Related papers: Certifying clusters from sum-of-norms clustering
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…
Standard conformal prediction methods provide a marginal coverage guarantee, which means that for a random test point, the conformal prediction set contains the true label with a user-specified probability. In many classification problems,…
A new clustering accuracy measure is proposed to determine the unknown number of clusters and to assess the quality of clustering of a data set given in any dimensional space. Our validity index applies the classical nonparametric…
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…
A general scheme for divisive hierarchical clustering algorithms is proposed. It is made of three main steps : first a splitting procedure for the subdivision of clusters into two subclusters, second a local evaluation of the bipartitions…
Estimation is the computational task of recovering a hidden parameter $x$ associated with a distribution $D_x$, given a measurement $y$ sampled from the distribution. High dimensional estimation problems arise naturally in statistics,…
We study the complexity of finding an optimal hierarchical clustering of an unweighted similarity graph under the recently introduced Dasgupta objective function. We introduce a proof technique, called the normalization procedure, that…
When scholars suspect units are dependent on each other within clusters but independent of each other across clusters, they employ cluster-robust standard errors (CRSEs). Nevertheless, what to cluster over is sometimes unknown. For…
We revisit the $(f,g)$-clustering problem that we introduced in a recent work [SODA'25], and which subsumes fundamental clustering problems such as $k$-Center, $k$-Median, Min-Sum of Radii, and Min-Load $k$-Clustering. This problem assigns…
We give an efficient algorithm for robustly clustering of a mixture of two arbitrary Gaussians, a central open problem in the theory of computationally efficient robust estimation, assuming only that the the means of the component Gaussians…
Clustering is a long-standing research problem and a fundamental tool in AI and data analysis. The traditional k-center problem, a fundamental theoretical challenge in clustering, has a best possible approximation ratio of 2, and any…
Subspace clustering methods based on $\ell_1$, $\ell_2$ or nuclear norm regularization have become very popular due to their simplicity, theoretical guarantees and empirical success. However, the choice of the regularizer can greatly impact…
Determining the number of clusters is a central challenge in unsupervised learning, where ground-truth labels are unavailable. The Silhouette coefficient is a widely used internal validation metric for this task, yet its standard…
Clustering is a fundamental problem in many areas, which aims to partition a given data set into groups based on some distance measure, such that the data points in the same group are similar while that in different groups are dissimilar.…
$ $In many optimization problems, a feasible solution induces a multi-dimensional cost vector. For example, in load-balancing a schedule induces a load vector across the machines. In $k$-clustering, opening $k$ facilities induces an…
Consistency is a key property of all statistical procedures analyzing randomly sampled data. Surprisingly, despite decades of work, little is known about consistency of most clustering algorithms. In this paper we investigate consistency of…
Deep clustering is a deep neural network-based speech separation algorithm that first trains the mixed component of signals with high-dimensional embeddings, and then uses a clustering algorithm to separate each mixture of sources. In this…
Knowledge of functional groupings of neurons can shed light on structures of neural circuits and is valuable in many types of neuroimaging studies. However, accurately determining which neurons carry out similar neurological tasks via…
Decentralized optimization is well studied for smooth unconstrained problems. However, constrained problems or problems with composite terms are an open direction for research. We study structured (or composite) optimization problems, where…
We analyze the clustering problem through a flexible probabilistic model that aims to identify an optimal partition on the sample X 1 , ..., X n. We perform exact clustering with high probability using a convex semidefinite estimator that…