Related papers: Differentially-Private Hierarchical Clustering wit…

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,…

We study the problem of performing counting queries at different levels in hierarchical structures while preserving individuals' privacy. Motivated by applications, we propose a new error measure for this problem by considering a…

Clustering is an unsupervised machine learning methodology where unlabeled elements/objects are grouped together aiming to the construction of well-established clusters that their elements are classified according to their similarity. The…

Clustering is a fundamental data processing task used for grouping records based on one or more features. In the vertically partitioned setting, data is distributed among entities, with each holding only a subset of those features. A key…

Spectral clustering has been one of the widely used methods for community detection in networks. However, large-scale networks bring computational challenges to the eigenvalue decomposition therein. In this paper, we study the spectral…

The most widely used internal measure for clustering evaluation is the silhouette coefficient, whose naive computation requires a quadratic number of distance calculations, which is clearly unfeasible for massive datasets. Surprisingly,…

Cluster analysis, or clustering, plays a crucial role across numerous scientific and engineering domains. Despite the wealth of clustering methods proposed over the past decades, each method is typically designed for specific scenarios and…

We consider stochastic settings for clustering, and develop provably-good approximation algorithms for a number of these notions. These algorithms yield better approximation ratios compared to the usual deterministic clustering setting.…

This paper focuses on density-based clustering, particularly the Density Peak (DP) algorithm and the one based on density-connectivity DBSCAN; and proposes a new method which takes advantage of the individual strengths of these two methods…

We propose a hierarchical correlation clustering method that extends the well-known correlation clustering to produce hierarchical clusters applicable to both positive and negative pairwise dissimilarities. Then, in the following, we study…

Meila (2018) introduces an optimization based method called the Sublevel Set method, to guarantee that a clustering is nearly optimal and "approximately correct" without relying on any assumptions about the distribution that generated the…

This paper characterizes hierarchical clustering methods that abide by two previously introduced axioms -- thus, denominated admissible methods -- and proposes tractable algorithms for their implementation. We leverage the fact that, for…

Differential privacy (DP) is a compelling privacy definition that explains the privacy-utility tradeoff via formal, provable guarantees. Inspired by recent progress toward general-purpose data release algorithms, we propose a private…

With the emergence of Artificial Intelligence, numerical algorithms are moving towards more approximate approaches. For methods such as PCA or diffusion maps, it is necessary to compute eigenvalues of a large matrix, which may also be dense…

Topological methods have the potential of exploring data clouds without making assumptions on their the structure. Here we propose a hierarchical topological clustering algorithm that can be implemented with any distance choice. The…

We address the classical problem of hierarchical clustering, but in a framework where one does not have access to a representation of the objects or their pairwise similarities. Instead, we assume that only a set of comparisons between…

This article presents a novel pretopology-based algorithm designed to address the challenges of clustering mixed data without the need for dimensionality reduction. Leveraging Disjunctive Normal Form, our approach formulates customizable…

In this note, we consider the problem of differentially privately (DP) computing an anonymized histogram, which is defined as the multiset of counts of the input dataset (without bucket labels). In the low-privacy regime $\epsilon \geq 1$,…

We study the problem of privacy-preserving $k$-means clustering in the horizontally federated setting. Existing federated approaches using secure computation suffer from substantial overheads and do not offer output privacy. At the same…

Clustering analysis by nonnegative low-rank approximations has achieved remarkable progress in the past decade. However, most approximation approaches in this direction are still restricted to matrix factorization. We propose a new low-rank…