Related papers: Persistent Clustering and a Theorem of J. Kleinber…

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,…

Cluster analysis is one of the essential tasks in data mining and knowledge discovery. Each type of data poses unique challenges in achieving relatively efficient partitioning of the data into homogeneous groups. While the algorithms for…

Data clustering is the process of identifying natural groupings or clusters within multidimensional data based on some similarity measure. Clustering is a fundamental process in many different disciplines. Hence, researchers from different…

We examine overlapping clustering schemes with functorial constraints, in the spirit of Carlsson--Memoli. This avoids issues arising from the chaining required by partition-based methods. Our principal result shows that any clustering…

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…

Clustering has been a major research topic in the field of machine learning, one to which Deep Learning has recently been applied with significant success. However, an aspect of clustering that is not addressed by existing deep clustering…

Multiple datasets containing different types of features may be available for a given task. For instance, users' profiles can be used to group users for recommendation systems. In addition, a model can also use users' historical behaviors…

Here we present a quantum algorithm for clustering data based on a variational quantum circuit. The algorithm allows to classify data into many clusters, and can easily be implemented in few-qubit Noisy Intermediate-Scale Quantum (NISQ)…

Complex systems are usually represented as an intricate set of relations between their components forming a complex graph or network. The understanding of their functioning and emergent properties are strongly related to their structural…

A novel framework for consensus clustering is presented which has the ability to determine both the number of clusters and a final solution using multiple algorithms. A consensus similarity matrix is formed from an ensemble using multiple…

It is well known that most of the common clustering objectives are NP-hard to optimize. In practice, however, clustering is being routinely carried out. One approach for providing theoretical understanding of this seeming discrepancy is to…

Clustering is an unsupervised machine learning task that consists of identifying groups of similar objects. It has numerous applications and is increasingly used in fairness-sensitive domains where objects represent individuals, such as…

Functional data clustering is to identify heterogeneous morphological patterns in the continuous functions underlying the discrete measurements/observations. Application of functional data clustering has appeared in many publications across…

Usual formulations of the clustering coefficient can be shown to be insufficient in the task of describing the local topology of very simple networks. Motivated by this, we review some alternatives in order to present an extension, the…

This paper proposes a centroid-based clustering algorithm which is capable of clustering data-points with n-features, without having to specify the number of clusters to be formed. The core logic behind the algorithm is a similarity…

Stability selection (Meinshausen and Buhlmann, 2010) makes any feature selection method more stable by returning only those features that are consistently selected across many subsamples. We prove (in what is, to our knowledge, the first…

The paper develops a general framework for constrained clustering which is based on the close connection of geometric clustering and diagrams. Various new structural and algorithmic results are proved (and known results generalized and…

Clustering methods must be tailored to the dataset it operates on, as there is no objective or universal definition of ``cluster,'' but nevertheless arbitrariness in the clustering method must be minimized. This paper develops a…

We study the design of interactive clustering algorithms for data sets satisfying natural stability assumptions. Our algorithms start with any initial clustering and only make local changes in each step; both are desirable features in many…

Consensus clustering fuses diverse basic partitions (i.e., clustering results obtained from conventional clustering methods) into an integrated one, which has attracted increasing attention in both academic and industrial areas due to its…