Related papers: Topology Based Scalable Graph Kernels
Neural networks are often represented as graphs of connections between neurons. However, despite their wide use, there is currently little understanding of the relationship between the graph structure of the neural network and its…
We elaborate the notion of a Ricci curvature lower bound for parametrized statistical models. Following the seminal ideas of Lott-Strum-Villani, we define this notion based on the geodesic convexity of the Kullback-Leibler divergence in a…
Recent development of network structure analysis shows that it plays an important role in characterizing complex system of many branches of sciences. Different from previous network centrality measures, this paper proposes the notion of…
Identifying (a) systemic barriers to quality healthcare access and (b) key indicators of care efficacy in the United States remains a significant challenge. To improve our understanding of regional disparities in care delivery, we introduce…
Many algorithms for ranked data become computationally intractable as the number of objects grows due to the complex geometric structure induced by rankings. An additional challenge is posed by partial rankings, i.e. rankings in which the…
Graph-structured data arise in wide applications, such as computer vision, bioinformatics, and social networks. Quantifying similarities among graphs is a fundamental problem. In this paper, we develop a framework for computing graph…
Graph kernels have recently emerged as a promising approach for tackling the graph similarity and learning tasks at the same time. In this paper, we propose a general framework for designing graph kernels. The proposed framework capitalizes…
Graph connectivity is a fundamental combinatorial optimization problem that arises in many practical applications, where usually a spanning subgraph of a network is used for its operation. However, in the real world, links may fail…
A clustering algorithm partitions a set of data points into smaller sets (clusters) such that each subset is more tightly packed than the whole. Many approaches to clustering translate the vector data into a graph with edges reflecting a…
Many applications in network science have recently been discovered for the "curvature" of a network, but there is no consensus on the definition for this term. A common approach in these applications is to derive from the curvature either a…
Topological metrics of graphs provide a natural way to describe the prominent features of various types of networks. Graph metrics describe the structure and interplay of graph edges and have found applications in many scientific fields. In…
A neighborhood graph, which represents the instances as vertices and their relations as weighted edges, is the basis of many semi-supervised and relational models for node labeling and link prediction. Most methods employ a sequential…
Graphs are a basic tool for the representation of modern data. The richness of the topological information contained in a graph goes far beyond its mere interpretation as a one-dimensional simplicial complex. We show how topological…
Ricci curvature and Ricci flow have proven to be powerful tools for analyzing the geometry of discrete structures, particularly on undirected graphs, where they have been applied to tasks ranging from community detection to graph…
We study the curvature-dimension inequality in regular graphs. We develop techniques for calculating the curvature of such graphs, and we give characterizations of classes of graphs with positive, zero, and negative curvature. Our main…
The topological (or graph) structures of real-world networks are known to be predictive of multiple dynamic properties of the networks. Conventionally, a graph structure is represented using an adjacency matrix or a set of hand-crafted…
We use the discrete Ollivier-Ricci graph curvature with Ricci flow to examine the intrinsic geometry of financial markets through the empirical correlation graph of the NASDAQ 100 index. Our main result is the development of a technique to…
One way of characterizing the topological and structural properties of vertices and edges in a graph is by using structural similarity measures. Measures like Cosine, Jaccard and Dice compute the similarities restricted to the immediate…
We define the Ricci curvature on simplicial complexes by modifying the definition of the Ricci curvature on graphs, and we prove the upper and lower bounds of the Ricci curvature. These properties are generalizations of previous studies.…
Most complex systems can be captured by graphs or networks. Networks connect nodes (e.g.\ neurons) through edges (synapses), thus summarizing the system's structure. A popular way of interrogating graphs is community detection, which…