Related papers: Fitting trees to $\ell_1$-hyperbolic distances
There are several tools available to infer phylogenetic trees, which depict the evolutionary relationships among biological entities such as viral and bacterial strains in infectious outbreaks, or cancerous cells in tumor progression trees.…
A widely used method for determining the similarity of two labeled trees is to compute a maximum agreement subtree of the two trees. Previous work on this similarity measure is only concerned with the comparison of labeled trees of two…
This is an expository article on visual metrics on boundaries of hyperbolic metric spaces. We discuss the construction of visual metrics, quasisymmetries and their invariants, Hausdorff and conformal dimension, and constructions and…
Hyperbolic geometry is an effective geometry for embedding hierarchical data structures. Hyperbolic learning has therefore become increasingly prominent in machine learning applications where data is hierarchically organized or governed by…
Predicting Internet round-trip time (RTT) is critical for routing optimization, quality-of-service (QoS) provisioning, and traffic engineering, yet remains challenging due to long-term temporal dependencies, evolving routing dynamics, and…
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…
Hyperbolic space is becoming a popular choice for representing data due to the hierarchical structure - whether implicit or explicit - of many real-world datasets. Along with it comes a need for algorithms capable of solving fundamental…
We initiate the study of metric embeddings with \emph{outliers}. Given some metric space $(X,\rho)$ we wish to find a small set of outlier points $K \subset X$ and either an isometric or a low-distortion embedding of $(X\setminus K,\rho)$…
Network embedding is a fervid topic in current networks science and observes that most real complex systems can be embedded in hidden metrics space and emerge as the geometrical property, where the geometric distance between nodes…
Designing well-connected graphs is a fundamental problem that frequently arises in various contexts across science and engineering. The weighted number of spanning trees, as a connectivity measure, emerges in numerous problems and plays a…
Tree perception is an essential building block toward autonomous forestry operations. Current developments generally consider input data from lidar sensors to solve forest navigation, tree detection and diameter estimation problems. Whereas…
We introduce a semiparametric approach to neighbor-based classification. We build off the recently proposed Boundary Trees algorithm by Mathy et al.(2015) which enables fast neighbor-based classification, regression and retrieval in large…
The problem of {\em efficiently} finding the best match for a query in a given set with respect to the Euclidean distance or the cosine similarity has been extensively studied in literature. However, a closely related problem of efficiently…
Metric embeddings into structured spaces, particularly hierarchically well-separated trees (HSTs), are a fundamental tool in the design of online algorithms. In the classical online embedding setting, points arrive sequentially and must be…
We extend decision tree and random forest algorithms to product space manifolds: Cartesian products of Euclidean, hyperspherical, and hyperbolic manifolds. Such spaces have extremely expressive geometries capable of representing many…
We present a new approximation algorithm for the treewidth problem which finds an upper bound on the treewidth and constructs a corresponding tree decomposition as well. Our algorithm is a faster variation of Reed's classical algorithm. For…
Treewidth and hypertree width have proven to be highly successful structural parameters in the context of the Constraint Satisfaction Problem (CSP). When either of these parameters is bounded by a constant, then CSP becomes solvable in…
Let $G = (V,E)$ denote a simple graph with the vertex set $V$ and the edge set $E$. The profile of a vertex set $V'\subseteq V$ denotes the multiset of pairwise distances between the vertices of $V'$. Two disjoint subsets of $V$ are…
Phylogenetic trees and networks are leaf-labelled graphs used to model evolution. Display graphs are created by identifying common leaf labels in two or more phylogenetic trees or networks. The treewidth of such graphs is bounded as a…
An embedding is a function that maps entities from one algebraic structure into another while preserving certain characteristics. Embeddings are being used successfully for mapping relational data or text into vector spaces where they can…