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An introduction to topological data analysis: fundamental and practical aspects for data scientists
With the recent explosion in the amount, the variety, and the dimensionality of available
data, identifying, extracting, and exploiting their underlying structure has become a problem …
data, identifying, extracting, and exploiting their underlying structure has become a problem …
[كتاب][B] Topological data analysis with applications
G Carlsson, M Vejdemo-Johansson - 2021 - books.google.com
The continued and dramatic rise in the size of data sets has meant that new methods are
required to model and analyze them. This timely account introduces topological data …
required to model and analyze them. This timely account introduces topological data …
Scalar field comparison with topological descriptors: Properties and applications for scientific visualization
In topological data analysis and visualization, topological descriptors such as persistence
diagrams, merge trees, contour trees, Reeb graphs, and Morse–Smale complexes play an …
diagrams, merge trees, contour trees, Reeb graphs, and Morse–Smale complexes play an …
Topological data analysis for neural network analysis: A comprehensive survey
This survey provides a comprehensive exploration of applications of Topological Data
Analysis (TDA) within neural network analysis. Using TDA tools such as persistent homology …
Analysis (TDA) within neural network analysis. Using TDA tools such as persistent homology …
Statistical analysis and parameter selection for mapper
In this article, we study the question of the statistical convergence of the 1-dimensional
Mapper to its continuous analogue, the Reeb graph. We show that the Mapper is an optimal …
Mapper to its continuous analogue, the Reeb graph. We show that the Mapper is an optimal …
Exposition and interpretation of the topology of neural networks
Convolutional neural networks (CNN's) are powerful and widely used tools. However, their
interpretability is far from ideal. One such shortcoming is the difficulty of deducing a …
interpretability is far from ideal. One such shortcoming is the difficulty of deducing a …
SFCM: a fuzzy clustering algorithm of extracting the shape information of data
Topological data analysis is a new theoretical trend using topological techniques to mine
data. This approach helps determine topological data structures. It focuses on investigating …
data. This approach helps determine topological data structures. It focuses on investigating …
Topological data analysis reveals a core gene expression backbone that defines form and function across flowering plants
Since they emerged approximately 125 million years ago, flowering plants have evolved to
dominate the terrestrial landscape and survive in the most inhospitable environments on …
dominate the terrestrial landscape and survive in the most inhospitable environments on …
Topological data analysis of COVID-19 using artificial intelligence and machine learning techniques in big datasets of hausdorff spaces
In this paper, we carry out an in-depth topological data analysis (TDA) of COVID-19
pandemic using artificial intelligence (AI) and Machine Learning (ML) techniques. We show …
pandemic using artificial intelligence (AI) and Machine Learning (ML) techniques. We show …
Functional coordination of non‐myocytes plays a key role in adult zebrafish heart regeneration
Cardiac regeneration occurs primarily through proliferation of existing cardiomyocytes, but
also involves complex interactions between distinct cardiac cell types including non …
also involves complex interactions between distinct cardiac cell types including non …