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Found 11 papers, 4 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.
Weighted least-squares approximation with determinantal point processes and generalized volume sampling
We first provide a generalized version of volume-rescaled sampling yielding quasi-optimality results in expectation with a number of samples $n = O(m\log(m))$, that means that the expected $L^2$ error is bounded by a constant times the best approximation error in $L^2$.
Kernel-Based Testing for Single-Cell Differential Analysis
Single-cell technologies offer insights into molecular feature distributions, but comparing them poses challenges.
Learning with tree tensor networks: complexity estimates and model selection
We propose and analyze a complexity-based model selection method for tree tensor networks in an empirical risk minimization framework and we analyze its performance over a wide range of smoothness classes.
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.
An introduction to Topological Data Analysis: fundamental and practical aspects for data scientists
Topological Data Analysis is a recent and fast growing field providing a set of new topological and geometric tools to infer relevant features for possibly complex data.
Data driven estimation of Laplace-Beltrami operator
Approximations of Laplace-Beltrami operators on manifolds through graph Lapla-cians have become popular tools in data analysis and machine learning.
Robust Topological Inference: Distance To a Measure and Kernel Distance
However, the empirical distance function is highly non-robust to noise and outliers.
Statistics Theory Computational Geometry Algebraic Topology Statistics Theory
Subsampling Methods for Persistent Homology
Persistent homology is a multiscale method for analyzing the shape of sets and functions from point cloud data arising from an unknown distribution supported on those sets.
Algebraic Topology Computational Geometry Applications
Sparse Bayesian Unsupervised Learning
This paper is about variable selection, clustering and estimation in an unsupervised high-dimensional setting.
Optimal rates of convergence for persistence diagrams in Topological Data Analysis
In this paper, we study topological persistence in general metric spaces, with a statistical approach.
