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The purpose of this paper is twofold. On a technical side, we propose an extension of the Hausdorff distance from metric spaces to spaces equipped with asymmetric distance measures. Specifically, we focus on the family of Bregman…
Pairwise comparison of graphs is key to many applications in Machine learning ranging from clustering, kernel-based classification/regression and more recently supervised graph prediction. Distances between graphs usually rely on…
Whether comparing networks to each other or to random expectation, measuring dissimilarity is essential to understanding the complex phenomena under study. However, determining the structural dissimilarity between networks is an ill-defined…
Time series data play an important role in many applications and their analysis reveals crucial information for understanding the underlying processes. Among the many time series learning tasks of great importance, we here focus on…
In this paper, a new measurement to compare two large-scale graphs based on the theory of quantum probability is proposed. An explicit form for the spectral distribution of the corresponding adjacency matrix of a graph is established. Our…
Similarity search is a fundamental building block for information retrieval on a variety of datasets. The notion of a neighbor is often based on binary considerations, such as the k nearest neighbors. However, considering that data is often…
Nearest neighbor search is a fundamental data structure problem with many applications in machine learning, computer vision, recommendation systems and other fields. Although the main objective of the data structure is to quickly report…
A geometric graph is a combinatorial graph, endowed with a geometry that is inherited from its embedding in a Euclidean space. Formulation of a meaningful measure of (dis-)similarity in both the combinatorial and geometric structures of two…
In this paper, we present a new metric distance for comparing two large graphs to find similarities and differences between them based on one of the most important graph structural properties, which is Node Adjacency Information, for all…
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…
The problem of node-similarity in networks has motivated a plethora of such measures between node-pairs, which make use of the underlying graph structure. However, higher-order relations cannot be losslessly captured by mere graphs and…
This paper presents a spectral framework for quantifying the differentiation between graph data samples by introducing a novel metric named Graph Geodesic Distance (GGD). For two different graphs with the same number of nodes, our framework…
Graph isomorphism is a problem for which there is no known polynomial-time solution. Nevertheless, assessing (dis)similarity between two or more networks is a key task in many areas, such as image recognition, biology, chemistry, computer…
Gromov-Hausdorff distances measure shape difference between the objects representable as compact metric spaces, e.g. point clouds, manifolds, or graphs. Computing any Gromov-Hausdorff distance is equivalent to solving an NP-Hard…
The emergence of geometric deep learning as a novel framework to deal with graph-based representations has faded away traditional approaches in favor of completely new methodologies. In this paper, we propose a new framework able to combine…
Evaluating similarity between graphs is of major importance in several computer vision and pattern recognition problems, where graph representations are often used to model objects or interactions between elements. The choice of a distance…
Measuring similarity between complex objects is a fundamental task in many scientific fields. When objects are represented as graphs, graph similarity/distance measures offer a powerful framework for quantifying structural resemblance.…
Quantifying the similarity between two graphs is a fundamental algorithmic problem at the heart of many data analysis tasks for graph-based data. In this paper, we study the computational complexity of a family of similarity measures based…
Graph comparison plays a major role in many network applications. We often need a similarity metric for comparing networks according to their structural properties. Various network features - such as degree distribution and clustering…
The degree distribution is an important characteristic of complex networks. In many data analysis applications, the networks should be represented as fixed-length feature vectors and therefore the feature extraction from the degree…