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This work explores the clustering of wireless users by examining the distances between their channel covariance matrices, which reside on the Riemannian manifold of positive definite matrices. Specifically, we consider an estimator of the…
With contemporary data sets becoming too large to analyze the data directly, various forms of aggregated data are becoming common. The original individual data are points, but after aggregation, the observations are interval-valued (e.g.).…
We propose a novel approach to concentration for non-independent random variables. The main idea is to ``pretend'' that the random variables are independent and pay a multiplicative price measuring how far they are from actually being…
In this paper, we obtain general representations for the joint distributions and copulas of arbitrary dependent random variables absolutely continuous with respect to the product of given one-dimensional marginal distributions. The…
Spatial models for areal data are often constructed such that all pairs of adjacent regions are assumed to have near-identical spatial autocorrelation. In practice, data can exhibit dependence structures more complicated than can be…
In this paper we propose and study a class of simple, nonparametric, yet interpretable measures of association between two random variables $X$ and $Y$ taking values in general topological spaces. These nonparametric measures -- defined…
For the first time, we introduce "Scaling invariable Benford distance" and "Benford cyclic graph", which can be used to analyze any data set. Using the quantity and the graph, we analyze some date sets with common distributions, such as…
Sensors are the key to environmental monitoring, which impart benefits to smart cities in many aspects, such as providing real-time air quality information to assist human decision-making. However, it is impractical to deploy massive…
Classical multivariate statistics measures the outlyingness of a point by its Mahalanobis distance from the mean, which is based on the mean and the covariance matrix of the data. A multivariate depth function is a function which, given a…
This work applies a quantitative metric well-known to the data assimilation community to a new context in order to capture the relative representativeness of non-simultaneous or non-co-located observations and quantify how these…
Advances in satellite imaging and GPS tracking devices have given rise to a new era of remote sensing and geospatial analysis. In environmental science and conservation ecology, biotelemetric data is often high-dimensional, spatially and/or…
High-dimensional multivariate spatial-temporal data arise frequently in a wide range of applications; however, there are relatively few statistical methods that can simultaneously deal with spatial, temporal and variable-wise dependencies…
Mutual information is fundamentally important for measuring statistical dependence between variables and for quantifying information transfer by signaling and communication mechanisms. It can, however, be challenging to evaluate for…
We propose a general framework for non-normal multivariate data analysis called multivariate covariance generalized linear models (McGLMs), designed to handle multivariate response variables, along with a wide range of temporal and spatial…
The average distance from a node to all other nodes in a graph, or from a query point in a metric space to a set of points, is a fundamental quantity in data analysis. The inverse of the average distance, known as the (classic) closeness…
The study of multivariate extremes is dominated by multivariate regular variation, although it is well known that this approach does not provide adequate distinction between random vectors whose components are not always simultaneously…
Distance correlation is a recent extension of Pearson's correlation, that characterises general statistical independence between Euclidean-space-valued random variables, not only linear relations. This review delves into how and when…
Analysis and processing of data is a vital part of our modern society and requires vast amounts of computational resources. To reduce the computational burden, compressing and approximating data has become a central topic. We consider the…
We introduce continuous indexed points for improved multivariate volume visualization. Indexed points represent linear structures in parallel coordinates and can be used to encode local correlation of multivariate (including multifield,…
In the past several years, social media (e.g., Twitter and Facebook) has been experiencing a spectacular rise and popularity, and becoming a ubiquitous discourse for content sharing and social networking. With the widespread of mobile…