Related papers: Efficient two-parameter persistence computation vi…
This paper addresses the challenging problem of parameter estimation in bilinear systems under colored noise. A novel approach, termed B-PF-RLS, is proposed, combining a particle filter (PF) with a recursive least squares (RLS) estimator.…
We consider sequences of absolute and relative homology and cohomology groups that arise naturally for a filtered cell complex. We establish algebraic relationships between their persistence modules, and show that they contain equivalent…
We present a unified pipeline for univariate time series classification via complex networks and persistent homology. A time series is mapped to a graph through one of five constructions across three families (visibility (natural and…
Edge-preserving smoothing is a fundamental procedure for many computer vision and graphic applications. This can be achieved with either local methods or global methods. In most cases, global methods can yield superior performance over…
We propose the labeled \v{C}ech complex, the plain labeled Vietoris-Rips complex, and the locally scaled labeled Vietoris-Rips complex to perform persistent homology inference of decision boundaries in classification tasks. We provide…
Extracting informative features from images has been of capital importance in computer vision. In this paper, we propose a way to extract such features from images by a method based on algebraic topology. To that end, we construct a…
In this work, we develop a pipeline that associates Persistence Diagrams to digital data via the most appropriate filtration for the type of data considered. Using a grid search approach, this pipeline determines optimal representation…
Persistent homology is a natural tool for probing the topological characteristics of weighted graphs, essentially focusing on their $0$-dimensional homology. While this area has been substantially studied, we present a new approach to…
The Delaunay-Rips filtration is a lighter and faster alternative to the well-known Rips filtration for low-dimensional Euclidean point clouds. Despite these advantages, it has seldom been studied. In this paper, we aim to bridge this gap by…
Optimization, a key tool in machine learning and statistics, relies on regularization to reduce overfitting. Traditional regularization methods control a norm of the solution to ensure its smoothness. Recently, topological methods have…
Recently, multi-scale notions of local homology (a variant of persistent homology) have been used to study the local structure of spaces around a given point from a point cloud sample. Current reconstruction guarantees rely on constructing…
The degree-Rips bifiltration is the most computable of the parameter-free, density-sensitive bifiltrations in topological data analysis. It is known that this construction is stable to small perturbations of the input data, but its…
Persistent homology (PH) is a popular tool for topological data analysis that has found applications across diverse areas of research. It provides a rigorous method to compute robust topological features in discrete experimental…
Existing fast algorithms for bilateral and nonlocal means filtering mostly work with grayscale images. They cannot easily be extended to high-dimensional data such as color and hyperspectral images, patch-based data, flow-fields, etc. In…
In this work, we study several variants of matrix reduction via Gaussian elimination that try to keep the reduced matrix sparse. The motivation comes from the growing field of topological data analysis where matrix reduction is the major…
Persistence diagrams, combining geometry and topology for an effective shape description used in pattern recognition, have already proven to be an effective tool for shape representation with respect to a certainfiltering function.…
Boissonnat and Pritam introduced an algorithm to reduce a filtration of flag (or clique) complexes, which can in particular speed up the computation of its persistent homology. They used so-called edge collapse to reduce the input flag…
Building upon [2308.02636], we investigate the constraining power of persistent homology on cosmological parameters and primordial non-Gaussianity in a likelihood-free inference pipeline utilizing machine learning. We evaluate the ability…
Feature selection is an important tool to deal with high dimensional data. In unsupervised case, many popular algorithms aim at maintaining the structure of the original data. In this paper, we propose a simple and effective feature…
Computed tomography is widely used as an imaging tool to visualize three-dimensional structures with expressive bone-soft tissue contrast. However, CT resolution and radiation dose are tightly entangled, highlighting the importance of…