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Internal cluster validity measures (such as the Calinski-Harabasz, Dunn, or Davies-Bouldin indices) are frequently used for selecting the appropriate number of partitions a dataset should be split into. In this paper we consider what…
Cluster analysis is widely used in the areas of machine learning and data mining. Fuzzy clustering is a particular method that considers that a data point can belong to more than one cluster. Fuzzy clustering helps obtain flexible clusters,…
Clustering is an important part of many modern data analysis pipelines, including network analysis and data retrieval. There are many different clustering algorithms developed by various communities, and it is often not clear which…
A computational theory for clustering and a semi-supervised clustering algorithm is presented. Clustering is defined to be the obtainment of groupings of data such that each group contains no anomalies with respect to a chosen grouping…
Due to its ability to combine multiple base clusterings into a probably better and more robust clustering, the ensemble clustering technique has been attracting increasing attention in recent years. Despite the significant success, one…
We address the problem of validating the ouput of clustering algorithms. Given data $\mathcal{D}$ and a partition $\mathcal{C}$ of these data into $K$ clusters, when can we say that the clusters obtained are correct or meaningful for the…
Validation plays a crucial role in the clustering process. Many different internal validity indexes exist for the purpose of determining the best clustering solution(s) from a given collection of candidates, e.g., as produced by different…
This paper presents and analyzes an approach to cluster-based inference for dependent data. The primary setting considered here is with spatially indexed data in which the dependence structure of observed random variables is characterized…
We develop a clustering framework for observations from a population with a smooth probability distribution function and derive its asymptotic properties. A clustering criterion based on a linear combination of order statistics is proposed.…
Unsupervised machine learning, and in particular data clustering, is a powerful approach for the analysis of datasets and identification of characteristic features occurring throughout a dataset. It is gaining popularity across scientific…
A network has a non-overlapping community structure if the nodes of the network can be partitioned into disjoint sets such that each node in a set is densely connected to other nodes inside the set and sparsely connected to the nodes out-…
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…
The objective of clustering is to discover natural groups in datasets and to identify geometrical structures which might reside there, without assuming any prior knowledge on the characteristics of the data. The problem can be seen as…
To evaluate clustering results is a significant part of cluster analysis. There are no true class labels for clustering in typical unsupervised learning. Thus, a number of internal evaluations, which use predicted labels and data, have been…
This paper considers metric spaces where distances between a pair of nodes are represented by distance intervals. The goal is to study methods for the determination of hierarchical clusters, i.e., a family of nested partitions indexed by a…
To evaluate clustering results is a significant part of cluster analysis. Since there are no true class labels for clustering in typical unsupervised learning, many internal cluster validity indices (CVIs), which use predicted labels and…
Clustering is an essential data mining tool that aims to discover inherent cluster structure in data. For most applications, applying clustering is only appropriate when cluster structure is present. As such, the study of clusterability,…
In the context of cluster analysis and graph partitioning, many external evaluation measures have been proposed in the literature to compare two partitions of the same set. This makes the task of selecting the most appropriate measure for a…
Clustering is an essential data mining tool that aims to discover inherent cluster structure in data. As such, the study of clusterability, which evaluates whether data possesses such structure, is an integral part of cluster analysis. Yet,…
We propose a change-point detection method for large scale multiple testing problems with data having clustered signals. Unlike the classic change-point setup, the signals can vary in size within a cluster. The clustering structure on the…