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In this paper, we introduce the notion of a dual topological graph of a given topological graph, and show that it defines a C*-algebra isomorphic to the C*-algebra of the given one. Repeating to take a dual, and taking a projective limit,…
Graph serves as a powerful tool for modeling data that has an underlying structure in non-Euclidean space, by encoding relations as edges and entities as nodes. Despite developments in learning from graph-structured data over the years, one…
Real-world data is often times associated with irregular structures that can analytically be represented as graphs. Having access to this graph, which is sometimes trivially evident from domain knowledge, provides a better representation of…
Baker devised a powerful technique to obtain approximation schemes for various problems restricted to planar graphs. Her technique can be directly extended to various other graph classes, among the most general ones the graphs avoiding a…
Reeb graphs are simple topological descriptors with applications in many areas like topological data analysis and computational geometry. Despite their prevalence, visualization of Reeb graphs has received less attention. In this paper, we…
We present a form of algebraic reasoning for computational objects which are expressed as graphs. Edges describe the flow of data between primitive operations which are represented by vertices. These graphs have an interface made of…
A main challenge in mining network-based data is finding effective ways to represent or encode graph structures so that it can be efficiently exploited by machine learning algorithms. Several methods have focused in network representation…
In this study, we investigate the problem of classifying, characterizing, and designing efficient algorithms for hard inference problems on planar graphs, in the limit of infinite size. The problem is considered hard if, for a deterministic…
We consider the problem of discretizing one-dimensional, real-valued functions as graphs. The goal is to find a small set of points, from which we can approximate the remaining function values. The method for approximating the unknown…
A computational graph in a deep neural network (DNN) denotes a specific data flow diagram (DFD) composed of many tensors and operators. Existing toolkits for visualizing computational graphs are not applicable when the structure is highly…
We study the problem of graph structure identification, i.e., of recovering the graph of dependencies among time series. We model these time series data as components of the state of linear stochastic networked dynamical systems. We assume…
The graph is one of the most widely used mathematical structures in engineering and science because of its representational power and inherent ability to demonstrate the relationship between objects. The objective of this work is to…
We propose an algorithm to estimate the topology of an embedded metric graph from a well-sampled finite subset of the underlying graph.
We propose a functional view of matrix decomposition problems on graphs such as geometric matrix completion and graph regularized dimensionality reduction. Our unifying framework is based on the key idea that using a reduced basis to…
Machine learning on graphs is an important and ubiquitous task with applications ranging from drug design to friendship recommendation in social networks. The primary challenge in this domain is finding a way to represent, or encode, graph…
Vertex splitting replaces a vertex by two copies and partitions its incident edges amongst the copies. This problem has been studied as a graph editing operation to achieve desired properties with as few splits as possible, most often…
We study a large family of graph covering problems, whose definitions rely on distances, for graphs of bounded cyclomatic number (that is, the minimum number of edges that need to be removed from the graph to destroy all cycles). These…
We describe a linear-time algorithm that finds a planar drawing of every graph of a simple line or pseudoline arrangement within a grid of area O(n^{7/6}). No known input causes our algorithm to use area \Omega(n^{1+\epsilon}) for any…
Optimal curve methods provide a fundamental framework for tubular centerline tracking. Point-wise approaches, such as minimal paths, are theoretically elegant but often suffer from shortcut and short-branch combination problems in complex…
Due to the advent of the expressions of data other than tabular formats, the topological compositions which make samples interrelated came into prominence. Analogically, those networks can be interpreted as social connections, dataflow…