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Found 10 papers, 7 papers with code
Differentiable Mapper For Topological Optimization Of Data Representation
While highly generic and applicable, its use has been hampered so far by the manual tuning of its many parameters-among these, a crucial one is the so-called filter: it is a continuous function whose variations on the data set are the main ingredient for both building the Mapper representation and assessing the presence and sizes of its topological structures.
A Framework for Fast and Stable Representations of Multiparameter Persistent Homology Decompositions
One of the most important such descriptors is {\em persistent homology}, which encodes the change in shape as a filtration parameter changes; a typical parameter is the feature scale.
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.
MAGDiff: Covariate Data Set Shift Detection via Activation Graphs of Deep Neural Networks
Despite their successful application to a variety of tasks, neural networks remain limited, like other machine learning methods, by their sensitivity to shifts in the data: their performance can be severely impacted by differences in distribution between the data on which they were trained and that on which they are deployed.
RipsNet: a general architecture for fast and robust estimation of the persistent homology of point clouds
The use of topological descriptors in modern machine learning applications, such as Persistence Diagrams (PDs) arising from Topological Data Analysis (TDA), has shown great potential in various domains.
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.
Statistical analysis of Mapper for stochastic and multivariate filters
The stability and quantification of the rate of convergence of the Mapper to the Reeb space has been studied a lot in recent works [BBMW19, CO17, CMO18, MW16], focusing on the case where a scalar-valued filter is used for the computation of Mapper.
PersLay: A Neural Network Layer for Persistence Diagrams and New Graph Topological Signatures
Persistence diagrams, the most common descriptors of Topological Data Analysis, encode topological properties of data and have already proved pivotal in many different applications of data science.
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.
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