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Comparison of graph structure is a ubiquitous task in data analysis and machine learning, with diverse applications in fields such as neuroscience, cyber security, social network analysis, and bioinformatics, among others. Discovery and…
Classification and Regression Trees (CARTs) are off-the-shelf techniques in modern Statistics and Machine Learning. CARTs are traditionally built by means of a greedy procedure, sequentially deciding the splitting predictor variable(s) and…
Scaling has been proposed as a powerful tool to analyze the properties of complex systems, and in particular for cities where it describes how various properties change with population. The empirical study of scaling on a wide range of…
Graph embedding algorithms are used to efficiently represent (encode) a graph in a low-dimensional continuous vector space that preserves the most important properties of the graph. One aspect that is often overlooked is whether the graph…
The structure of road networks plays a pivotal role in shaping transportation dynamics. It also provides insights into how drivers experience city streets and helps uncover each urban environment's unique characteristics and challenges.…
Building on progress in feature representations for image retrieval, image-based localization has seen a surge of research interest. Image-based localization has the advantage of being inexpensive and efficient, often avoiding the use of 3D…
Human mobility similarity comparison plays a critical role in mobility estimation/prediction model evaluation, mobility clustering and mobility matching, which exerts an enormous impact on improving urban mobility, accessibility, and…
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…
Despite diverse mobility needs worldwide, existing mapping tools fail to address the varied experiences of different mobility device users. This paper presents a large-scale online survey exploring how five mobility groups -- users of…
Traffic congestion research is on the rise, thanks to urbanization, economic growth, and industrialization. Developed countries invest a lot of research money in collecting traffic data using Radio Frequency Identification (RFID), loop…
Euler diagrams are a tool for the graphical representation of set relations. Due to their simple way of visualizing elements in the sets by geometric containment, they are easily readable by an inexperienced reader. Euler diagrams where the…
Decision making under uncertainty is a cross-cutting challenge in science and engineering. Most approaches to this challenge employ probabilistic representations of uncertainty. In complicated systems accessible only via data or black-box…
We introduce the set of (non-spanning) tree-decorated planar maps, and show that they are in bijection with the Cartesian product between the set of trees and the set of maps with a simple boundary. As a consequence, we count the number of…
Visual insights into a wide variety of statistical methods, for both didactic and data analytic purposes, can often be achieved through geometric diagrams and geometrically based statistical graphs. This paper extols and illustrates the…
Graph convexity has been used as an important tool to better understand the structure of classes of graphs. Many studies are devoted to determine if a graph equipped with a convexity is a {\em convex geometry}. In this work we survey…
In the computational study of political redistricting, feasibility necessitates the use of a discretization of regions such as states, counties, and towns. In nearly all cases, researchers use a dual graph, whose vertices represent small…
We apply persistent homology, the main method in topological data analysis, to the study of demographic data. Persistence diagrams efficiently summarize information about clusters or peaks in a region's demographic data. To illustrate how…
Schematic maps are in daily use to show the connectivity of subway systems and to facilitate travellers to plan their journeys effectively. This study surveys up-to-date algorithmic approaches in order to give an overview of the state of…
Orthogonal arrays are arguably one of the most fascinating and important statistical tools for efficient data collection. They have a simple, natural definition, desirable properties when used as fractional factorials, and a rich and…
Circuity, the ratio of network distances to straight-line distances, is an important measure of urban street network structure and transportation efficiency. Circuity results from a circulation network's configuration, planning, and…