Related papers: Persistent Path Laplacian
Persistent homology is a method for computing the topological features present in a given data. Recently, there has been much interest in the integration of persistent homology as a computational step in neural networks or deep learning. In…
Persistent homology has recently emerged as a powerful technique in topological data analysis for analyzing the emergence and disappearance of topological features throughout a filtered space, shown via persistence diagrams. Additionally,…
Biological and physical systems often exhibit distinct structures at different spatial/temporal scales. Persistent homology is an algebraic tool that provides a mathematical framework for analyzing the multi-scale structures frequently…
Link prediction (LP), inferring the connectivity between nodes, is a significant research area in graph data, where a link represents essential information on relationships between nodes. Although graph neural network (GNN)-based models…
Persistent homology is a popular data analysis technique that is used to capture the changing topology of a filtration associated with some simplicial complex $K$. These topological changes are summarized in persistence diagrams. We propose…
Persistent homology analysis provides means to capture the connectivity structure of data sets in various dimensions. On the mathematical level, by defining a metric between the objects that persistence attaches to data sets, we can…
To analyze the topological properties of the given discrete data, one needs to consider a continuous transform called filtration. Persistent homology serves as a tool to track changes of homology in the filtration. The outcome of the…
Topological Data Analysis (TDA) is a novel statistical technique, particularly powerful for the analysis of large and high dimensional data sets. Much of TDA is based on the tool of persistent homology, represented visually via persistence…
We explore the recently introduced persistent reachability homology (PRH) of digraph data, i.e. data in the form of directed graphs. In particular, we study the effectiveness of PRH in network classification task in a key neuroscience…
Topological data analysis (TDA) is an area of data science that focuses on using invariants from algebraic topology to provide multiscale shape descriptors for geometric data sets such as point clouds. One of the most important such…
The theory of multidimensional persistent homology was initially developed in the discrete setting, and involved the study of simplicial complexes filtered through an ordering of the simplices. Later, stability properties of…
Persistent Homology (PH) is a useful tool to study the underlying structure of a data set. Persistence Diagrams (PDs), which are 2D multisets of points, are a concise summary of the information found by studying the PH of a data set.…
We use methods from topological data analysis to study the topological features of certain distributions of string vacua. Topological data analysis is a multi-scale approach used to analyze the topological features of a dataset by…
Determining whether two graphs are isomorphic is a fundamental problem with practical applications in areas such as molecular chemistry or social network analysis, yet it remains a challenging task, with exact solutions often being…
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…
Persistent homology theory is a relatively new but powerful method in data analysis. Using simplicial complexes, classical persistent homology is able to reveal high dimensional geometric structures of datasets, and represent them as…
Accurate prediction of protein-ligand binding affinity remains a central challenge in structure-based drug discovery. The effectiveness of machine learning models critically depends on the quality of molecular descriptors, for which…
We propose PLLay, a novel topological layer for general deep learning models based on persistence landscapes, in which we can efficiently exploit the underlying topological features of the input data structure. In this work, we show…
Graphs with diverse structural characteristics play a central role in modelling and optimization tasks. The ability to generate different types of graphs that exhibit shared properties is likewise essential for algorithm selection and…
Spatial transcriptomics studies are becoming increasingly large and commonplace, necessitating simultaneous analysis of a large number of spatially resolved variables. Correspondingly, a diverse range of methodologies have been proposed to…