Related papers: Achieving the Bayes Error Rate in Synchronization …
In this paper we consider the cluster estimation problem under the Stochastic Block Model. We show that the semidefinite programming (SDP) formulation for this problem achieves an error rate that decays exponentially in the signal-to-noise…
We consider the problem of estimating the discrete clustering structures under the Sub-Gaussian Mixture Model. Our main results establish a hidden integrality property of a semidefinite programming (SDP) relaxation for this problem: while…
We study graph clustering in the Stochastic Block Model (SBM) in the presence of both large clusters and small, unrecoverable clusters. Previous convex relaxation approaches achieving exact recovery do not allow any small clusters of size…
Resolving a conjecture of Abbe, Bandeira and Hall, the authors have recently shown that the semidefinite programming (SDP) relaxation of the maximum likelihood estimator achieves the sharp threshold for exactly recovering the community…
The stochastic block model (SBM) is a popular tool for community detection in networks, but fitting it by maximum likelihood (MLE) involves a computationally infeasible optimization problem. We propose a new semidefinite programming (SDP)…
The binary symmetric stochastic block model deals with a random graph of $n$ vertices partitioned into two equal-sized clusters, such that each pair of vertices is connected independently with probability $p$ within clusters and $q$ across…
We consider the problem of identifying underlying community-like structures in graphs. Towards this end we study the Stochastic Block Model (SBM) on $k$-clusters: a random model on $n=km$ vertices, partitioned in $k$ equal sized clusters,…
We consider semidefinite programming (SDP) for the binary stochastic block model with equal-sized communities. Prior work of Hajek, Wu, and Xu proposed an SDP (sym-SDP) for the symmetric case where the intra-community edge probabilities are…
We study the phase synchronization problem with noisy measurements $Y=z^*z^{*H}+\sigma W\in\mathbb{C}^{n\times n}$, where $z^*$ is an $n$-dimensional complex unit-modulus vector and $W$ is a complex-valued Gaussian random matrix. It is…
We propose a semidefinite programming (SDP) algorithm for community detection in the stochastic block model, a popular model for networks with latent community structure. We prove that our algorithm achieves exact recovery of the latent…
In this paper, we consider the problem of partitioning a small data sample of size $n$ drawn from a mixture of 2 sub-gaussian distributions in $\R^p$. We consider semidefinite programming relaxations of an integer quadratic program that is…
This paper produces an efficient Semidefinite Programming (SDP) solution for community detection that incorporates non-graph data, which in this context is known as side information. SDP is an efficient solution for standard community…
Semidefinite programming (SDP) is a powerful tool for tackling a wide range of computationally hard problems such as clustering. Despite the high accuracy, semidefinite programs are often too slow in practice with poor scalability on large…
Statistical inference problems arising within signal processing, data mining, and machine learning naturally give rise to hard combinatorial optimization problems. These problems become intractable when the dimensionality of the data is…
The problem of community detection with two equal-sized communities is closely related to the minimum graph bisection problem over certain random graph models. In the stochastic block model distribution over networks with community…
Semidefinite programming (SDP) is a powerful framework from convex optimization that has striking potential for data science applications. This paper develops a provably correct randomized algorithm for solving large, weakly constrained SDP…
We investigate the clustering performances of the relaxed $K$means in the setting of sub-Gaussian Mixture Model (sGMM) and Stochastic Block Model (SBM). After identifying the appropriate signal-to-noise ratio (SNR), we prove that the…
Motivated by applications in wireless communications, this paper develops semidefinite programming (SDP) relaxation techniques for some mixed binary quadratically constrained quadratic programs (MBQCQP) and analyzes their approximation…
Clustering is a widely deployed unsupervised learning tool. Model-based clustering is a flexible framework to tackle data heterogeneity when the clusters have different shapes. Likelihood-based inference for mixture distributions often…
Clustering is one of the most important unsupervised problems in machine learning and statistics. Among many existing algorithms, kernel k-means has drawn much research attention due to its ability to find non-linear cluster boundaries and…