Related papers: Nearest Embedded and Embedding Self-Nested Trees
The graph edit distance is used for comparing graphs in various domains. Due to its high computational complexity it is primarily approximated. Widely-used heuristics search for an optimal assignment of vertices based on the distance…
Approximate nearest neighbor algorithms are used to speed up nearest neighbor search in a wide array of applications. However, current indexing methods feature several hyperparameters that need to be tuned to reach an acceptable…
This paper addresses the problem of finding a representation of a subtree distance, which is an extension of the tree metric. We show that a minimal representation is uniquely determined by a given subtree distance, and give a linear time…
Structural network embedding is a crucial step in enabling effective downstream tasks for complex systems that aims to project a network into a lower-dimensional space while preserving similarities among nodes. We introduce a simple and…
This work presents novel algorithms for learning Bayesian network structures with bounded treewidth. Both exact and approximate methods are developed. The exact method combines mixed-integer linear programming formulations for structure…
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…
We combine two methods for the lossless compression of unlabeled graphs - entropy compressing adjacency lists and computing canonical names for vertices - and solve an ensuing novel optimisation problem: Minimum-Entropy Tree-Extraction…
Recent theoretical work has demonstrated that Neighbor Joining applied to concatenated DNA sequences is a statistically consistent method of species tree reconstruction. This brief note compares the accuracy of this approach to other…
The largest common embeddable subtree problem asks for the largest possible tree embeddable into two input trees and generalizes the classical maximum common subtree problem. Several variants of the problem in labeled and unlabeled rooted…
Single-level density-based approach has long been widely acknowledged to be a conceptually and mathematically convincing clustering method. In this paper, we propose an algorithm called "best-scored clustering forest" that can obtain the…
We study the inference of network archaeology in growing random geometric graphs. We consider the root finding problem for a random nearest neighbor tree in dimension $d \in \mathbb{N}$, generated by sequentially embedding vertices…
Finding a minimum spanning tree (MST) for $n$ points in an arbitrary metric space is a fundamental primitive for hierarchical clustering and many other ML tasks, but this takes $\Omega(n^2)$ time to even approximate. We introduce a…
In this paper, we study the online nearest neighbor random tree in dimension $d\in \mathbb N$ (called $d$-NN tree for short) defined as follows. We fix the torus $\mathbb T^d_n$ of dimension $d$ and area $n$ and equip it with the metric…
We present Neural Random Forest Imitation - a novel approach for transforming random forests into neural networks. Existing methods propose a direct mapping and produce very inefficient architectures. In this work, we introduce an imitation…
Cubicity of a graph $G$ is the smallest dimension $d$, for which $G$ is a unit disc graph in ${\mathbb{R}}^d$, under the $l^\infty$ metric, i.e. $G$ can be represented as an intersection graph of $d$-dimensional (axis-parallel) unit…
Finding the exact close neighbors of each fluid element in mesh-free computational hydrodynamical methods, such as the Smoothed Particle Hydrodynamics (SPH), often becomes a main bottleneck for scaling their performance beyond a few million…
We present improved learning-augmented algorithms for finding an approximate minimum spanning tree (MST) for points in an arbitrary metric space. Our work follows a recent framework called metric forest completion (MFC), where the learned…
We consider the numerical taxonomy problem of fitting a positive distance function ${D:{S\choose 2}\rightarrow \mathbb R_{>0}}$ by a tree metric. We want a tree $T$ with positive edge weights and including $S$ among the vertices so that…
An algorithm is proposed for constructing directed spanning forests of the minimum weight, in which the maximum possible degree of affinity between the minimum forests is preserved when the number of trees changes. The correctness of the…
Metric learning has the aim to improve classification accuracy by learning a distance measure which brings data points from the same class closer together and pushes data points from different classes further apart. Recent research has…