Related papers: A Block Decomposition Algorithm for Sparse Optimiz…
We develop and analyze stochastic optimization algorithms for problems in which the expected loss is strongly convex, and the optimum is (approximately) sparse. Previous approaches are able to exploit only one of these two structures,…
Sparse representation has been applied successfully in abnormal event detection, in which the baseline is to learn a dictionary accompanied by sparse codes. While much emphasis is put on discriminative dictionary construction, there are no…
This paper studies high-dimensional sparse clustering, a combinatorial NP-hard problem arising from the bilinear coupling between cluster assignment and feature selection. We analyze semidefinite programming (SDP) relaxations of $K$-means…
We consider compressed sensing of block-sparse signals, i.e., sparse signals that have nonzero coefficients occuring in clusters. Based on an uncertainty relation for block-sparse signals, we define a block-coherence measure and we show…
Block coordinate descent (BCD) methods are prevalent in large scale optimization problems due to the low memory and computational costs per iteration, the predisposition to parallelization, and the ability to exploit the structure of the…
Sparse signal recovery from a small number of random measurements is a well known NP-hard to solve combinatorial optimization problem, with important applications in signal and image processing. The standard approach to the sparse signal…
In this paper, we present a new stochastic algorithm, namely the stochastic block mirror descent (SBMD) method for solving large-scale nonsmooth and stochastic optimization problems. The basic idea of this algorithm is to incorporate the…
Sparsity-constrained optimization is an important and challenging problem that has wide applicability in data mining, machine learning, and statistics. In this paper, we focus on sparsity-constrained optimization in cases where the cost…
We discuss a method for sparse signal approximation, which is based on the correlation of the target signal with a pseudo-random signal, and uses a modification of the greedy matching pursuit algorithm. We show that this approach provides…
Sparse matrices are favorable objects in machine learning and optimization. When such matrices are used, in place of dense ones, the overall complexity requirements in optimization can be significantly reduced in practice, both in terms of…
In this paper we analyze several new methods for solving nonconvex optimization problems with the objective function formed as a sum of two terms: one is nonconvex and smooth, and another is convex but simple and its structure is known.…
Nonsmooth composite optimization with orthogonality constraints has a wide range of applications in statistical learning and data science. However, this problem is challenging due to its nonsmooth objective and computationally expensive…
Convolutional sparse coding improves on the standard sparse approximation by incorporating a global shift-invariant model. The most efficient convolutional sparse coding methods are based on the alternating direction method of multipliers…
Building upon our earlier work of a martingale approach to global optimization, a powerful stochastic search scheme for the global optimum of cost functions is proposed on the basis of change of measures on the states that evolve as…
We propose a variant of the classical conditional gradient method for sparse inverse problems with differentiable measurement models. Such models arise in many practical problems including superresolution, time-series modeling, and matrix…
An approach for effective implementation of greedy selection methodologies, to approximate an image partitioned into blocks, is proposed. The method is specially designed for approximating partitions on a transformed image. It evolves by…
This work introduces a new method to efficiently solve optimization problems constrained by partial differential equations (PDEs) with uncertain coefficients. The method leverages two sources of inexactness that trade accuracy for speed:…
In this paper, we propose a novel sparse coding and counting method under Bayesian framwork for visual tracking. In contrast to existing methods, the proposed method employs the combination of L0 and L1 norm to regularize the linear…
This work presents a parallel variant of the algorithm introduced in [Acceleration of block coordinate descent methods with identification strategies Comput. Optim. Appl. 72(3):609--640, 2019] to minimize the sum of a partially separable…
We present a novel stagewise strategy for improving greedy algorithms for sparse recovery. We demonstrate its efficiency both for synthesis and analysis sparse priors, where in both cases we demonstrate its computational efficiency and…