Related papers: Differential network analysis and graph classifica…

Due to the ever rising importance of the network paradigm across several areas of science, comparing and classifying graphs represent essential steps in the networks analysis of complex systems. Both tasks have been recently tackled via…

Highlighting similarities and differences between networks is an informative task in investigating many biological processes. Typical examples are detecting differences between an inferred network and the corresponding gold standard, or…

Traditional graph centrality measures effectively quantify node importance but fail to capture the structural uniqueness of multi-scale connectivity patterns -- critical for understanding network resilience and function. This paper…

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…

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…

This document reviews the definition of the kernel distance, providing a gentle introduction tailored to a reader with background in theoretical computer science, but limited exposure to technology more common to machine learning,…

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…

Even though machine learning algorithms already play a significant role in data science, many current methods pose unrealistic assumptions on input data. The application of such methods is difficult due to incompatible data formats, or…

Identifying networks with similar characteristics in a given ensemble, or detecting pattern discontinuities in a temporal sequence of networks, are two examples of tasks that require an effective metric capable of quantifying network…

Kernel-based non-linear dimensionality reduction methods, such as Local Linear Embedding (LLE) and Laplacian Eigenmaps, rely heavily upon pairwise distances or similarity scores, with which one can construct and study a weighted graph…

For many machine learning problem settings, particularly with structured inputs such as sequences or sets of objects, a distance measure between inputs can be specified more naturally than a feature representation. However, most standard…

Learning a distance metric from the given training samples plays a crucial role in many machine learning tasks, and various models and optimization algorithms have been proposed in the past decade. In this paper, we generalize several…

We develop the theoretical foundations of a generalized Gromov-Hausdorff distance between functions on networks that has recently been applied to various subfields of topological data analysis and optimal transport. These functional…

Protein structures can be encoded into binary sequences, these are used to define a Hamming distance in conformational space: the distance between two different molecular conformations is the number of different bits in their sequences.…

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.…

Understanding and adequately assessing the difference between a true and a learnt causal graphs is crucial for causal inference under interventions. As an extension to the graph-based structural Hamming distance and structural intervention…

Sequence classification has numerous applications in various fields. Despite extensive studies in the last decades, many challenges still exist, particularly in pattern-based methods. Existing pattern-based methods measure the…

Starting with a similarity function between objects, it is possible to define a distance metric on pairs of objects, and more generally on probability distributions over them. These distance metrics have a deep basis in functional analysis,…

We provide a unifying framework linking two classes of statistics used in two-sample and independence testing: on the one hand, the energy distances and distance covariances from the statistics literature; on the other, maximum mean…

We provide a unifying framework linking two classes of statistics used in two-sample and independence testing: on the one hand, the energy distances and distance covariances from the statistics literature; on the other, distances between…