On the effectiveness of persistent homology
Persistent homology (PH) is one of the most popular methods in Topological Data Analysis.
Even though PH has been used in many different types of applications, the reasons behind …
Even though PH has been used in many different types of applications, the reasons behind …
Noise robustness of persistent homology on greyscale images, across filtrations and signatures
Topological data analysis is a recent and fast growing field that approaches the analysis of
datasets using techniques from (algebraic) topology. Its main tool, persistent homology (PH) …
datasets using techniques from (algebraic) topology. Its main tool, persistent homology (PH) …
Nonembeddability of persistence diagrams with 𝑝> 2 Wasserstein metric
A Wagner - Proceedings of the American Mathematical Society, 2021 - ams.org
Persistence diagrams do not admit an inner product structure compatible with any
Wasserstein metric. Hence, when applying kernel methods to persistence diagrams, the …
Wasserstein metric. Hence, when applying kernel methods to persistence diagrams, the …
Strong topology on the set of persistence diagrams
We endow the set of persistence diagrams with the strong topology (the topology of
countable direct limit of increasing sequence of bounded subsets considered in the …
countable direct limit of increasing sequence of bounded subsets considered in the …
The space of persistence diagrams on 𝑛 points coarsely embeds into Hilbert space
We prove that the space of persistence diagrams on $ n $ points (with the bottleneck or a
Wasserstein distance) coarsely embeds into Hilbert space by showing it is of asymptotic …
Wasserstein distance) coarsely embeds into Hilbert space by showing it is of asymptotic …
Signatures, lipschitz-free spaces, and paths of persistence diagrams
Paths of persistence diagrams provide a summary of the dynamic topological structure of a
one-parameter family of metric spaces. These summaries can be used to study and …
one-parameter family of metric spaces. These summaries can be used to study and …
Enhancing the Vietoris–Rips simplicial complex for topological data analysis: applications in cancer gene expression datasets
The aim of this study is to enhance the extraction of informative features from complex data
through the application of topological data analysis (TDA) using novel topological …
through the application of topological data analysis (TDA) using novel topological …
A new measure for the attitude to mobility of Italian students and graduates: a topological data analysis approach
M Vittorietti, O Giambalvo, VG Genova… - Statistical Methods & …, 2023 - Springer
Students' and graduates' mobility is an interesting topic of discussion especially for the
Italian education system and universities. The main reasons for migration and for the so …
Italian education system and universities. The main reasons for migration and for the so …
Topological data analysis of time series data for B2B customer relationship management
R Rivera-Castro, P Pilyugina, A Pletnev… - arXiv preprint arXiv …, 2019 - arxiv.org
Topological Data Analysis (TDA) is a recent approach to analyze data sets from the
perspective of their topological structure. Its use for time series data has been limited to the …
perspective of their topological structure. Its use for time series data has been limited to the …
Topology-based clusterwise regression for user segmentation and demand forecasting
R Rivera-Castro, A Pletnev, P Pilyugina… - … Conference on Data …, 2019 - ieeexplore.ieee.org
Topological Data Analysis (TDA) is a recent approach to analyze data sets from the
perspective of their topological structure. Its use for time series data has been limited. In this …
perspective of their topological structure. Its use for time series data has been limited. In this …