Related papers: Sketch-and-Lift: Scalable Subsampled Semidefinite …
We propose a manifold optimization approach to solve linear semidefinite programs (SDP) with low-rank solutions, with an emphasis on SDP relaxations for polynomial optimization problems. This approach incorporates the inexact augmented…
Clustering is one of the most fundamental tools in data science and machine learning, and k-means clustering is one of the most common such methods. There is a variety of approximate algorithms for the k-means problem, but computing the…
Kernel-based clustering algorithms have the ability to capture the non-linear structure in real world data. Among various kernel-based clustering algorithms, kernel k-means has gained popularity due to its simple iterative nature and ease…
The randomized coordinate descent (RCD) method is a classical algorithm with simple, lightweight iterations that is widely used for various optimization problems, including the solution of positive semidefinite linear systems. As a linear…
This article explores and analyzes the unsupervised clustering of large partially observed graphs. We propose a scalable and provable randomized framework for clustering graphs generated from the stochastic block model. The clustering is…
We give new rounding schemes for SDP relaxations for the problems of maximizing cubic polynomials over the unit sphere and the $n$-dimensional hypercube. In both cases, the resulting algorithms yield a $O(\sqrt{n/k})$ multiplicative…
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…
In the presence of heterogeneous data, where randomly rotated objects fall into multiple underlying categories, it is challenging to simultaneously classify them into clusters and synchronize them based on pairwise relations. This gives…
In this paper we target the class of modal clustering methods where clusters are defined in terms of the local modes of the probability density function which generates the data. The most well-known modal clustering method is the k-means…
The nowadays massive amounts of generated and communicated data present major challenges in their processing. While capable of successfully classifying nonlinearly separable objects in various settings, subspace clustering (SC) methods…
Semidefinite programming (SDP) is the task of optimizing a linear function over the common solution set of finitely many linear matrix inequalities (LMIs). For the running time of SDP solvers, the maximal matrix size of these LMIs is…
There is an increasing interest in quantum algorithms for optimization problems. Within convex optimization, interior-point methods and other recently proposed quantum algorithms are non-trivial to implement on noisy quantum devices. Here,…
We consider optimization problems containing nonconvex quadratic functions for which semidefinite programming (SDP) relaxations often yield strong bounds. We investigate linear inequalities that outer approximate the positive semidefinite…
We study Semidefinite Programming, \SDPc relaxations for Sensor Network Localization, \SNLc with anchors and with noisy distance information. The main point of the paper is to view \SNL as a (nearest) Euclidean Distance Matrix, \EDM,…
In Multi-Input Multi-Output (MIMO) systems, Maximum-Likelihood (ML) decoding is equivalent to finding the closest lattice point in an N-dimensional complex space. In general, this problem is known to be NP hard. In this paper, we propose a…
This paper investigates the minimization of the expectation of piecewise polynomial loss functions over Wasserstein balls. This optimization problem often appears as a key sub-problem of distributionally robust optimization problems. We…
Low-rank methods for semidefinite programming (SDP) have gained a lot of interest recently, especially in machine learning applications. Their analysis often involves determinant-based or Schatten-norm penalties, which are hard to implement…
In this paper, we investigate the learning-augmented $k$-median clustering problem, which aims to improve the performance of traditional clustering algorithms by preprocessing the point set with a predictor of error rate $\alpha \in [0,1)$.…
Many problems in control theory can be formulated as semidefinite programs (SDPs). For large-scale SDPs, it is important to exploit the inherent sparsity to improve the scalability. This paper develops efficient first-order methods to solve…
Random projection, a dimensionality reduction technique, has been found useful in recent years for reducing the size of optimization problems. In this paper, we explore the use of sparse sub-gaussian random projections to approximate…