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Clustering a graph means identifying internally dense subgraphs which are only sparsely interconnected. Formalizations of this notion lead to measures that quantify the quality of a clustering and to algorithms that actually find…
We study cross-graph charging schemes for graphs drawn in the plane. These are charging schemes where charge is moved across vertices of different graphs. Such methods have been recently applied to obtain various properties of…
We present a new algorithm for estimating the star discrepancy of arbitrary point sets. Similar to the algorithm for discrepancy approximation of Winker and Fang [SIAM J. Numer. Anal. 34 (1997), 2028--2042] it is based on the optimization…
This study demonstrates that incorporating a consistency heuristic into the point-matching algorithm \cite{yerebakan2023hierarchical} improves robustness in matching anatomical locations across pairs of medical images. We validated our…
We consider the task of drawing a graph on multiple horizontal layers, where each node is assigned a layer, and each edge connects nodes of different layers. Known algorithms determine the orders of nodes on each layer to minimize crossings…
A graph is near-planar if it can be obtained from a planar graph by adding an edge. We show the surprising fact that it is NP-hard to compute the crossing number of near-planar graphs. A graph is 1-planar if it has a drawing where every…
Selecting regularization parameters in penalized high-dimensional graphical models in a principled, data-driven, and computationally efficient manner continues to be one of the key challenges in high-dimensional statistics. We present…
Graph embedding learns low-dimensional representations for nodes in a graph and effectively preserves the graph structure. Recently, a significant amount of progress has been made toward this emerging research area. However, there are…
Spectral embedding is a popular technique for the representation of graph data. Several regularization techniques have been proposed to improve the quality of the embedding with respect to downstream tasks like clustering. In this paper, we…
Variational regularization is a classical technique to solve statistical inference tasks and inverse problems, with modern data-driven approaches parameterizing regularizers via deep neural networks showcasing impressive empirical…
We propose a new fast word embedding technique using hash functions. The method is a derandomization of a new type of random projections: By disregarding the classic constraint used in designing random projections (i.e., preserving pairwise…
Embedding image features into a binary Hamming space can improve both the speed and accuracy of large-scale query-by-example image retrieval systems. Supervised hashing aims to map the original features to compact binary codes in a manner…
Neural network ensembling is a common and robust way to increase model efficiency. In this paper, we propose a new neural network ensemble algorithm based on Audibert's empirical star algorithm. We provide optimal theoretical minimax bound…
The definition of $1$-planar graphs naturally extends graph planarity, namely a graph is $1$-planar if it can be drawn in the plane with at most one crossing per edge. Unfortunately, while testing graph planarity is solvable in linear time,…
Grouping the nodes of a graph into clusters is a standard technique for studying networks. We study a problem where we are given a directed network and are asked to partition the graph into a sequence of coherent groups. We assume that…
Image segmentation plays a crucial role in extracting objects of interest and identifying their boundaries within an image. However, accurate segmentation becomes challenging when dealing with occlusions, obscurities, or noise in corrupted…
Presently with technology node scaling, an accurate prediction model at early design stages can significantly reduce the design cycle. Especially during logic synthesis, predicting cell congestion due to improper logic combination can…
Given a network, the critical node detection problem finds a subset of nodes whose removal disrupts the network connectivity. Since many real-world systems are naturally modeled as graphs, assessing the vulnerability of the network is…
Graph Crossing Number is a fundamental problem with various applications. In this problem, the goal is to draw an input graph $G$ in the plane so as to minimize the number of crossings between the images of its edges. Despite extensive…
In recent years, the embedding approach for solving switched optimal control problems has been developed in a series of papers. However, the embedding approach, which advantageously converts the hybrid optimal control problem to a classical…