Related papers: Topology across Scales on Heterogeneous Cell Data
Persistent homology (PH) has recently emerged as a powerful tool for extracting topological features. Integrating PH into machine learning and deep learning models enhances topology awareness and interpretability. However, most PH methods…
Topological methods can provide a way of proposing new metrics and methods of scrutinising data, that otherwise may be overlooked. In this work, a method of quantifying the shape of data, via a topic called topological data analysis will be…
Topological Data Analysis (TDA) provides tools to describe the shape of data, but integrating topological features into deep learning pipelines remains challenging, especially when preserving local geometric structure rather than…
Persistent homology probes topological properties from point clouds and functions. By looking at multiple scales simultaneously, one can record the births and deaths of topological features as the scale varies. In this paper we use a…
Recently, persistent homology has had tremendous success in biomolecular data analysis. It works by examining the topological relationship or connectivity of a group of atoms in a molecule at a variety of scales, then rendering a family of…
A central problem in data-driven scientific inquiry is how to interpret structure in noisy, high-dimensional data. Topological data analysis (TDA) provides a solution via persistent homology, which encodes features of interest as…
Inferring topological and geometrical information from data can offer an alternative perspective on machine learning problems. Methods from topological data analysis, e.g., persistent homology, enable us to obtain such information,…
The machinery of topological data analysis becomes increasingly popular in a broad range of machine learning tasks, ranging from anomaly detection and manifold learning to graph classification. Persistent homology is one of the key…
Including intricate topological information (e.g., cycles) provably enhances the expressivity of message-passing graph neural networks (GNNs) beyond the Weisfeiler-Leman (WL) hierarchy. Consequently, Persistent Homology (PH) methods are…
Topology applied to real world data using persistent homology has started to find applications within machine learning, including deep learning. We present a differentiable topology layer that computes persistent homology based on level set…
The application of network techniques to the analysis of neural data has greatly improved our ability to quantify and describe these rich interacting systems. Among many important contributions, networks have proven useful in identifying…
Long lived topological features are distinguished from short lived ones (considered as topological noise) in simplicial complexes constructed from complex networks. A new topological invariant, persistent homology, is determined and…
A central challenge in topological data analysis is the interpretation of barcodes. The classical algebraic-topological approach to interpreting homology classes is to build maps to spaces whose homology carries semantics we understand and…
Path homology proposed by S.-T.Yau and his co-workers provides a new mathematical model for directed graphs and networks. Persistent path homology (PPH) extends the path homology with filtration to deal with asymmetry structures. However,…
In data clustering, it is often desirable to find not just a single partition into clusters but a sequence of partitions that describes the data at different scales (or levels of coarseness). A natural problem then is to analyse and compare…
Hyperuniform structures are disordered, correlated systems in which density fluctuations are suppressed at large scales. Such a property generalizes the concept of order in patterns and is relevant across diverse physical systems. We…
Persistent homology is a topological data analysis tool that has been widely generalized, extending its scope beyond the field of topology. Among its extensions, steady and ranging persistence were developed to study a wide variety of graph…
Features such as photon rings, jets, or hot. spots can leave particular topological signatures in a black hole image. As such, topological data analysis can be used to characterize images resulting from high resolution observations…
In this paper, we consider topological featurizations of data defined over simplicial complexes, like images and labeled graphs, obtained by convolving this data with various filters before computing persistence. Viewing a convolution…
In many applications concerning the comparison of data expressed by $\mathbb{R}^m$-valued functions defined on a topological space $X$, the invariance with respect to a given group $G$ of self-homeomorphisms of $X$ is required. While…