Clustering, as an unsupervised learning, is aimed at discovering the natural groupings of a
set of patterns, points, or objects. In clustering algorithms, a significant problem is the …

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 …

We study a decomposition-based scalable approach to kernel ridge regression, and show
that it achieves minimax optimal convergence rates under relatively mild conditions. The …

Abstract The Average Silhouette Width (ASW) is a popular cluster validation index to
estimate the number of clusters. The question whether it also is suitable as a general …

The brain network is usually constructed by estimating the connectivity matrix and
thresholding it at an arbitrary level. The problem with this standard method is that we do not …

The abundance of functional observations in scientific endeavors has led to a significant
development in tools for functional data analysis (FDA). This kind of data comes with several …

We study hierarchical clustering schemes under an axiomatic view. We show that within this
framework, one can prove a theorem analogous to one of Kleinberg (2002), in which one …

Clustering refers to the process of extracting maximally coherent groups from a set of objects
using pairwise, or high-order, similarities. Traditional approaches to this problem are based …

Hierarchical clustering is a data analysis method that has been used for decades. Despite its
widespread use, the method has an underdeveloped analytical foundation. Having a well …

Graph clustering is a fundamental task in many data-mining and machine-learning
pipelines. In particular, identifying a good hierarchical structure is at the same time a …