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Clustering is a common technique for statistical data analysis, which is used in many fields, including machine learning, data mining, pattern recognition, image analysis and bioinformatics. Clustering is the process of grouping similar…
Generalized likelihood ratio (GLR) test statistics are often used in the detection of spatial clustering in case-control and case-population datasets to check for a significantly large proportion of cases within some scanning window. The…
Partitioning a set of elements into subsets of a priori unknown sizes is essential in many applications. These subset sizes are rarely explicitly learned - be it the cluster sizes in clustering applications or the number of shared versus…
Global physical properties of random media change qualitatively at a percolation threshold, where isolated clusters merge to form one infinite connected component. The precise knowledge of percolation thresholds is thus of paramount…
Well-spread samples are desirable in many disciplines because they improve estimation when target variables exhibit spatial structure. This paper introduces an integrated methodological framework for spreading samples over the population's…
We propose to bridge the gap between semi-supervised and unsupervised image recognition with a flexible method that performs well for both generalized category discovery (GCD) and image clustering. Despite the overlap in motivation between…
Clustering analysis is one of the most widely used statistical tools in many emerging areas such as microarray data analysis. For microarray and other high-dimensional data, the presence of many noise variables may mask underlying…
In many applications, data cluster. Failing to take the cluster structure into consideration generally leads to underestimated variances of point estimators and inflated type I errors in hypothesis tests. Many circumstance-dependent…
The global clustering coefficient serves as a powerful metric for the structural analysis and comparison of complex networks. Random geometric graphs offer a realistic framework for representing the spatial constraints and geometry often…
We discuss topological aspects of cluster analysis and show that inferring the topological structure of a dataset before clustering it can considerably enhance cluster detection: theoretical arguments and empirical evidence show that…
This paper introduces a method for studying the correlation structure of a range of responses modelled by a multivariate generalised linear mixed model (MGLMM). The methodology requires the existence of clusters of observations and that…
Categorical random variables are a common staple in machine learning methods and other applications across disciplines. Many times, correlation within categorical predictors exists, and has been noted to have an effect on various algorithm…
The clustering coefficient quantifies the abundance of connected triangles in a network and is a major descriptive statistics of networks. For example, it finds an application in the assessment of small-worldness of brain networks, which is…
This paper develops new combinatorial approaches to analyze and compute special set partitions, called complementary set partitions, which are fundamental in the study of generalized cumulants. Moving away from traditional graph-based and…
We study the following distribution clustering problem: Given a hidden partition of $k$ distributions into two groups, such that the distributions within each group are the same, and the two distributions associated with the two clusters…
Semi-supervised learning has become increasingly popular in medical image segmentation due to its ability to leverage large amounts of unlabeled data to extract additional information. However, most existing semi-supervised segmentation…
Clustering has many important applications in computer science, but real-world datasets often contain outliers. Moreover, the presence of outliers can make the clustering problems to be much more challenging. To reduce the complexities,…
This manuscript is concerned with relating two approaches that can be used to explore complex dependence structures between categorical variables, namely Bayesian partitioning of the covariate space incorporating a variable selection…
Density estimation is a fundamental technique employed in various fields to model and to understand the underlying distribution of data. The primary objective of density estimation is to estimate the probability density function of a random…
Understanding the complex structure of multivariate extremes is a major challenge in various fields from portfolio monitoring and environmental risk management to insurance. In the framework of multivariate Extreme Value Theory, a common…