Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
Results
Showing 1 to 20 of 24 for “"Topological Data Analysis"”.
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Characterizing quantum morphology through topological data analysis
Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2025-05-01
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From Protein Folds to Chromatin: Topological Data Analysis and Deep Learning at Multiple Scales
… frameworks that integrate geometric, topological, and spatial modeling with deep learning to elucidate these structure–function relationships. CASTpFold extends the Computed Atlas of Surface Topography of Proteins by combining computational geometry, topological data analysis, and …
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Exploring topological data analysis in gene expression data topology-driven biomarker discovery and clinical outcome prediction in oncology
… in the fundamental observation that biological data has shape and this shape matters. Beneath the high-dimensional, often noisy landscape of gene expression profiles lie hidden topological structures (connected components, loops and voids) that capture the complex relationships driving cancer …
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Topological and geometric inference of data
… this in practice. Following ideas from topological data analysis, simplicial complexes are used as discrete analogues of spaces suitable for computation. By utilising the prior assumption that the data lie on a manifold, topologically inspired techniques are proposed for refining the …
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The Horizontal Tunnelability Graph is Dual to Level Set Trees
Time series data, reflecting phenomena like climate patterns and stock prices, offer key insights for prediction and trend analysis. Contemporary research has independently developed disparate geometric approaches to time series analysis. These include tree methods, visibility algorithms, as well …
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Computational topology on neural networks: from the data to the model
Machine learning is drawn from a dataset that needs to be explained. Following this aim, a model is described to make predictions. These datasets can be of very different nature, as well as the problems they pose: supervised or unsupervised classification, regression... In this work, we have …
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Plumbing the Depths of the Shallow End: Exploring Persistent Homology Using Small Data
<p>Persistent homology is a prominent tool in topological data analysis. This thesis is designed to be an introduction and guide to a beginner in persistent homology. This comprehensive overview discusses the math used behind it, the code needed to apply it, and its current place in the field. We …
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Computing Exact Bottleneck Distance on Random Point Sets
… applications in machine learning as well as topological data analysis. One can use the classical Hopcroft-Karp (HK-) Algorithm to find the bottleneck matching. In this thesis, we consider the case where A and B are points that are generated uniformly at random from a unit square. Instead of …
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Non-Commutative Probability for the Spectral Analysis of Simplicial Complexes
… of non-commutative and free probability to topological data analysis. The relevant result from the preprint reveals a new interpretation of Betti numbers for simplicial complexes in terms of distributions in an operator-valued probability space. This thesis is mostly an exposition of the …
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Techniques for Accelerating Aggregated Range Queries on Large Multidimensional Datasets in Interactive Visual Exploration
Visual exploration of large multidimensional datasets has seen tremendous progress in recent years, allowing users to express rich data queries that produce informative visual summaries, all in real-time. The fundamental insight of these techniques is that the performance of interactive visual data …
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Generalized Rank Invariant : Structure, Möbius Inversion, and Persistence Diagram
Topological Data Analysis relies on persistent homology to quantify the shape of data. Unlike the one-parameter case, multiparameter persistence modules lack a complete discrete invariant analogous to barcodes, and their classification requires tools that can capture subtle interactions across the …
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Topics in applied topology
… homology has emerged as a powerful tool in Topological Data Analysis (TDA) for extracting structural information from complex datasets by tracking topological features across varying scales. While 1-parameter persistent homology offers a mature theory with well-defined invariants like …
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Using Persistent Homology for Topological Analysis of Protein Interaction Network of Candida Antarctica Lipase B Molecular Dynamic Simulation Model
… (homology groups) in different states. Employing topological analysis, we compare the active form of CalB at high temperatures to its inactive states to account for possible topological contributions to the protein functionality. By discovering a prominent 1-dimensional hole in the active form of …
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Declarative Analytics on Heterogeneous HPC Systems
… However, declarative languages, like Datalog, can directly leverage these advancements due to their ability to express complex problems through simple rules and queries, which can be efficiently compiled into relational algebra operations for execution on GPGPUs. Integrating Datalog's …
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The Evolution of Topological Concepts in Online Social Networks
… to discussions and share their content. The data created in these platforms contain relationships between users and user generated content. User relationships can be represented by a social network, while user generated content takes the form of text, images and video. There are unique …
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Geometric Dimensionality Reduction
… Geometric Dimensionality Reduction, a non-linear data compression technique that utilizes low dimensional manifolds embedded in dimensional spaces to form composite contraction-and-projection maps. Geometric Dimensionality Reduction is predominantly demonstrated through a novel algorithm entitled …
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Data-driven Methods for Resting-state fMRI Biomarker Discovery in Mental Illness
The objective of this dissertation is to develop data-driven methods for discovering the biological markers of mental illness from functional neuroimaging data. We focused on two broader research areas, the first of which is the characterization of brain networks in functional magnetic resonance …
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Geometric Multimedia Time Series
… new take on problems in multimedia times series analysis by using a shape-based perspective to quantify patterns in time, which is complementary to more traditional analysis-based time series techniques. Inspired by the dynamical systems community, we turn time series into shapes via sliding …
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Exploiting multimodality and structure in world representations
… several models that were evaluated on the novel dataset. This produced initial performance estimates for environment understanding, through the lens of a more challenging VQA downstream task. The second work presents two ways of obtaining hierarchical representations of graph-structured data. …
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