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We study the task of differentially private clustering. For several basic clustering problems, including Euclidean DensestBall, 1-Cluster, k-means, and k-median, we give efficient differentially private algorithms that achieve essentially…

Community detection in network analysis is an attractive research area recently. Here, under the degree-corrected mixed membership (DCMM) model, we propose an efficient approach called mixed regularized spectral clustering (Mixed-RSC for…

We propose a globally-accelerated, first-order method for the optimization of smooth and (strongly or not) geodesically-convex functions in a wide class of Hadamard manifolds. We achieve the same convergence rates as Nesterov's accelerated…

The alternating direction method of multipliers (ADMM) were extensively investigated in the past decades for solving separable convex optimization problems. Fewer researchers focused on exploring its convergence properties for the nonconvex…

In statistical machine learning, kernel methods allow to consider infinite dimensional feature spaces with a computational cost that only depends on the number of observations. This is usually done by solving an optimization problem…

We study the problem of approximation of 2D set of points. Such type of problems always occur in physical experiments, econometrics, data analysis and other areas. The often problems of outliers or spikes usually make researchers to apply…

In this paper, we proposed a novel two-stage optimization method for network community partition, which is based on inherent network structure information. The introduced optimization approach utilizes the new network centrality measure of…

We propose a penalized likelihood method to jointly estimate multiple precision matrices for use in quadratic discriminant analysis and model based clustering. A ridge penalty and a ridge fusion penalty are used to introduce shrinkage and…

Low-rank matrix approximation (LRMA) has been arisen in many applications, such as dynamic MRI, recommendation system and so on. The alternating direction method of multipliers (ADMM) has been designed for the nuclear norm regularized least…

In this paper, we consider a class of nonconvex problems with linear constraints appearing frequently in the area of image processing. We solve this problem by the penalty method and propose the iteratively reweighted alternating…

We analyse the convergence of an approximate, fully inexact, ADMM algorithm under additive, deterministic and probabilistic error models. We consider the generalized ADMM scheme that is derived from generalized Lagrangian penalty with…

In this two-part work, we propose an algorithmic framework for solving non-convex problems whose objective function is the sum of a number of smooth component functions plus a convex (possibly non-smooth) or/and smooth (possibly non-convex)…

In the Euclidean setting, the proximal gradient method and its accelerated variants are a class of efficient algorithms for optimization problems with decomposable objective. In this paper, we develop a Riemannian proximal gradient method…

Affinity propagation is one of the most effective unsupervised pattern recognition algorithms for data clustering in high-dimensional feature space. However, the numerous attempts to test its performance for community detection in complex…

Nonconvex and structured optimization problems arise in many engineering applications that demand scalable and distributed solution methods. The study of the convergence properties of these methods is in general difficult due to the…

Precision matrix estimation is a fundamental topic in multivariate statistics and modern machine learning. This paper proposes an adversarially perturbed precision matrix estimation framework, motivated by recent developments in adversarial…

Rectified Flow (RF) models achieve state-of-the-art generation quality, yet controlling them for precise tasks -- such as semantic editing or blind image recovery -- remains a challenge. Current approaches bifurcate into inversion-based…

Assessing the partitioning performance of community detection algorithms is one of the most important issues in complex network analysis. Artificially generated networks are often used as benchmarks for this purpose. However, previous…

We initiate the study of sparse recovery problems under the Earth-Mover Distance (EMD). Specifically, we design a distribution over m x n matrices A such that for any x, given Ax, we can recover a k-sparse approximation to x under the EMD…

We consider a community finding problem called Co-located Community Detection (CCD) over geo-social networks, which retrieves communities that satisfy both high structural tightness and spatial closeness constraints. To provide a solution…