Related papers: The Neighbor-Net Algorithm
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…
Similarity search is a fundamental building block for information retrieval on a variety of datasets. The notion of a neighbor is often based on binary considerations, such as the k nearest neighbors. However, considering that data is often…
We compare the performance of three nearest neighbor search algorithms: the Orchard, ball tree, and VP-tree algorithms. These algorithms are commonly used for nearest-neighbor searches and are known for their efficiency in large datasets.…
In this paper, we will analyze the behavior of the Neighbor Joining algorithm on five taxa and we will show that the partition of the sample (data) space for estimation of a tree topology with five taxa into subspaces, within each of which…
Distance-based approaches in phylogenetics such as Neighbor-Joining are a fast and popular approach for building trees. These methods take pairs of sequences from them construct a value that, in expectation, is additive under a stochastic…
In pattern recognition or machine learning, it is a very fundamental task to find nearest neighbors of a given point. All the methods for the task work basically by comparing the given point to all the points in the data set. That is why…
In this work we study the interleaving distance between merge trees from a combinatorial point of view. We use a particular type of matching between trees to obtain a novel formulation of the distance. With such formulation, we tackle the…
We present approximation algorithms for the following NP-hard optimization problems related to bottleneck spanning trees in metric spaces. 1. The disjoint bottleneck spanning tree problem: Given $n$ pairs of points in a metric space, find…
Computing fixed-radius near-neighbor graphs is an important first step for many data analysis algorithms. Near-neighbor graphs connect points that are close under some metric, endowing point clouds with a combinatorial structure. As…
A critical piece of the modern information retrieval puzzle is approximate nearest neighbor search. Its objective is to return a set of $k$ data points that are closest to a query point, with its accuracy measured by the proportion of exact…
This paper introduces a hierarchical clustering algorithm, the Clustroid Hierarchical Nearest Neighbor ($\mathrm{CHN}^2$), designed for datasets with a countably infinite number of points. The method builds clusters across successive levels…
Regression trees and their ensemble methods are popular methods for nonparametric regression: they combine strong predictive performance with interpretable estimators. To improve their utility for locally smooth response surfaces, we study…
Connected clustering denotes a family of constrained clustering problems in which we are given a distance metric and an undirected connectivity graph $G$ that can be completely unrelated to the metric. The aim is to partition the $n$…
The use of complex networks as a modern approach to understanding the world and its dynamics is well-established in literature. The adjacency matrix, which provides a one-to-one representation of a complex network, can also yield several…
A central task in the study of molecular sequence data from present-day species is the reconstruction of the ancestral relationships. The most established approach to tree reconstruction is the maximum likelihood (ML) method. In this…
In this article, we propose a new fast nearest neighbor search algorithm, based on vector quantization. Like many other branch and bound search algorithms [1,10], a preprocessing recursively partitions the data set into disjointed subsets…
In this paper, we investigate the topology convergence problem for the gossip-based Gradient overlay network. In an overlay network where each node has a local utility value, a Gradient overlay network is characterized by the properties…
We propose a nearest neighbor based clustering algorithm that results in a naturally defined hierarchy of clusters. In contrast to the agglomerative and divisive hierarchical clustering algorithms, our approach is not dependent on the…
Nearest neighbor (kNN) methods have been gaining popularity in recent years in light of advances in hardware and efficiency of algorithms. There is a plethora of methods to choose from today, each with their own advantages and…
We consider the problem of uniformly generating a spanning tree, of a connected undirected graph. This process is useful to compute statistics, namely for phylogenetic trees. We describe a Markov chain for producing these trees. For cycle…