Related papers: Sublinear Time and Space Algorithms for Correlatio…
Subspace sparse coding (SSC) algorithms have proven to be beneficial to clustering problems. They provide an alternative data representation in which the underlying structure of the clusters can be better captured. However, most of the…
This paper considers the problem of clustering a collection of unlabeled data points assumed to lie near a union of lower-dimensional planes. As is common in computer vision or unsupervised learning applications, we do not know in advance…
We give sublinear-time approximation algorithms for some optimization problems arising in machine learning, such as training linear classifiers and finding minimum enclosing balls. Our algorithms can be extended to some kernelized versions…
Finding the dense regions of a graph and relations among them is a fundamental problem in network analysis. Core and truss decompositions reveal dense subgraphs with hierarchical relations. The incremental nature of algorithms for computing…
We describe approximation algorithms in Linial's classic LOCAL model of distributed computing to find maximum-weight matchings in a hypergraph of rank $r$. Our main result is a deterministic algorithm to generate a matching which is an…
In Bipartite Correlation Clustering (BCC) we are given a complete bipartite graph $G$ with `+' and `-' edges, and we seek a vertex clustering that maximizes the number of agreements: the number of all `+' edges within clusters plus all `-'…
With the recent popularity of graphical clustering methods, there has been an increased focus on the information between samples. We show how learning cluster structure using edge features naturally and simultaneously determines the most…
We consider the problem of detecting a cycle in a directed graph that grows by arc insertions, and the related problems of maintaining a topological order and the strong components of such a graph. For these problems, we give two…
Graph neural networks (GNNs) have been widely investigated in the field of semi-supervised graph machine learning. Most methods fail to exploit adequate graph information when labeled data is limited, leading to the problem of…
Let $G$ be an edge-weighted directed graph with $n$ vertices embedded on an orientable surface of genus $g$. We describe a simple deterministic lexicographic perturbation scheme that guarantees uniqueness of minimum-cost flows and shortest…
The Minimum Consistent Subset (MCS) problem arises naturally in the context of supervised clustering and instance selection. In supervised clustering, one aims to infer a meaningful partitioning of data using a small labeled subset.…
This paper studies the nucleus decomposition problem, which has been shown to be useful in finding dense substructures in graphs. We present a novel parallel algorithm that is efficient both in theory and in practice. Our algorithm achieves…
In the Colored Clustering problem, one is asked to cluster edge-colored (hyper-)graphs whose colors represent interaction types. More specifically, the goal is to select as many edges as possible without choosing two edges that share an…
This paper describes a graph clustering algorithm that aims to minimize the normalized cut criterion and has a model order selection procedure. The performance of the proposed algorithm is comparable to spectral approaches in terms of…
The Massively Parallel Computation (MPC) model is an emerging model which distills core aspects of distributed and parallel computation. It has been developed as a tool to solve (typically graph) problems in systems where the input is…
We show how to efficiently solve a clustering problem that arises in a method to evaluate functions of matrices. The problem requires finding the connected components of a graph whose vertices are eigenvalues of a real or complex matrix and…
Given a planar graph G on n vertices and an integer parameter r<n, an r-division of G with few holes is a decomposition of G into O(n/r) regions of size at most r such that each region contains at most a constant number of faces that are…
Local graph clustering is an important algorithmic technique for analysing massive graphs, and has been widely applied in many research fields of data science. While the objective of most (local) graph clustering algorithms is to find a…
We improve on random sampling techniques for approximately solving problems that involve cuts and flows in graphs. We give a near-linear-time construction that transforms any graph on n vertices into an O(n\log n)-edge graph on the same…
Hypergraphs are a useful abstraction for modeling multiway relationships in data, and hypergraph clustering is the task of detecting groups of closely related nodes in such data. Graph clustering has been studied extensively, and there are…