Matrix analysis
Real and complex analysis, 3rd ed.
Real and complex analysis, 3rd ed.
Sparse Approximate Solutions to Linear Systems
SIAM Journal on Computing
On the Optimality of the Backward Greedy Algorithm for the Subset Selection Problem
SIAM Journal on Matrix Analysis and Applications
Low-Rank Approximations with Sparse Factors I: Basic Algorithms and Error Analysis
SIAM Journal on Matrix Analysis and Applications
On Tractable Approximations of Uncertain Linear Matrix Inequalities Affected by Interval Uncertainty
SIAM Journal on Optimization
Convex Optimization
Generalized spectral bounds for sparse LDA
ICML '06 Proceedings of the 23rd international conference on Machine learning
On Model Selection Consistency of Lasso
The Journal of Machine Learning Research
Full regularization path for sparse principal component analysis
Proceedings of the 24th international conference on Machine learning
Sparse eigen methods by D.C. programming
Proceedings of the 24th international conference on Machine learning
Decoding by linear programming
IEEE Transactions on Information Theory
Efficient computation of PCA with SVD in SQL
Proceedings of the 2nd Workshop on Data Mining using Matrices and Tensors
Online Learning for Matrix Factorization and Sparse Coding
The Journal of Machine Learning Research
Generalized Power Method for Sparse Principal Component Analysis
The Journal of Machine Learning Research
Bayesian orthogonal component analysis for sparse representation
IEEE Transactions on Signal Processing
Improve robustness of sparse PCA by L1-norm maximization
Pattern Recognition
Group Lasso Estimation of High-dimensional Covariance Matrices
The Journal of Machine Learning Research
Learning with Structured Sparsity
The Journal of Machine Learning Research
Improved Bounds on Restricted Isometry Constants for Gaussian Matrices
SIAM Journal on Matrix Analysis and Applications
Theory and Applications of Robust Optimization
SIAM Review
Sparse PCA by iterative elimination algorithm
Advances in Computational Mathematics
Convex approximations to sparse PCA via Lagrangian duality
Operations Research Letters
Sparse non Gaussian component analysis by semidefinite programming
Machine Learning
Weak Recovery Conditions from Graph Partitioning Bounds and Order Statistics
Mathematics of Operations Research
Truncated power method for sparse eigenvalue problems
The Journal of Machine Learning Research
Feature selection for k-means clustering stability: theoretical analysis and an algorithm
Data Mining and Knowledge Discovery
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Given a sample covariance matrix, we examine the problem of maximizing the variance explained by a linear combination of the input variables while constraining the number of nonzero coefficients in this combination. This is known as sparse principal component analysis and has a wide array of applications in machine learning and engineering. We formulate a new semidefinite relaxation to this problem and derive a greedy algorithm that computes a full set of good solutions for all target numbers of non zero coefficients, with total complexity O(n3), where n is the number of variables. We then use the same relaxation to derive sufficient conditions for global optimality of a solution, which can be tested in O(n3), per pattern. We discuss applications in subset selection and sparse recovery and show on artificial examples and biological data that our algorithm does provide globally optimal solutions in many cases.