Related papers: Clustering in statistical ill-posed linear inverse…

Identifying the number $K$ of clusters in a dataset is one of the most difficult problems in clustering analysis. A choice of $K$ that correctly characterizes the features of the data is essential for building meaningful clusters. In this…

Ensemble clustering has demonstrated great success in practice; however, its theoretical foundations remain underexplored. This paper examines the generalization performance of ensemble clustering, focusing on generalization error, excess…

Spectral clustering is a fundamental technique in the field of data mining and information processing. Most existing spectral clustering algorithms integrate dimensionality reduction into the clustering process assisted by manifold learning…

Recommendation algorithms perform differently if the users, recommendation contexts, applications, and user interfaces vary even slightly. It is similarly observed in other fields, such as combinatorial problem solving, that algorithms…

Clustering can be defined as the process of assembling objects into a number of groups whose elements are similar to each other in some manner. As a technique that is used in many domains, such as face clustering, plant categorization,…

Consensus clustering, a fundamental task in machine learning and data analysis, aims to aggregate multiple input clusterings of a dataset, potentially based on different non-sensitive attributes, into a single clustering that best…

This paper considers the problem of clustering a partially observed unweighted graph---i.e., one where for some node pairs we know there is an edge between them, for some others we know there is no edge, and for the remaining we do not know…

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…

Nonnegative matrix factorization (NMF) is widely used for clustering with strong interpretability. Among general NMF problems, symmetric NMF is a special one that plays an important role in graph clustering where each element measures the…

With rapidly increasing data, clustering algorithms are important tools for data analytics in modern research. They have been successfully applied to a wide range of domains; for instance, bioinformatics, speech recognition, and financial…

We develop a geometric framework that links objective accuracy to structural recovery in prototype-based clustering. The analysis is algorithm-agnostic and applies to a broad class of admissible loss functions. We define a clustering…

Clustering is often a challenging problem because of the inherent ambiguity in what the "correct" clustering should be. Even when the number of clusters $K$ is known, this ambiguity often still exists, particularly when there is variation…

Clustering functional data is a challenging task due to intrinsic infinite-dimensionality and the need for stable, data-adaptive partitioning. In this work, we propose a clustering framework based on Random Projections, which simultaneously…

Clustering is a powerful and extensively used data science tool. While clustering is generally thought of as an unsupervised learning technique, there are also supervised variations such as Spath's clusterwise regression that attempt to…

We study the linear ill-posed inverse problem with noisy data in the statistical learning setting. Approximate reconstructions from random noisy data are sought with general regularization schemes in Hilbert scale. We discuss the rates of…

The clustering of a data set is one of the core tasks in data analytics. Many clustering algorithms exhibit a strong contrast between a favorable performance in practice and bad theoretical worst-cases. Prime examples are least-squares…

Missing values frequently arise in modern biomedical studies due to various reasons, including missing tests or complex profiling technologies for different omics measurements. Missing values can complicate the application of clustering…

Center-based clustering has attracted significant research interest from both theory and practice. In many practical applications, input data often contain background knowledge that can be used to improve clustering results. In this work,…

In temporal ordered clustering, given a single snapshot of a dynamic network in which nodes arrive at distinct time instants, we aim at partitioning its nodes into $K$ ordered clusters $\mathcal{C}_1 \prec \cdots \prec \mathcal{C}_K$ such…

In the graph clustering problem with a planted solution, the input is a graph on $n$ vertices partitioned into $k$ clusters, and the task is to infer the clusters from graph structure. A standard assumption is that clusters induce…