相关论文: Optimisation of Spectral Wavelets for Persistence-…

Persistent homology is constrained to purely topological persistence while multiscale graphs account only for geometric information. This work introduces persistent spectral theory to create a unified low-dimensional multiscale paradigm for…

We consider the problem of designing spectral graph filters for the construction of dictionaries of atoms that can be used to efficiently represent signals residing on weighted graphs. While the filters used in previous spectral graph…

Persistent homology is a mathematical tool used for studying the shape of data by extracting its topological features. It has gained popularity in network science due to its applicability in various network mining problems, including…

Persistent homology is a central methodology in topological data analysis that has been successfully implemented in many fields and is becoming increasingly popular and relevant. The output of persistent homology is a persistence diagram --…

Extended persistence is a technique from topological data analysis to obtain global multiscale topological information from a graph. This includes information about connected components and cycles that are captured by the so-called…

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…

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…

We introduce graphcodes, a novel multi-scale summary of the topological properties of a dataset that is based on the well-established theory of persistent homology. Graphcodes handle datasets that are filtered along two real-valued scale…

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. However, since the (metric) space of…

Persistent homology, a technique from computational topology, has recently shown strong empirical performance in the context of graph classification. Being able to capture long range graph properties via higher-order topological features,…

Recently, graph neural networks have been widely used for network embedding because of their prominent performance in pairwise relationship learning. In the real world, a more natural and common situation is the coexistence of pairwise…

Graph classification aims to categorise graphs based on their structure and node attributes. In this work, we propose to tackle this task using tools from graph signal processing by deriving spectral features, which we then use to design…

This article aims to study the topological invariant properties encoded in node graph representational embeddings by utilizing tools available in persistent homology. Specifically, given a node embedding representation algorithm, we…

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…

This work develops a flexible and mathematically sound framework for the design and analysis of graph scattering networks with variable branching ratios and generic functional calculus filters. Spectrally-agnostic stability guarantees for…

Modeling information that resides on vertices of large graphs is a key problem in several real-life applications, ranging from social networks to the Internet-of-things. Signal Processing on Graphs and, in particular, graph wavelets can…

Recently a new feature representation and data analysis methodology based on a topological tool called persistent homology (and its corresponding persistence diagram summary) has started to attract momentum. A series of methods have been…

Persistence diagrams (PDs), often characterized as sets of death and birth of homology class, have been known for providing a topological representation of a graph structure, which is often useful in machine learning tasks. Prior works rely…

Spectral graph convolutional networks are generalizations of standard convolutional networks for graph-structured data using the Laplacian operator. A common misconception is the instability of spectral filters, i.e. the impossibility to…

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…