Sparse PCA With Multiple Components

Sparse Principal Component Analysis is a cardinal technique for obtaining combinations of features, or principal components (PCs), that explain the variance of high-dimensional datasets in an interpretable manner. At its heart, this involves solving a sparsity and orthogonality constrained convex maximization problem, which is extremely computationally challenging. Most existing work address sparse PCA via heuristics … Read more

A new sufficient condition for non-convex sparse recovery via weighted $\ell_r\!-\!\ell_1$ minimization

In this letter, we discuss the reconstruction of sparse signals from undersampled data, which belongs to the core content of compressed sensing. A new sufficient condition in terms of the restricted isometry constant (RIC) and restricted orthogonality constant (ROC) is first established for the performance guarantee of recently proposed non-convex weighted $\ell_r-\ell_1$ minimization in recovering … Read more

The Null Space Property of the Weighted $\ell_r-\ell_1$ Minimization

The null space property (NSP), which relies merely on the null space of the sensing matrix column space, has drawn numerous interests in sparse signal recovery. This article studies NSP of the weighted $\ell_r-\ell_1$ minimization. Several versions of NSP of the weighted $\ell_r-\ell_1$ minimization including the weighted $\ell_r-\ell_1$ NSP, the weighted $\ell_r-\ell_1$ stable NSP, the … Read more

The Combinatorial Brain Surgeon: Pruning Weights That Cancel One Another in Neural Networks

Neural networks tend to achieve better accuracy with training if they are larger — even if the resulting models are overparameterized. Nevertheless, carefully removing such excess parameters before, during, or after training may also produce models with similar or even improved accuracy. In many cases, that can be curiously achieved by heuristics as simple as … Read more

Mixed-Integer Programming Techniques for the Minimum Sum-of-Squares Clustering Problem

The minimum sum-of-squares clustering problem is a very important problem in data mining and machine learning with very many applications in, e.g., medicine or social sciences. However, it is known to be NP-hard in all relevant cases and to be notoriously hard to be solved to global optimality in practice. In this paper, we develop … Read more

Stable Recovery of Sparse Signals With Non-convex Weighted $r$-Norm Minus $1$-Norm

Given the measurement matrix $A$ and the observation signal $y$, the central purpose of compressed sensing is to find the most sparse solution of the underdetermined linear system $y=Ax+z$, where $x$ is the $s$-sparse signal to be recovered and $z$ is the noise vector. Zhou and Yu \cite{Zhou and Yu 2019} recently proposed a novel … Read more

Time-series aggregation for the optimization of energy systems: goals, challenges, approaches, and opportunities

The rising significance of renewable energy increases the importance of representing time-varying input data in energy system optimization studies. Time-series aggregation, which reduces temporal model complexity, has emerged in recent years to address this challenge. We provide a comprehensive review of time-series aggregation for the optimization of energy systems. We show where time series affect … Read more

New interior-point approach for one- and two-class linear support vector machines using multiple variable splitting

Multiple variable splitting is a general technique for decomposing problems by using copies of variables and additional linking constraints that equate their values. The resulting large optimization problem can be solved with a specialized interior-point method that exploits the problem structure and computes the Newton direction with a combination of direct and iterative solvers (i.e., … Read more

Analysis non-sparse recovery for non-convex relaxed $\ell_q$ minimization

This paper studies construction of signals, which are sparse or nearly sparse with respect to a tight frame $D$ from underdetermined linear systems. In the paper, we propose a non-convex relaxed $\ell_q(0 Article Download View Analysis non-sparse recovery for non-convex relaxed $ell_q$ minimization