sparse pca

Sparse Principal Component Analysis with Non-Oblivious Adversarial Perturbations

  • Yuqing He
  • Guanyi Wang
  • Yu Yang
    • Categories (Mixed) Integer Nonlinear Programming Tags , ,

    Sparse Principal Component Analysis (sparse PCA) is a fundamental dimension-reduction tool that enhances interpretability in various high-dimensional settings. An important variant of sparse PCA studies the scenario when samples are adversarially perturbed. Notably, most existing statistical studies on this variant focus on recovering the ground truth and verifying the robustness of classical algorithms when the … Read more

    Beyond Symmetry: Best Submatrix Selection for the Sparse Truncated SVD

  • Yongchun Li
  • Weijun Xie
    • Categories Combinatorial Optimization, Data-Mining, Integer Programming Tags , , , ,

    Truncated singular value decomposition (SVD), also known as the best low-rank matrix approximation, has been successfully applied to many domains such as biology, healthcare, and others, where high-dimensional datasets are prevalent. To enhance the interpretability of the truncated SVD, sparse SVD (SSVD) is introduced to select a few rows and columns of the original matrix … Read more

    A Penalty-free Infeasible Approach for a Class of Nonsmooth Optimization Problems over the Stiefel Manifold

  • Nachuan Xiao
  • Xin Liu
  • Ya-xiang Yuan
    • Categories Applications - Science and Engineering, Constrained Nonlinear Optimization Tags , , , ,

    Transforming into an exact penalty function model with convex compact constraints yields efficient infeasible approaches for optimization problems with orthogonality constraints. For smooth and L21-norm regularized cases, these infeasible approaches adopt simple and orthonormalization-free updating schemes and show high efficiency in some numerical experiments. However, to avoid orthonormalization while enforcing the feasibility of the final … Read more

    Exact and Approximation Algorithms for Sparse PCA

  • Yongchun Li
  • Weijun Xie
    • Categories Integer Programming Tags , , , , ,

    Sparse Principal Component Analysis (SPCA) is designed to enhance the interpretability of traditional Principal Component Analysis (PCA) by optimally selecting a subset of features that comprise the first principal component. Given the NP-hard nature of SPCA, most current approaches resort to approximate solutions, typically achieved through tractable semidefinite programs (SDPs) or heuristic methods. To solve SPCA to … Read more

    An Augmented Lagrangian Approach for Sparse Principal Component Analysis

  • Zhaosong Lu
  • Yong Zhang
    • Categories Constrained Nonlinear Optimization, Nonsmooth Optimization, Statistics Tags , , ,

    Principal component analysis (PCA) is a widely used technique for data analysis and dimension reduction with numerous applications in science and engineering. However, the standard PCA suffers from the fact that the principal components (PCs) are usually linear combinations of all the original variables, and it is thus often difficult to interpret the PCs. To … Read more

    Generalized power method for sparse principal component analysis

  • Michel Journee
  • Yurii Nesterov
  • Peter Richtarik
  • Rodolphe Sepulchre
    • Categories Applications - Science and Engineering, Nonlinear Optimization, Nonsmooth Optimization Tags , , , ,

    In this paper we develop a new approach to sparse principal component analysis (sparse PCA). We propose two single-unit and two block optimization formulations of the sparse PCA problem, aimed at extracting a single sparse dominant principal component of a data matrix, or more components at once, respectively. While the initial formulations involve nonconvex functions, … Read more