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Found 7 papers, 2 papers with code
Stable Vectorization of Multiparameter Persistent Homology using Signed Barcodes as Measures
Most applications of PH focus on the one-parameter case -- where the descriptors summarize the changes in topology of data as it is filtered by a single quantity of interest -- and there is now a wide array of methods enabling the use of one-parameter PH descriptors in data science, which rely on the stable vectorization of these descriptors as elements of a Hilbert space.
A Gradient Sampling Algorithm for Stratified Maps with Applications to Topological Data Analysis
We introduce a novel gradient descent algorithm extending the well-known Gradient Sampling methodology to the class of stratifiably smooth objective functions, which are defined as locally Lipschitz functions that are smooth on some regular pieces-called the strata-of the ambient Euclidean space.
Large Scale computation of Means and Clusters for Persistence Diagrams using Optimal Transport
Persistence diagrams (PDs) are now routinely used to summarize the underlying topology of complex data.
Two-Tier Mapper: a user-independent clustering method for global gene expression analysis based on topology
We have developed a topology-based analysis tool called Two-Tier Mapper (TTMap) to detect subgroups in global gene expression datasets and identify their distinguishing features.
Sliced Wasserstein Kernel for Persistence Diagrams
To incorporate PDs in a learning pipeline, several kernels have been proposed for PDs with a strong emphasis on the stability of the RKHS distance w. r. t.
Ranked #2 on
Graph Classification
on NEURON-MULTI
Computing Zigzag Persistent Cohomology
First, we compare its performance with zigzag persistent homology algorithm and show the interest of cohomology in zigzag persistence.
Computational Geometry
A Fuzzy Clustering Algorithm for the Mode Seeking Framework
In this paper, we propose a new fuzzy clustering algorithm based on the mode-seeking framework.
