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The problem of clustering noisy and incompletely observed high-dimensional data points into a union of low-dimensional subspaces and a set of outliers is considered. The number of subspaces, their dimensions, and their orientations are…

Machine Learning · Statistics 2015-08-24 Reinhard Heckel , Helmut Bölcskei

Supervised classification can be effective for prediction but sometimes weak on interpretability or explainability (XAI). Clustering, on the other hand, tends to isolate categories or profiles that can be meaningful but there is no…

Machine Learning · Computer Science 2021-04-27 Vincent Lemaire , Oumaima Alaoui Ismaili , Antoine Cornuéjols , Dominique Gay

We consider the problem of clustering datasets in the presence of arbitrary outliers. Traditional clustering algorithms such as k-means and spectral clustering are known to perform poorly for datasets contaminated with even a small number…

Machine Learning · Statistics 2021-02-02 Prateek R. Srivastava , Purnamrita Sarkar , Grani A. Hanasusanto

Clustering objects from the LiDAR point cloud is an important research problem with many applications such as autonomous driving. To meet the real-time requirement, existing research proposed to apply the connected-component-labeling (CCL)…

Computer Vision and Pattern Recognition · Computer Science 2021-09-20 Yiming Zhao , Xiao Zhang , Xinming Huang

Spectral clustering is a popular clustering method. It first maps data into the spectral embedding space and then uses Kmeans to find clusters. However, the two decoupled steps prohibit joint optimization for the optimal solution. In…

Machine Learning · Computer Science 2024-12-17 Wengang Guo , Wei Ye

We incorporate group fairness into the algorithmic centroid clustering problem, where $k$ centers are to be located to serve $n$ agents distributed in a metric space. We refine the notion of proportional fairness proposed in [Chen et al.,…

Computer Science and Game Theory · Computer Science 2022-04-01 Bo Li , Lijun Li , Ankang Sun , Chenhao Wang , Yingfan Wang

Clustering is one of the main tasks in exploratory data analysis and descriptive statistics where the main objective is partitioning observations in groups. Clustering has a broad range of application in varied domains like climate,…

Databases · Computer Science 2012-03-20 Saptarsi Goswami , Amlan Chakrabarti

This paper studies a factor modeling-based approach for clustering high-dimensional data generated from a mixture of strongly correlated variables. Statistical modeling with correlated structures pervades modern applications in economics,…

Statistics Theory · Mathematics 2024-08-23 Shange Tang , Soham Jana , Jianqing Fan

Dirichlet process mixtures are flexible non-parametric models, particularly suited to density estimation and probabilistic clustering. In this work we study the posterior distribution induced by Dirichlet process mixtures as the sample size…

Statistics Theory · Mathematics 2022-11-29 Filippo Ascolani , Antonio Lijoi , Giovanni Rebaudo , Giacomo Zanella

Spectral clustering became a popular choice for data clustering for its ability of uncovering clusters of different shapes. However, it is not always preferable over other clustering methods due to its computational demands. One of the…

Machine Learning · Computer Science 2023-02-23 Mashaan Alshammari , John Stavrakakis , Masahiro Takatsuka

In this paper we present deterministic conditions for success of sparse subspace clustering (SSC) under missing data, when data is assumed to come from a Union of Subspaces (UoS) model. We consider two algorithms, which are variants of SSC…

Information Theory · Computer Science 2016-07-13 Wenqi Wang , Shuchin Aeron , Vaneet Aggarwal

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…

Statistics Theory · Mathematics 2008-12-18 Luis A. García-Escudero , Alfonso Gordaliza , Carlos Matrán , Agustin Mayo-Iscar

Most convex and nonconvex clustering algorithms come with one crucial parameter: the $k$ in $k$-means. To this day, there is not one generally accepted way to accurately determine this parameter. Popular methods are simple yet theoretically…

Machine Learning · Computer Science 2021-08-04 Sibylle Hess , Wouter Duivesteijn

Dynamic tensor data are becoming prevalent in numerous applications. Existing tensor clustering methods either fail to account for the dynamic nature of the data, or are inapplicable to a general-order tensor. Also there is often a gap…

Machine Learning · Statistics 2018-09-17 Will Wei Sun , Lexin Li

A univariate clustering criterion for stationary processes satisfying a $\beta$-mixing condition is proposed extending the work of \cite{KB2} to the dependent setup. The approach is characterized by an alternative sample criterion function…

Statistics Theory · Mathematics 2013-11-19 Karthik Bharath

Spectral clustering techniques are valuable tools in signal processing and machine learning for partitioning complex data sets. The effectiveness of spectral clustering stems from constructing a non-linear embedding based on creating a…

Machine Learning · Computer Science 2021-02-02 Farhad Pourkamali-Anaraki

We examine the potential improvements in constraints on the dark energy equation of state parameter $w$ and matter density $\Omega_M$ from using clustering information along with number counts for future samples of thermal…

Cosmology and Nongalactic Astrophysics · Physics 2026-01-13 Junhao Zhan , Christian L. Reichardt

We present a unified framework that yields EPASes for constrained $(k,z)$-clustering in metric spaces of bounded (algorithmic) scatter dimension, a notion introduced by Abbasi et al. (FOCS 2023). They showed that several well known metric…

Data Structures and Algorithms · Computer Science 2026-02-10 Sujoy Bhore , Ameet Gadekar , Tanmay Inamdar

We investigate the estimation of multivariate extreme models with a discrete spectral measure using spherical clustering techniques. The primary contribution involves devising a method for selecting the order, that is, the number of…

Methodology · Statistics 2025-02-20 Shiyuan Deng , He Tang , Shuyang Bai

Two important optimization problems in the analysis of geometric data sets are clustering and sketching. Here, clustering refers to the problem of partitioning some input metric measure space (mm-space) into k clusters, minimizing some…

Computational Geometry · Computer Science 2018-10-19 Facundo Mémoli , Anastasios Sidiropoulos , Kritika Singhal