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 persistence landscape theory
Download
Selcuk_Thesis.pdf
Date
2022-7
Author
Gürses, Selçuk
Metadata
Show full item record
This work is licensed under a
Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License
.
Item Usage Stats
448
views
318
downloads
Cite This
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 statistical and machine learning technologies. This new summary has various advantages: First, since it is a function, calculations are significantly more quickly than conventional TDA tools. Second, it can be seen as a random variable with values in a Banach space, so it conforms to some statistical theorems such as strong law of large numbers and central limit theorem. Third, it provides a unique average unlike persistence diagrams and barcodes. This thesis is a survey that represents how the persistence landscape is constructed and contributes to the applications.
Subject Keywords
Topological data analysis
,
Persistence homology
,
Persistence landscape
URI
https://hdl.handle.net/11511/98161
Collections
Graduate School of Natural and Applied Sciences, Thesis
Suggestions
OpenMETU
Core
A survey on multidimensional persistence theory
Karagüler, Dilan; Pamuk, Semra; Department of Mathematics (2021-8)
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 n...
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...
A systematic approach to the integration of overlapping partitions in service-oriented data grids
Sunercan, H. Kevser; Alpdemir, M. Nedim; Çiçekli, Fehime Nihan (Elsevier BV, 2011-06-01)
This paper aims to provide a service-oriented data integration solution over data Grids for cases where distributed data sources are partitioned with overlapping sections of various proportions. This is an interesting variation which combines both replicated and partitioned data within the same data management framework. Thus, the data management infrastructure has to deal with specific challenges regarding the identification, access and aggregation of partitioned data with varying proportions of overlappin...
Investigation of Stationarity for Graph Time Series Data Sets
Güneyi, Eylem Tuğçe; Vural, Elif (2021-01-07)
Graphs permit the analysis of the relationships in complex data sets effectively. Stationarity is a feature that facilitates the analysis and processing of random time signals. Since graphs have an irregular structure, the definition of classical stationarity does not apply to graphs. In this study, we study how stationarity is defined for graph random processes and examine the validity of the stationarity assumption with experiments on synthetic and real data sets.
Bayesian solutions and performance analysis in bioelectric inverse problems
Serinağaoğlu Doğrusöz, Yeşim; MacLeod, RS (Institute of Electrical and Electronics Engineers (IEEE), 2005-06-01)
In bioelectric inverse problems, one seeks to recover bioelectric sources from remote measurements using a mathematical model that relates the sources to the measurements. Due to attenuation and spatial smoothing in the medium between the sources and the measurements, bioelectric inverse problems are generally ill-posed. Bayesian methodology has received increasing attention recently to combat this ill-posedness, since it offers a general formulation of regularization constraints and additionally provides s...
Citation Formats
IEEE
ACM
APA
CHICAGO
MLA
BibTeX
S. Gürses, “A survey on persistence landscape theory,” M.S. - Master of Science, Middle East Technical University, 2022.