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We study bipartite community detection in networks, or more generally the network biclustering problem. We present a fast two-stage procedure based on spectral initialization followed by the application of a pseudo-likelihood classifier…
This article develops the theory of risk budgeting portfolios, when we would like to impose weight constraints. It appears that the mathematical problem is more complex than the traditional risk budgeting problem. The formulation of the…
The minimum sum-of-squares clustering (MSSC), or k-means type clustering, is traditionally considered an unsupervised learning task. In recent years, the use of background knowledge to improve the cluster quality and promote…
In this paper, we consider the problem of partitioning a small data sample of size $n$ drawn from a mixture of 2 sub-gaussian distributions in $\R^p$. We consider semidefinite programming relaxations of an integer quadratic program that is…
We derive and analyze a generic, recursive algorithm for estimating all splits in a finite cluster tree as well as the corresponding clusters. We further investigate statistical properties of this generic clustering algorithm when it…
Notwithstanding the popularity of conventional clustering algorithms such as K-means and probabilistic clustering, their clustering results are sensitive to the presence of outliers in the data. Even a few outliers can compromise the…
When approaching a clustering problem, choosing the right clustering algorithm and parameters is essential, as each clustering algorithm is proficient at finding clusters of a particular nature. Due to the unsupervised nature of clustering…
Research on cluster analysis for categorical data continues to develop, with new clustering algorithms being proposed. However, in this context, the determination of the number of clusters is rarely addressed. In this paper, we propose a…
Given a set of points, clustering consists of finding a partition of a point set into $k$ clusters such that the center to which a point is assigned is as close as possible. Most commonly, centers are points themselves, which leads to the…
A major challenge in cluster analysis is that the number of data clusters is mostly unknown and it must be estimated prior to clustering the observed data. In real-world applications, the observed data is often subject to heavy tailed noise…
Inspired by regularization techniques in statistics and machine learning, we study complementary composite minimization in the stochastic setting. This problem corresponds to the minimization of the sum of a (weakly) smooth function endowed…
Maximum diversity aims at selecting a diverse set of high-quality objects from a collection, which is a fundamental problem and has a wide range of applications, e.g., in Web search. Diversity under a uniform or partition matroid constraint…
Population-based methods can cope with a variety of different problems, including problems of remarkably higher complexity than those traditional methods can handle. The main procedure consists of successively updating a population of…
We consider the problem of clustering in the learning-augmented setting, where we are given a data set in $d$-dimensional Euclidean space, and a label for each data point given by an oracle indicating what subsets of points should be…
This study investigates the optimal selection of parameters for collaborative clustering while ensuring data privacy. We focus on key clustering algorithms within a collaborative framework, where multiple data owners combine their data. A…
Spectral algorithms leverage spectral regularization techniques to analyze and process data, providing a flexible framework for addressing supervised learning problems. To deepen our understanding of their performance in real-world…
Graph clustering involves the task of dividing nodes into clusters, so that the edge density is higher within clusters as opposed to across clusters. A natural, classic and popular statistical setting for evaluating solutions to this…
The Expectation-Maximization (EM) algorithm is an iterative method to maximize the log-likelihood function for parameter estimation. Previous works on the convergence analysis of the EM algorithm have established results on the asymptotic…
We introduce a general semiparametric clusterwise elliptical distribution to assess how latent cluster structure shapes continuous outcomes. Using a subjectwise representation, we first estimate cluster-specific mean vectors and a…
This paper focuses on scalability and robustness of spectral clustering for extremely large-scale datasets with limited resources. Two novel algorithms are proposed, namely, ultra-scalable spectral clustering (U-SPEC) and ultra-scalable…