相关论文: Clustering using Max-norm Constrained Optimization

This paper considers the optimization problem in the form of $\min_{X \in \mathcal{F}_v} f(x) + \lambda \|X\|_1,$ where $f$ is smooth, $\mathcal{F}_v = \{X \in \mathbb{R}^{n \times q} : X^T X = I_q, v \in \mathrm{span}(X)\}$, and $v$ is a…

We use convex relaxation techniques to provide a sequence of solutions to the matrix completion problem. Using the nuclear norm as a regularizer, we provide simple and very efficient algorithms for minimizing the reconstruction error…

This paper proposes a new algorithm for simultaneous graph matching and clustering. For the first time in the literature, these two problems are solved jointly and synergetically without relying on any training data, which brings advantages…

We perform a maximum likelihood analysis of the cluster abundance measured in the SDSS using the maxBCG cluster finding algorithm. Our analysis is aimed at constraining the power spectrum normalization $\sigma_8$, and assumes flat…

This paper discusses a deterministic clustering approach to capacitated resource allocation problems. In particular, the Deterministic Annealing (DA) algorithm from the data-compression literature, which bears a distinct analogy to the…

We propose a new framework for deriving screening rules for convex optimization problems. Our approach covers a large class of constrained and penalized optimization formulations, and works in two steps. First, given any approximate point,…

In this paper we extend an earlier result within Dempster-Shafer theory ["Fast Dempster-Shafer Clustering Using a Neural Network Structure," in Proc. Seventh Int. Conf. Information Processing and Management of Uncertainty in Knowledge-Based…

It has been observed in practical applications and in theoretical analysis that over-parametrization helps to find good minima in neural network training. Similarly, in this article we study widening and deepening neural networks by a…

Recently, there has been substantial interest in clustering research that takes a beyond worst-case approach to the analysis of algorithms. The typical idea is to design a clustering algorithm that outputs a near-optimal solution, provided…

The minimization of a nonconvex composite function can model a variety of imaging tasks. A popular class of algorithms for solving such problems are majorization-minimization techniques which iteratively approximate the composite nonconvex…

We propose a simple and efficient clustering method for high-dimensional data with a large number of clusters. Our algorithm achieves high-performance by evaluating distances of datapoints with a subset of the cluster centres. Our…

In this paper, we study the strength of convex relaxations obtained by convexification of aggregation of constraints for a set $S$ described by two bilinear bipartite equalities. Aggregation is the process of rescaling the original…

Dual decomposition has been successfully employed in a variety of distributed convex optimization problems solved by a network of computing and communicating nodes. Often, when the cost function is separable but the constraints are coupled,…

We consider the limits of super-resolution using imaging constraints. Due to various theoretical and practical limitations, reconstruction-based methods have been largely restricted to small increases in resolution. In addition, motion-blur…

This paper is devoted to the theoretical and numerical investigation of an augmented Lagrangian method for the solution of optimization problems with geometric constraints. Specifically, we study situations where parts of the constraints…

We present a novel clustering approach for moving object trajectories that are constrained by an underlying road network. The approach builds a similarity graph based on these trajectories then uses modularity-optimization hiearchical graph…

This paper proposes a novel framework for accelerating support vector clustering. The proposed method first computes much smaller compressed data sets while preserving the key cluster properties of the original data sets based on a novel…

Maximum diversity aims at selecting a diverse set of high-quality objects from a collection, which is a fundamental problem and has a wide range of applications, e.g., in Web search. Diversity under a uniform or partition matroid constraint…

Assessing how adequate clusters fit a dataset and finding an optimum number of clusters is a difficult process. A membership matrix and the degree of membership matrix is suggested to determine the homogeneity of a cluster fit. Maximisation…

We study the use of approximate Lagrange multipliers and discrete actions in solving convex optimisation problems. We observe that descent, which can be ensured using a wide range of approaches (gradient, subgradient, Newton, etc.), is…