Related papers: Graph Comparison via the Non-backtracking Spectrum
Graphs are versatile tools for representing structured data. As a result, a variety of machine learning methods have been studied for graph data analysis. Although many such learning methods depend on the measurement of differences between…
Comparison among graphs is ubiquitous in graph analytics. However, it is a hard task in terms of the expressiveness of the employed similarity measure and the efficiency of its computation. Ideally, graph comparison should be invariant to…
Graph is an abstract representation commonly used to model networked systems and structure. In problems across various fields, including computer vision and pattern recognition, and neuroscience, graphs are often brought into comparison (a…
The shape and orientation of data clouds reflect variability in observations that can confound pattern recognition systems. Subspace methods, utilizing Grassmann manifolds, have been a great aid in dealing with such variability. However,…
Distance matrices of graphs were introduced by Graham and Pollack in 1971 to study a problem in communications. Since then, there has been extensive research on the distance matrices of graphs -- a 2014 survey by Aouchiche and Hansen on…
Graph embedding techniques are useful to characterize spectral signature relations for hyperspectral images. However, such images consists of disjoint classes due to spatial details that are often ignored by existing graph computing tools.…
Graphs can be used to represent a wide variety of data belonging to different domains. Graphs can capture the relationship among data in an efficient way, and have been widely used. In recent times, with the advent of Big Data, there has…
In this paper, matching pairs of random graphs under the community structure model is considered. The problem emerges naturally in various applications such as privacy, image processing and DNA sequencing. A pair of randomly generated…
This article introduces a concept and measure of graph compartmentalization. This new measure allows for principled comparison between graphs of arbitrary structure, unlike existing measures such as graph modularity. The proposed measure is…
The graph edit distance (GED) is a well-established distance measure widely used in many applications. However, existing methods for the GED computation suffer from several drawbacks including oversized search space, huge memory…
The newly introduced neighborhood matrix extends the power of adjacency and distance matrices to describe the topology of graphs. The adjacency matrix enumerates which pairs of vertices share an edge and it may be summarized by the degree…
Statistical graph models aim at modeling graphs as random realization among a set of possible graphs. One issue is to evaluate whether or not a graph is likely to have been generated by one particular model. In this paper we introduce the…
Graph embedding has become a key component of many data mining and analysis systems. Current graph embedding approaches either sample a large number of node pairs from a graph to learn node embeddings via stochastic optimization or…
As large graph datasets become increasingly common across many fields, sampling is often needed to reduce the graphs into manageable sizes. This procedure raises critical questions about representativeness as no sample can capture the…
Recent advances in self-supervised learning and neural network scaling have enabled the creation of large models, known as foundation models, which can be easily adapted to a wide range of downstream tasks. The current paradigm for…
The main goal of this note is to illustrate the advantage of analyzing the non-backtracking spectrum of a regular graph rather than the ordinary spectrum. We show that by switching to non-backtracking spectrum, the method of proof used in…
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…
Due to their capacity to encode rich structural information, labeled graphs are often used for modeling various kinds of objects such as images, molecules, and chemical compounds. If pattern recognition problems such as clustering and…
In this paper, we introduce a graph matching method that can account for constraints of arbitrary order, with arbitrary potential functions. Unlike previous decomposition approaches that rely on the graph structures, we introduce a…
Recently, one has seen a surge of interest in developing such methods including ones for learning such representations for (undirected) graphs (while preserving important properties). However, most of the work to date on embedding graphs…