Related papers: Reconstructing Embedded Graphs from Persistence Di…
Persistence diagrams have been widely used to quantify the underlying features of filtered topological spaces in data visualization. In many applications, computing distances between diagrams is essential; however, computing these distances…
Graphs are a representation of structured data that captures the relationships between sets of objects. With the ubiquity of available network data, there is increasing industrial and academic need to quickly analyze graphs with billions of…
Persistent homology is a popular technique in topological data analysis that tracks the lifespans of homological features in a nested sequence of spaces. This data is typically presented in a multi-set called a persistence diagram or a…
Large time-varying graphs are increasingly common in financial, social and biological settings. Feature extraction that efficiently encodes the complex structure of sparse, multi-layered, dynamic graphs presents computational and…
Graphs are commonly used to encode relationships among entities, yet their abstractness makes them difficult to analyze. Node-link diagrams are popular for drawing graphs, and force-directed layouts provide a flexible method for node…
Node embedding learns low-dimensional vectors for nodes in the graph. Recent state-of-the-art embedding approaches take Personalized PageRank (PPR) as the proximity measure and factorize the PPR matrix or its adaptation to generate…
Graph embedding algorithms are used to efficiently represent (encode) a graph in a low-dimensional continuous vector space that preserves the most important properties of the graph. One aspect that is often overlooked is whether the graph…
We study an issue commonly seen with graph data analysis: many real-world complex systems involving high-order interactions are best encoded by hypergraphs; however, their datasets often end up being published or studied only in the form of…
We consider the following graph reconstruction problem: given an unweighted connected graph $G = (V,E)$ with visible vertex set $V$ and an oracle which takes two vertices $u,v \in V$ and returns the shortest path distance between $u$ and…
The standard approach to representation learning on attributed graphs -- i.e., simultaneously reconstructing node attributes and graph structure -- is geometrically flawed, as it merges two potentially incompatible metric spaces. This…
Node embedding is the task of extracting concise and informative representations of certain entities that are connected in a network. Various real-world networks include information about both node connectivity and certain node attributes,…
Persistent homology, a central tool of topological data analysis, provides invariants of data called barcodes (also known as persistence diagrams). A barcode is simply a multiset of real intervals. Recent work of Edelsbrunner, Jablonski,…
Persistent cycles, especially the minimal ones, are useful geometric features functioning as augmentations for the intervals in a purely topological persistence diagram (also termed as barcode). In our earlier work, we showed that computing…
We follow up on previous work which found that commonly used graph evolution moves lead to conserved quantities that can be expressed in terms of the braiding of the graph in its embedding space. We study non-embedded graphs under three…
We study the two inference problems of detecting and recovering an isolated community of \emph{general} structure planted in a random graph. The detection problem is formalized as a hypothesis testing problem, where under the null…
Given a large graph, how can we summarize it with fewer nodes and edges while maintaining its key properties, such as spectral property? Although graphs play more and more important roles in many real-world applications, the growth of their…
While message passing graph neural networks result in informative node embeddings, they may suffer from describing the topological properties of graphs. To this end, node filtration has been widely used as an attempt to obtain the…
Learning faithful graph representations as sets of vertex embeddings has become a fundamental intermediary step in a wide range of machine learning applications. The quality of the embeddings is usually determined by how well the geometry…
Topological data analysis (TDA) is a rising field in the intersection of mathematics, statistics, and computer science/data science. The cornerstone of TDA is persistent homology, which produces a summary of topological information called a…
Difficulties in replication and reproducibility of empirical evidences in machine learning research have become a prominent topic in recent years. Ensuring that machine learning research results are sound and reliable requires…