Related papers: Efficient Optimization Algorithms for Robust Princ…
In the field of unsupervised feature selection, sparse principal component analysis (SPCA) methods have attracted more and more attention recently. Compared to spectral-based methods, SPCA methods don't rely on the construction of a…
We consider the problem of maximizing the variance explained from a data matrix using orthogonal sparse principal components that have a support of fixed cardinality. While most existing methods focus on building principal components (PCs)…
We consider the problem of designing efficient regularization algorithms when regularization is encoded by a (strongly) convex functional. Unlike classical penalization methods based on a relaxation approach, we propose an iterative method…
We study iterative regularization for linear models, when the bias is convex but not necessarily strongly convex. We characterize the stability properties of a primal-dual gradient based approach, analyzing its convergence in the presence…
In the era of big data, reducing data dimensionality is critical in many areas of science. Widely used Principal Component Analysis (PCA) addresses this problem by computing a low dimensional data embedding that maximally explain variance…
Robust principal component analysis (RPCA) is a powerful method for learning low-rank feature representation of various visual data. However, for certain types as well as significant amount of error corruption, it fails to yield…
Probabilistic principal component analysis (PPCA) is a probabilistic reformulation of principal component analysis (PCA), under the framework of a Gaussian latent variable model. To improve the robustness of PPCA, it has been proposed to…
Principal Component Analysis (PCA) is a well known procedure to reduce intrinsic complexity of a dataset, essentially through simplifying the covariance structure or the correlation structure. We introduce a novel algebraic, model-based…
This paper proposes distributed algorithms to solve robust convex optimization (RCO) when the constraints are affected by nonlinear uncertainty. We adopt a scenario approach by randomly sampling the uncertainty set. To facilitate the…
Model instability and poor prediction of long-term behavior are common problems when modeling dynamical systems using nonlinear "black-box" techniques. Direct optimization of the long-term predictions, often called simulation error…
Optimization models with non-convex constraints arise in many tasks in machine learning, e.g., learning with fairness constraints or Neyman-Pearson classification with non-convex loss. Although many efficient methods have been developed…
In this paper, we propose an improved numerical algorithm for solving minimax problems based on nonsmooth optimization, quadratic programming and iterative process. We also provide a rigorous proof of convergence for our algorithm under…
Quadratic constrained quadratic programming problems often occur in various fields such as engineering practice, management science, and network communication. This article mainly studies a non convex quadratic programming problem with…
Subspace clustering (SC) is a popular method for dimensionality reduction of high-dimensional data, where it generalizes Principal Component Analysis (PCA). Recently, several methods have been proposed to enhance the robustness of PCA and…
Robust principal component analysis (RPCA) has drawn significant attentions due to its powerful capability in recovering low-rank matrices as well as successful appplications in various real world problems. The current state-of-the-art…
In this paper, we propose new sequential randomized algorithms for convex optimization problems in the presence of uncertainty. A rigorous analysis of the theoretical properties of the solutions obtained by these algorithms, for full…
Robust principal component analysis is an important representative method in data analysis. It is usually viewed as an optimization problem involving the rank and $\ell_0$-norm of matrices. In this paper, we study the rank and $\ell_0$…
Principal component analysis (PCA) is possibly one of the most widely used statistical tools to recover a low-rank structure of the data. In the high-dimensional settings, the leading eigenvector of the sample covariance can be nearly…
This paper studies first-order algorithms for solving fully composite optimization problems over convex and compact sets. We leverage the structure of the objective by handling its differentiable and non-differentiable components…
An efficient computational approach for optimal reconstructing parameters of binary-type physical properties for models in biomedical applications is developed and validated. The methodology includes gradient-based multiscale optimization…