Related papers: A Simple Spectral Algorithm for Recovering Planted…

Finding a hidden partition in a random environment is a general and important problem, which contains as subproblems many famous questions, such as finding a hidden clique, finding a hidden coloring, finding a hidden bipartition etc. In…

We consider the probability that a spanning tree chosen uniformly at random from a graph can be partitioned into a fixed number $k$ of trees of equal size by removing $k-1$ edges. In that case, the spanning tree is called {\em splittable}.…

We introduce a graph partitioning problem motivated by computational topology and propose two algorithms that produce approximate solutions. Specifically, given a weighted, undirected graph $G$ and a positive integer $k$, we desire to find…

For $f(x)$ a separable polynomial of degree $d$ over a discretely valued field $K$, we describe how the cluster picture of $f(x)$ over $K$, in other words the set of tuples $\{(\mathrm{ord}(x_i-x_j),i,j) : 1\leq i< j \leq d \}$ where…

This paper considers the problem of clustering a partially observed unweighted graph---i.e., one where for some node pairs we know there is an edge between them, for some others we know there is no edge, and for the remaining we do not know…

In this work, a graph partitioning problem in a fixed number of connected components is considered. Given an undirected graph with costs on the edges, the problem consists of partitioning the set of nodes into a fixed number of subsets with…

We consider the problem of recovering signals from their power spectral density. This is a classical problem referred to in literature as the phase retrieval problem, and is of paramount importance in many fields of applied sciences. In…

Graph alignment aims at finding the vertex correspondence between two correlated graphs, a task that frequently occurs in graph mining applications such as social network analysis. Attributed graph alignment is a variant of graph alignment,…

In this paper, we propose and study a new semi-random model for graph partitioning problems. We believe that it captures many properties of real--world instances. The model is more flexible than the semi-random model of Feige and Kilian and…

Spectral clustering has become one of the most popular algorithms in data clustering and community detection. We study the performance of classical two-step spectral clustering via the graph Laplacian to learn the stochastic block model.…

We give a simple, greedy $O(n^{\omega+0.5})=O(n^{2.872})$-time algorithm to list-decode planted cliques in a semirandom model introduced in [CSV17] (following [FK01]) that succeeds whenever the size of the planted clique is $k\geq…

Clustering is a NP-hard problem. Thus, no optimal algorithm exists, heuristics are applied to cluster the data. Heuristics can be very resource-intensive, if not applied properly. For substantially large data sets computational efficiencies…

Is it possible to find the sparsest vector (direction) in a generic subspace $\mathcal{S} \subseteq \mathbb{R}^p$ with $\mathrm{dim}(\mathcal{S})= n < p$? This problem can be considered a homogeneous variant of the sparse recovery problem,…

Consider a problem where 4k given vectors need to be partitioned into k clusters of four vectors each. A cluster of four vectors is called a quad, and the cost of a quad is the sum of the component-wise maxima of the four vectors in the…

The problems of computing graph colorings and clique covers are central challenges in combinatorial optimization. Both of these are known to be NP-hard, and thus computationally intractable in the worst-case instance. A prominent approach…

This paper studies clustering algorithms for dynamically evolving graphs $\{G_t\}$, in which new edges (and potential new vertices) are added into a graph, and the underlying cluster structure of the graph can gradually change. The paper…

We design replicable algorithms in the context of statistical clustering under the recently introduced notion of replicability from Impagliazzo et al. [2022]. According to this definition, a clustering algorithm is replicable if, with high…

Spectral clustering refers to a family of unsupervised learning algorithms that compute a spectral embedding of the original data based on the eigenvectors of a similarity graph. This non-linear transformation of the data is both the key of…

The unsupervised learning of community structure, in particular the partitioning vertices into clusters or communities, is a canonical and well-studied problem in exploratory graph analysis. However, like most graph analyses the…

In this paper, we study the problems of detection and recovery of hidden submatrices with elevated means inside a large Gaussian random matrix. We consider two different structures for the planted submatrices. In the first model, the…