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Cluster visualization is an essential task for nonlinear dimensionality reduction as a data analysis tool. It is often believed that Student t-Distributed Stochastic Neighbor Embedding (t-SNE) can show clusters for well clusterable data,…
Embedding static graphs in low-dimensional vector spaces plays a key role in network analytics and inference, supporting applications like node classification, link prediction, and graph visualization. However, many real-world networks…
Nearest neighbor search is a fundamental data structure problem with many applications in machine learning, computer vision, recommendation systems and other fields. Although the main objective of the data structure is to quickly report…
We study a well known noisy model of the graph isomorphism problem. In this model, the goal is to perfectly recover the vertex correspondence between two edge-correlated Erd\H{o}s-R\'{e}nyi random graphs, with an initial seed set of…
Graph clustering (or community detection) has long drawn enormous attention from the research on web mining and information networks. Recent literature on this topic has reached a consensus that node contents and link structures should be…
We present an efficient dynamic data structure that supports geodesic nearest neighbor queries for a set of point sites $S$ in a static simple polygon $P$. Our data structure allows us to insert a new site in $S$, delete a site from $S$,…
Geometric embeddings have recently received attention for their natural ability to represent transitive asymmetric relations via containment. Box embeddings, where objects are represented by n-dimensional hyperrectangles, are a particularly…
Circle packing is widely used in visualization due to its aesthetic appeal and simplicity, particularly in tasks where the spatial arrangement and relationships between data are of interest, such as understanding proximity relationships…
Analyzing large volumes of high-dimensional data is an issue of fundamental importance in data science, molecular simulations and beyond. Several approaches work on the assumption that the important content of a dataset belongs to a…
Many distributed learning techniques have been motivated by the increasing size of datasets and their inability to fit into main memory on a single machine. We propose an algorithm that finds the nearest neighbor in a graph locally without…
Over the last decade, random hyperbolic graphs have proved successful in providing geometric explanations for many key properties of real-world networks, including strong clustering, high navigability, and heterogeneous degree…
We introduce and study a new graph representation where vertices are embedded in three or more dimensions, and in which the edges are drawn on the projections onto the axis-parallel planes. We show that the complete graph on $n$ vertices…
Effective building pattern recognition is critical for understanding urban form, automating map generalization, and visualizing 3D city models. Most existing studies use object-independent methods based on visual perception rules and…
We propose a new method for embedding graphs while preserving directed edge information. Learning such continuous-space vector representations (or embeddings) of nodes in a graph is an important first step for using network information…
In the nearest neighbor problem, we are given a set $S$ of point sites that we want to store such that we can find the nearest neighbor of a (new) query point efficiently. In the dynamic version of the problem, the goal is to design a data…
We study the richness of the ensemble of graphical structures (i.e., unlabeled graphs) of the one-dimensional random geometric graph model defined by $n$ nodes randomly scattered in $[0,1]$ that connect if they are within the connection…
Determining how the brain stores information is one of the most pressing problems in neuroscience. In many instances, the collection of stimuli for a given neuron can be modeled by a convex set in $\mathbb{R}^d$. Combinatorial objects known…
Graph embedding methods embed the nodes in a graph in low dimensional vector space while preserving graph topology to carry out the downstream tasks such as link prediction, node recommendation and clustering. These tasks depend on a…
Dimensionality Reduction (DR) methods are widely used to visualize high-dimensional data. One key task in DR-based analysis is discovering neighborhoods, which relies on analyzing the fine-grained local structure of a projection. However,…
This paper addresses the basic question of how well can a tree approximate distances of a metric space or a graph. Given a graph, the problem of constructing a spanning tree in a graph which strongly preserves distances in the graph is a…