相关论文: Regularized Projection Matrix Approximation with A…

Community detection is an important problem in unsupervised learning. This paper proposes to solve a projection matrix approximation problem with an additional entrywise bounded constraint. Algorithmically, we introduce a new differentiable…

Community detection plays an important role in understanding and exploiting the structure of complex systems. Many algorithms have been developed for community detection using modularity maximization or other techniques. In this paper, we…

Spectral clustering is one of the most popular clustering approaches with the capability to handle some challenging clustering problems. Most spectral clustering methods provide a nonlinear map from the data manifold to a subspace. Only a…

A new exact projective penalty method is proposed for the equivalent reduction of constrained optimization problems to nonsmooth unconstrained ones. In the method, the original objective function is extended to infeasible points by summing…

We propose a penalized likelihood framework for estimating multiple precision matrices from different classes. Most existing methods either incorporate no information on relationships between the precision matrices, or require this…

We propose new methods to speed up convergence of the Alternating Direction Method of Multipliers (ADMM), a common optimization tool in the context of large scale and distributed learning. The proposed method accelerates the speed of…

Manifold regularization methods for matrix factorization rely on the cluster assumption, whereby the neighborhood structure of data in the input space is preserved in the factorization space. We argue that using the k-neighborhoods of all…

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 introduce a general framework for estimation of inverse covariance, or precision, matrices from heterogeneous populations. The proposed framework uses a Laplacian shrinkage penalty to encourage similarity among estimates from disparate,…

In [1], the distributed linear-quadratic problem with fixed communication topology (DFT-LQ) and the sparse feedback LQ problem (SF-LQ) are formulated into a nonsmooth and nonconvex optimization problem with affine constraints. Moreover, a…

We propose a distributed algorithm based on Alternating Direction Method of Multipliers (ADMM) to minimize the sum of locally known convex functions using communication over a network. This optimization problem emerges in many applications…

Optimization on Riemannian manifolds widely arises in eigenvalue computation, density functional theory, Bose-Einstein condensates, low rank nearest correlation, image registration, and signal processing, etc. We propose an adaptive…

The numerical properties of algorithms for finding the intersection of sets depend to some extent on the regularity of the sets, but even more importantly on the regularity of the intersection. The alternating projection algorithm of von…

Fast accumulation of large amounts of complex data has created a need for more sophisticated statistical methodologies to discover interesting patterns and better extract information from these data. The large scale of the data often…

Community structure in networks is observed in many different domains, and unsupervised community detection has received a lot of attention in the literature. Increasingly the focus of network analysis is shifting towards using network…

We consider a regularized least squares problem, with regularization by structured sparsity-inducing norms, which extend the usual $\ell_1$ and the group lasso penalty, by allowing the subsets to overlap. Such regularizations lead to…

The paper concerns optimization problems with general equality and inequality constraints and with constraints expressed by a convex set. In order to solve these problems, the general constraints are treated by an exact penalty functions…

We outline a new approach for solving optimization problems which enforce triangle inequalities on output variables. We refer to this as metric-constrained optimization, and give several examples where problems of this form arise in machine…

Alternating Direction Method of Multipliers (ADMM) is a popular algorithm for distributed learning, where a network of nodes collaboratively solve a regularized empirical risk minimization by iterative local computation associated with…

This paper introduces a dual-regularized ADMM approach to distributed, time-varying optimization. The proposed algorithm is designed in a prediction-correction framework, in which the computing nodes predict the future local costs based on…