Related papers: Labeled Interleaving Distance for Reeb Graphs
Trees with labelled leaves and with all other vertices of degree three play an important role in systematic biology and other areas of classification. A classical combinatorial result ensures that such trees can be uniquely reconstructed…
A multilabeled tree (or MUL-tree) is a rooted tree in which every leaf is labelled by an element from some set, but in which more than one leaf may be labelled by the same element of that set. In phylogenetics, such trees are used in…
A spanning 2-forest separating vertices $u$ and $v$ of an undirected connected graph is a spanning forest with 2 components such that $u$ and $v$ are in distinct components. Aside from their combinatorial significance, spanning 2-forests…
Three-way dissimilarities are a generalization of (two-way) dissimilarities which can be used to indicate the lack of homogeneity or resemblance between any three objects. Such maps have applications in cluster analysis, and have been used…
Techniques from metric geometry have become fundamental tools in modern mathematical data science, providing principled methods for comparing datasets modeled as finite metric spaces. Two of the central tools in this area are the…
This work focuses on the problem of multi-label learning with missing labels (MLML), which aims to label each test instance with multiple class labels given training instances that have an incomplete/partial set of these labels. The key…
Given a graph $G$, a labeling of $G$ is an injective function $f:V(G)\rightarrow\mathbb{Z}_{\ge 0}$. Under the labeling $f$, the label of a vertex $v$ is $f(v)$, and the induced label of an edge $uv$ is $|f(u) - f(v)|$. The labeling $f$ is…
Graphs are interesting structures: extremely useful to depict real-life problems, extremely easy to understand given a sketch, extremely complicated to represent formally, extremely complicated to compare. Phylogeny is the study of the…
We propose a novel unsupervised approach for linking records across arbitrarily many files, while simultaneously detecting duplicate records within files. Our key innovation is to represent the pattern of links between records as a {\em…
In this paper, we present a novel deep metric learning method to tackle the multi-label image classification problem. In order to better learn the correlations among images features, as well as labels, we attempt to explore a latent space,…
We unify several seemingly different graph and digraph classes under one umbrella. These classes are all broadly speaking different generalizations of interval graphs, and include, in addition to interval graphs, also adjusted interval…
Multi-label learning is concerned with the classification of data with multiple class labels. This is in contrast to the traditional classification problem where every data instance has a single label. Due to the exponential size of output…
Graph embedding maps a graph into a convenient vector-space representation for graph analysis and machine learning applications. Many graph embedding methods hinge on a sampling of context nodes based on random walks. However, random walks…
Interleaving distances are used widely in Topological Data Analysis (TDA) as a tool for comparing topological signatures of datasets. The theory of interleaving distances has been extended through various category-theoretic constructions,…
A graph is distance magic if it admits a bijective labeling of its vertices by integers from $1$ up to the order of the graph in such a way that the sum of the labels of all the neighbors of a vertex is independent of a given vertex. We…
In topological data analysis and visualization, topological descriptors such as persistence diagrams, merge trees, contour trees, Reeb graphs, and Morse-Smale complexes play an essential role in capturing the shape of scalar field data. We…
Given a map $f:X \to M$ from a topological space $X$ to a metric space $M$, a decorated Reeb space consists of the Reeb space, together with an attribution function whose values recover geometric information lost during the construction of…
The Reeb space is a fundamental data structure in computational topology that represents the fiber topology of a multi-field (or multiple scalar fields), extending the level set topology of a scalar field. Efficient algorithms have been…
The graph traversal edit distance (GTED), introduced by Ebrahimpour Boroojeny et al.~(2018), is an elegant distance measure defined as the minimum edit distance between strings reconstructed from Eulerian trails in two edge-labeled graphs.…
A \emph{mixed interval graph} is an interval graph that has, for every pair of intersecting intervals, either an arc (directed arbitrarily) or an (undirected) edge. We are particularly interested in scenarios where edges and arcs are…