Related papers: Hierarchical Clustering: New Bounds and Objective
Hierarchical clustering is a recursive partitioning of a dataset into clusters at an increasingly finer granularity. Motivated by the fact that most work on hierarchical clustering was based on providing algorithms, rather than optimizing a…
Hierarchical Clustering trees have been widely accepted as a useful form of clustering data, resulting in a prevalence of adopting fields including phylogenetics, image analysis, bioinformatics and more. Recently, Dasgupta (STOC 16')…
Hierarchical clustering has been a popular method in various data analysis applications. It partitions a data set into a hierarchical collection of clusters, and can provide a global view of (cluster) structure behind data across different…
Hierarchical clustering is a fundamental task in data analysis, yet for a long time it lacked a principled objective function. Dasgupta [STOC 2016] initiated a formal framework by introducing a discrete objective function for cluster trees.…
Hierarchical clustering (HC) is an important data analysis technique in which the goal is to recursively partition a dataset into a tree-like structure while grouping together similar data points at each level of granularity. Unfortunately,…
Recently, Hierarchical Clustering (HC) has been considered through the lens of optimization. In particular, two maximization objectives have been defined. Moseley and Wang defined the \emph{Revenue} objective to handle similarity…
Hierarchical clustering studies a recursive partition of a data set into clusters of successively smaller size, and is a fundamental problem in data analysis. In this work we study the cost function for hierarchical clustering introduced by…
A combinatorial cost function for hierarchical clustering was introduced by Dasgupta \cite{dasgupta2016cost}. It has been generalized by Cohen-Addad et al. \cite{cohen2019hierarchical} to a general form named admissible function. In this…
Dasgupta recently introduced a cost function for the hierarchical clustering of a set of points given pairwise similarities between them. He showed that this function is NP-hard to optimize, but a top-down recursive partitioning heuristic…
Hierarchical Clustering is an unsupervised data analysis method which has been widely used for decades. Despite its popularity, it had an underdeveloped analytical foundation and to address this, Dasgupta recently introduced an optimization…
Clustering is a fundamental building block of modern statistical analysis pipelines. Fair clustering has seen much attention from the machine learning community in recent years. We are some of the first to study fairness in the context of…
This paper presents two efficient hierarchical clustering (HC) algorithms with respect to Dasgupta's cost function. For any input graph $G$ with a clear cluster-structure, our designed algorithms run in nearly-linear time in the input size…
Similarity-based Hierarchical Clustering (HC) is a classical unsupervised machine learning algorithm that has traditionally been solved with heuristic algorithms like Average-Linkage. Recently, Dasgupta reframed HC as a discrete…
Hierarchical Clustering (HC) is a widely studied problem in exploratory data analysis, usually tackled by simple agglomerative procedures like average-linkage, single-linkage or complete-linkage. In this paper we focus on two objectives,…
The minimum height of vertex and edge partition trees are well-studied graph parameters known as, for instance, vertex and edge ranking number. While they are NP-hard to determine in general, linear-time algorithms exist for trees.…
Hierarchical clustering is a stronger extension of one of today's most influential unsupervised learning methods: clustering. The goal of this method is to create a hierarchy of clusters, thus constructing cluster evolutionary history and…
Hierarchical clustering is a popular unsupervised data analysis method. For many real-world applications, we would like to exploit prior information about the data that imposes constraints on the clustering hierarchy, and is not captured by…
In this paper, we introduce a local search algorithm for hierarchical clustering. For the local step, we consider a tree re-arrangement operation, known as the {\em interchange}, which involves swapping two closely positioned sub-trees…
Hierarchical clustering is a fundamental task often used to discover meaningful structures in data, such as phylogenetic trees, taxonomies of concepts, subtypes of cancer, and cascades of particle decays in particle physics. Typically…
Recent works on Hierarchical Clustering (HC), a well-studied problem in exploratory data analysis, have focused on optimizing various objective functions for this problem under arbitrary similarity measures. In this paper we take the first…