相关论文: Statistical and Computational Guarantees of Lloyd'…

We study clustering methods for binary data, first defining aggregation criteria that measure the compactness of clusters. Five new and original methods are introduced, using neighborhoods and population behavior combinatorial optimization…

The use of a finite mixture of normal distributions in model-based clustering allows to capture non-Gaussian data clusters. However, identifying the clusters from the normal components is challenging and in general either achieved by…

We introduce a new method for performing clustering with the aim of fitting clusters with different scatters and weights. It is designed by allowing to handle a proportion $\alpha$ of contaminating data to guarantee the robustness of the…

We consider the robust algorithms for the $k$-means clustering problem where a quantizer is constructed based on $N$ independent observations. Our main results are median of means based non-asymptotic excess distortion bounds that hold…

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…

We continue the investigation of problems concerning correlation clustering or clustering with qualitative information, which is a clustering formulation that has been studied recently. The basic setup here is that we are given as input a…

We study the problem of estimating the means of well-separated mixtures when an adversary may add arbitrary outliers. While strong guarantees are available when the outlier fraction is significantly smaller than the minimum mixing weight,…

We consider the problem of identifying multiway block structure from a large noisy tensor. Such problems arise frequently in applications such as genomics, recommendation system, topic modeling, and sensor network localization. We propose a…

The problem of multimodal clustering arises whenever the data are gathered with several physically different sensors. Observations from different modalities are not necessarily aligned in the sense there there is no obvious way to associate…

The paper tackles the problem of clustering multiple networks, directed or not, that do not share the same set of vertices, into groups of networks with similar topology. A statistical model-based approach based on a finite mixture of…

Mixed data comprises both numeric and categorical features, and mixed datasets occur frequently in many domains, such as health, finance, and marketing. Clustering is often applied to mixed datasets to find structures and to group similar…

We consider the problem of the statistical uncertainty of the correlation matrix in the optimization of a financial portfolio. We show that the use of clustering algorithms can improve the reliability of the portfolio in terms of the ratio…

We consider the problem of inferring an unknown number of clusters in replicated multinomial data. Under a model based clustering point of view, this task can be treated by estimating finite mixtures of multinomial distributions with or…

We study the structure of loops in networks using the notion of modulus of loop families. We introduce a new measure of network clustering by quantifying the richness of families of (simple) loops. Modulus tries to minimize the expected…

Designing efficient, effective, and consistent metric clustering algorithms is a significant challenge attracting growing attention. Traditional approaches focus on the stability of cluster centers; unfortunately, this neglects the…

Community-based graph clustering is one of the most popular topics in the analysis of complex social networks. This type of clustering involves grouping vertices that are considered to share more connections, whereas vertices in different…

Clustering is a fundamental task in data mining and machine learning, particularly for analyzing large-scale data. In this paper, we introduce Clust-Splitter, an efficient algorithm based on nonsmooth optimization, designed to solve the…

Cluster analysis faces two problems in high dimensions: first, the `curse of dimensionality' that can lead to overfitting and poor generalization performance; and second, the sheer time taken for conventional algorithms to process large…

Clustering is one of the most important tools for analysis of large datasets, and perhaps the most popular clustering algorithm is Lloyd's algorithm for $k$-means. This algorithm takes $n$ vectors $V=[v_1,\dots,v_n]\in\mathbb{R}^{d\times…

Network clustering reveals the organization of a network or corresponding complex system with elements represented as vertices and interactions as edges in a (directed, weighted) graph. Although the notion of clustering can be somewhat…