Feature Extraction In Computer Vision And Biomedical Signal Analysis" (2024). All ETDs from UAB. 3870.
https://digitalcommons.library.uab.edu/etd-collection/3870
