Persistent homology of complex networks for dynamic state detection
In this paper we develop an alternative topological data analysis (TDA) approach for
studying graph representations of time series of dynamical systems. Specifically, we show …
studying graph representations of time series of dynamical systems. Specifically, we show …
Prediction of cybersickness in virtual environments using topological data analysis and machine learning
Recent significant progress in Virtual Reality (VR) applications and environments raised
several challenges. They proved to have side effects on specific users, thus reducing the …
several challenges. They proved to have side effects on specific users, thus reducing the …
On the stability of persistent entropy and new summary functions for topological data analysis
Persistent homology and persistent entropy have recently become useful tools for patter
recognition. In this paper, we find requirements under which persistent entropy is stable to …
recognition. In this paper, we find requirements under which persistent entropy is stable to …
Towards personalized diagnosis of glioblastoma in fluid-attenuated inversion recovery (FLAIR) by topological interpretable machine learning
M Rucco, G Viticchi, L Falsetti - Mathematics, 2020 - mdpi.com
Glioblastoma multiforme (GBM) is a fast-growing and highly invasive brain tumor, which
tends to occur in adults between the ages of 45 and 70 and it accounts for 52 percent of all …
tends to occur in adults between the ages of 45 and 70 and it accounts for 52 percent of all …
Persistent entropy for separating topological features from noise in vietoris-rips complexes
Persistent homology studies the evolution of k-dimensional holes along a nested sequence
of simplicial complexes (called a filtration). The set of bars (ie intervals) representing birth …
of simplicial complexes (called a filtration). The set of bars (ie intervals) representing birth …
The data-driven optimization method and its application in feature extraction of ship-radiated noise with sample entropy
Y Li, X Chen, J Yu, X Yang, H Yang - Energies, 2019 - mdpi.com
The data-driven method is an important tool in the field of underwater acoustic signal
processing. In order to realize the feature extraction of ship-radiated noise (S-RN), we …
processing. In order to realize the feature extraction of ship-radiated noise (S-RN), we …
Multiscale persistent functions for biomolecular structure characterization
In this paper, we introduce multiscale persistent functions for biomolecular structure
characterization. The essential idea is to combine our multiscale rigidity functions (MRFs) …
characterization. The essential idea is to combine our multiscale rigidity functions (MRFs) …
On the stability of persistent entropy and new summary functions for TDA
N Atienza, R González-Díaz… - arXiv preprint arXiv …, 2018 - arxiv.org
Persistent homology and persistent entropy have recently become useful tools for patter
recognition. In this paper, we find requirements under which persistent entropy is stable to …
recognition. In this paper, we find requirements under which persistent entropy is stable to …
A new entropy based summary function for topological data analysis
N Atienza, R Gonzalez-Diaz… - Electronic Notes in …, 2018 - Elsevier
Topological data analysis (TDA) aims to obtain useful information from data sets using
topological concepts. In particular, it may help to infer from finite sample when a …
topological concepts. In particular, it may help to infer from finite sample when a …
Separating topological noise from features using persistent entropy
Topology is the branch of mathematics that studies shapes and maps among them. From the
algebraic definition of topology a new set of algorithms have been derived. These algorithms …
algebraic definition of topology a new set of algorithms have been derived. These algorithms …