Show/Hide Menu
Hide/Show Apps
Logout
Türkçe
Türkçe
Search
Search
Login
Login
OpenMETU
OpenMETU
About
About
Open Science Policy
Open Science Policy
Open Access Guideline
Open Access Guideline
Postgraduate Thesis Guideline
Postgraduate Thesis Guideline
Communities & Collections
Communities & Collections
Help
Help
Frequently Asked Questions
Frequently Asked Questions
Guides
Guides
Thesis submission
Thesis submission
MS without thesis term project submission
MS without thesis term project submission
Publication submission with DOI
Publication submission with DOI
Publication submission
Publication submission
Supporting Information
Supporting Information
General Information
General Information
Copyright, Embargo and License
Copyright, Embargo and License
Contact us
Contact us
A survey on multidimensional persistence theory
Download
Dilan_Thesis.pdf
Date
2021-8
Author
Karagüler, Dilan
Metadata
Show full item record
This work is licensed under a
Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License
.
Item Usage Stats
562
views
494
downloads
Cite This
Persistence homology is one of the commonly used theoretical methods in topological data analysis to extract information from given data using algebraic topology. Converting data to a filtered object and analyzing the topological features of each space in the filtration, we will obtain a way of representing these features called the shape of data. This will give us invariants like barcodes or persistence diagrams for the data. These invariants are stable under small perturbations. In most applications, we need multiscaled analysis of data, which is done by multidimensional persistence. This thesis is a survey that contains how to produce invariants for multiscaled filtration obtained from data and the related stability results.
Subject Keywords
Topological data analysis
,
Persistence homology
,
Multidimensional persistence
URI
https://hdl.handle.net/11511/92203
Collections
Graduate School of Natural and Applied Sciences, Thesis
Suggestions
OpenMETU
Core
A survey on persistence landscape theory
Gürses, Selçuk; Pamuk, Semra; Department of Mathematics (2022-7)
Topological data analysis (TDA) consists of a growing collection of techniques that reveal the shape of data. These techniques may be especially useful for comprehend ing global features of high-dimensional data that are inaccessible via other methods. The usage of TDA has been constrained by the difficulties of merging the subject’s primary tool, the barcode or persistence diagram, with statistics and machine learning. The persistence landscape is a stable topological summary that is easily combinable with...
New Formulation and Implementation of Vibrational Self-Consistent Field Theory
Hansen, Mikkel B.; Sparta, Manuel; Seidler, Peter; Toffolı, Danıele; Christiansen, Ove (2010-01-01)
A new implementation of the vibrational self-consistent field (VSCF) method is presented on the basis of a second quantization formulation. A so-called active terms algorithm is shown to be a significant improvement over a standard implementation reducing the computational effort by one order in the number of degrees of freedom. Various types of screening provide even further reductions in computational scaling and absolute CPU time. VSCF calculations on large polyaromatic hydrocarbon model systems are pres...
A Theoretical Analysis of Multi-Modal Representation Learning with Regular Functions
Vural, Elif (2021-01-07)
Multi-modal data analysis methods often learn representations that align different modalities in a new common domain, while preserving the within-class compactness and within-modality geometry and enhancing the between-class separation. In this study, we present a theoretical performance analysis for multi-modal representation learning methods. We consider a quite general family of algorithms learning a nonlinear embedding of the data space into a new space via regular functions. We derive sufficient condit...
A unified approach for the formulation of interaction problems by the boundary element method
Mengi, Y; Argeso, H (Wiley, 2006-04-30)
A unified formulation is presented, based on boundary element method, in a form suitable for performing the interaction analyses by substructure method for solid-solid and soil-structure problems. The proposed formulation permits the evaluation of all the elements of impedance and input motion matrices simultaneously at a single step in terms of system matrices of the boundary element method without solving any special problem, such as, unit displacement or load problem, as required in conventional methods....
A Study of the Classification of Low-Dimensional Data with Supervised Manifold Learning
Vural, Elif (2018-01-01)
Supervised manifold learning methods learn data representations by preserving the geometric structure of data while enhancing the separation between data samples from different classes. In this work, we propose a theoretical study of supervised manifold learning for classification. We consider nonlinear dimensionality reduction algorithms that yield linearly separable embeddings of training data and present generalization bounds for this type of algorithms. A necessary condition for satisfactory generalizat...
Citation Formats
IEEE
ACM
APA
CHICAGO
MLA
BibTeX
D. Karagüler, “A survey on multidimensional persistence theory,” M.S. - Master of Science, Middle East Technical University, 2021.