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Aggregation patterns are often visually detected in sets of location data. These clusters may be the result of interesting dynamics or the effect of pure randomness. We build an asymptotically Gaussian test for the hypothesis of randomness…
In longitudinal data analysis, observation points of repeated measurements over time often vary among subjects except in well-designed experimental studies. Additionally, measurements for each subject are typically obtained at only a few…
The size of datasets has been increasing rapidly both in terms of number of variables and number of events. As a result, the empty space phenomenon and the curse of dimensionality complicate the extraction of useful information. But, in…
Spatial clustering detection has a variety of applications in diverse fields, including identifying infectious disease outbreaks, assessing land use patterns, pinpointing crime hotspots, and identifying clusters of neurons in brain imaging…
The size and structure of spatial molecular and atomic clustering can significantly impact material properties and is therefore important to accurately quantify. Ripley's K-function (K(r)), a measure of spatial correlation, can be used to…
Clustering is widely used in unsupervised learning to find homogeneous groups of observations within a dataset. However, clustering mixed-type data remains a challenge, as few existing approaches are suited for this task. This study…
We introduce a statistical quantity, known as the $K$ function, related to the integral of the two--point correlation function. It gives us straightforward information about the scale where clustering dominates and the scale at which…
This thesis aims to invent new approaches for making inferences with the k-means algorithm. k-means is an iterative clustering algorithm that randomly assigns k centroids, then assigns data points to the nearest centroid, and updates…
We consider clustering in group decision making where the opinions are given by pairwise comparison matrices. In particular, the k-medoids model is suggested to classify the matrices since it has a linear programming problem formulation…
Estimating the number of clusters (K) is a critical and often difficult task in cluster analysis. Many methods have been proposed to estimate K, including some top performers using resampling approach. When performing cluster analysis in…
Detection of change-points in a sequence of high-dimensional observations is a very challenging problem, and this becomes even more challenging when the sample size (i.e., the sequence length) is small. In this article, we propose some…
Quantifying the similarity between two mathematical structures or datasets constitutes a particularly interesting and useful operation in several theoretical and applied problems. Aimed at this specific objective, the Jaccard index has been…
We develop a novel clustering method for distributional data, where each data point is regarded as a probability distribution on the real line. For distributional data, it has been challenging to develop a clustering method that utilizes…
Generally, there are three main factors that determine the practical usability of registration, i.e., accuracy, robustness, and efficiency. In real-time applications, efficiency and robustness are more important. To promote these two…
The popular K-means clustering algorithm potentially suffers from a major weakness for further analysis or interpretation. Some cluster may have disproportionately more (or fewer) points from one of the subpopulations in terms of some…
A unified metric is given for the evaluation of object tracking systems. The metric is inspired by KL-divergence or relative entropy, which is commonly used to evaluate clustering techniques. Since tracking problems are fundamentally…
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…
Clustering evaluation measures are frequently used to evaluate the performance of algorithms. However, most measures are not properly normalized and ignore some information in the inherent structure of clusterings. We model the relation…
We consider the problem of analyzing the heterogeneity of clustering distributions for multiple groups of observed data, each of which is indexed by a covariate value, and inferring global clusters arising from observations aggregated over…
The learning of mixture models can be viewed as a clustering problem. Indeed, given data samples independently generated from a mixture of distributions, we often would like to find the {\it correct target clustering} of the samples…