Related papers: CLIPPER+: A Fast Maximal Clique Algorithm for Robu…
The maximum clique problem, a well-known graph-based combinatorial optimization problem, has been addressed through various algorithmic approaches, though systematic analyses of the problem instances remain sparse. This study employs the…
A novel approach to complex problems has been previously applied to graph classification and the graph equivalence problem. Here we apply it to the NP complete problem of finding the largest perfect clique within a graph $G$.
We describe a variation of the iterative closest point (ICP) algorithm for aligning two point sets under a set of transformations. Our algorithm is superior to previous algorithms because (1) in determining the optimal alignment, it…
In a distinguishing problem, the input is a sample drawn from one of two distributions and the algorithm is tasked with identifying the source distribution. The performance of a distinguishing algorithm is measured by its advantage, i.e.,…
In this work, we focus on distance-based outliers in a metric space, where the status of an entity as to whether it is an outlier is based on the number of other entities in its neighborhood. In recent years, several solutions have tackled…
Identifying dense subgraphs known as quasi-cliques is pivotal in numerous graph mining tasks across domains such as social networks, biology, and e-commerce. While prior work has developed efficient algorithms for quasi-clique detection in…
The maximum clique problem is a classical NP-complete problem in graph theory and has important applications in many domains. In this paper we show, in a partially non-constructive way, the existence of an exact polynomial-time algorithm…
Registration is a fundamental but critical task in point cloud processing, which usually depends on finding element correspondence from two point clouds. However, the finding of reliable correspondence relies on establishing a robust and…
The edge clique cover (ECC) problem -- where the goal is to find a minimum cardinality set of cliques that cover all the edges of a graph -- is a classic NP-hard problem that has received much attention from both the theoretical and…
Reliable outlier detection is critical for real-world deployment of deep learning models. Although extensively studied, likelihoods produced by deep generative models have been largely dismissed as being impractical for outlier detection.…
Clustering is a fundamental task in data mining and machine learning, particularly for analyzing large-scale data. In this paper, we introduce Clust-Splitter, an efficient algorithm based on nonsmooth optimization, designed to solve the…
Given a large graph, the densest-subgraph problem asks to find a subgraph with maximum average degree. When considering the top-$k$ version of this problem, a na\"ive solution is to iteratively find the densest subgraph and remove it in…
In this paper we propose a graph-based data clustering algorithm which is based on exact clustering of a minimum spanning tree in terms of a minimum isoperimetry criteria. We show that our basic clustering algorithm runs in $O(n \log n)$…
Correlation Clustering is an elegant model that captures fundamental graph cut problems such as Min $s-t$ Cut, Multiway Cut, and Multicut, extensively studied in combinatorial optimization. Here, we are given a graph with edges labeled $+$…
Next-generation sequencing techniques have facilitated a large scale analysis of human genetic variation. Despite the advances in sequencing speeds, the computational discovery of structural variants is not yet standard. It is likely that…
Given a user-specified minimum degree threshold $\gamma$, a $\gamma$-quasi-clique is a subgraph $g=(V_g,E_g)$ where each vertex $v\in V_g$ connects to at least $\gamma$ fraction of the other vertices (i.e., $\lceil…
Hierarchical clustering over graphs is a fundamental task in data mining and machine learning with applications in domains such as phylogenetics, social network analysis, and information retrieval. Specifically, we consider the recently…
We present our work on scalable, GPU-accelerated algorithms for diffeomorphic image registration. The associated software package is termed CLAIRE. Image registration is a non-linear inverse problem. It is about computing a spatial mapping…
The study of approximate matching in the Massively Parallel Computations (MPC) model has recently seen a burst of breakthroughs. Despite this progress, however, we still have a far more limited understanding of maximal matching which is one…
Outlier detection is critical in real applications to prevent financial fraud, defend network intrusions, or detecting imminent device failures. To reduce the human effort in evaluating outlier detection results and effectively turn the…