Related papers: Edit Distance between Merge Trees

The graph edit distance (GED) is a flexible distance measure which is widely used for inexact graph matching. Since its exact computation is NP-hard, heuristics are used in practice. A popular approach is to obtain upper bounds for GED via…

A matching complex of a simple graph $G$ is a simplicial complex with faces given by the matchings of $G$. The topology of matching complexes is mysterious; there are few graphs for which the homotopy type is known. Marietti and Testa…

There is a rising interest in mapping trees using satellite or aerial imagery, but there is no standardized evaluation protocol for comparing and enhancing methods. In dense canopy areas, the high variability of tree sizes and their spatial…

Federated learning has emerged as a promising distributed learning paradigm that facilitates collaborative learning among multiple parties without transferring raw data. However, most existing federated learning studies focus on either…

A similarity join aims to find all similar pairs between two collections of records. Established approaches usually deal with synthetic differences like typos and abbreviations, but neglect the semantic relations between words. Such…

We consider unsupervised estimation of mixtures of discrete graphical models, where the class variable corresponding to the mixture components is hidden and each mixture component over the observed variables can have a potentially different…

Graph Edit Distance (GED) is a general and domain-agnostic metric to measure graph similarity, widely used in graph search or retrieving tasks. However, the exact GED computation is known to be NP-complete. For instance, the widely used A*…

Geodesic distance, commonly called shortest path length, has proved useful in a great variety of disciplines. It has been playing a significant role in search engine at present and so attracted considerable attention at the last few…

The topological information of a network can be retrieved equivalently from its complement consisting of the same nodes but complementary edges. Hence the partition of a network into certain substructures based on given criteria should be…

Phylogenetic mixtures model the inhomogeneous molecular evolution commonly observed in data. The performance of phylogenetic reconstruction methods where the underlying data is generated by a mixture model has stimulated considerable recent…

Clustering is a fundamental approach to understanding data patterns, wherein the intuitive Euclidean distance space is commonly adopted. However, this is not the case for implicit cluster distributions reflected by qualitative attribute…

We propose a flexible and multi-scale method for organizing, visualizing, and understanding datasets sampled from or near stratified spaces. The first part of the algorithm produces a cover tree using adaptive thresholds based on a…

Networks are important representations in computer science to communicate structural aspects of a given system of interacting components. The evolution of a network has several topological properties that can provide us information on the…

Identifying and comparing topological features, particularly cycles, across different topological objects remains a fundamental challenge in persistent homology and topological data analysis. This work introduces a novel framework for…

Metric embeddings are central to metric theory and its applications. Here we consider embeddings of a different sort: maps from a set to subsets of a metric space so that distances between points are approximated by minimal distances…

The tree edit distance (TED) between two rooted ordered trees with $n$ nodes labeled from an alphabet $\Sigma$ is the minimum cost of transforming one tree into the other by a sequence of valid operations consisting of insertions, deletions…

Tree-cut width is a parameter that has been introduced as an attempt to obtain an analogue of treewidth for edge cuts. Unfortunately, in spite of its desirable structural properties, it turned out that tree-cut width falls short as an…

Topological Data Analysis (TDA) uses insights from topology to create representations of data able to capture global and local geometric and topological properties. Its methods have successfully been used to develop estimations of fractal…

Community detection is one of the most active fields in complex networks analysis, due to its potential value in practical applications. Many works inspired by different paradigms are devoted to the development of algorithmic solutions…

The comprehensive characterization of the structure of complex networks is essential to understand the dynamical processes which guide their evolution. The discovery of the scale-free distribution and the small world property of real…