Trawling the Web for emerging cyber-communities
WWW '99 Proceedings of the eighth international conference on World Wide Web
Approximation of Dense-n/2-Subgraph and the Complement of Min-Bisection
Journal of Global Optimization
Complexity of finding dense subgraphs
Discrete Applied Mathematics
Finding Dense Subgraphs with Semidefinite Programming
APPROX '98 Proceedings of the International Workshop on Approximation Algorithms for Combinatorial Optimization
Discovering large dense subgraphs in massive graphs
VLDB '05 Proceedings of the 31st international conference on Very large data bases
Generalized spectral bounds for sparse LDA
ICML '06 Proceedings of the 23rd international conference on Machine learning
SIGIR '07 Proceedings of the 30th annual international ACM SIGIR conference on Research and development in information retrieval
Ruling Out PTAS for Graph Min-Bisection, Dense k-Subgraph, and Bipartite Clique
SIAM Journal on Computing
Sparse principal component analysis via regularized low rank matrix approximation
Journal of Multivariate Analysis
A constant approximation algorithm for the densest k-subgraph problem on chordal graphs
Information Processing Letters
Optimal Solutions for Sparse Principal Component Analysis
The Journal of Machine Learning Research
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
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
Decoding by linear programming
IEEE Transactions on Information Theory
Consistency of sparse PCA in High Dimension, Low Sample Size contexts
Journal of Multivariate Analysis
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This paper considers the sparse eigenvalue problem, which is to extract dominant (largest) sparse eigenvectors with at most k non-zero components. We propose a simple yet effective solution called truncated power method that can approximately solve the underlying nonconvex optimization problem. A strong sparse recovery result is proved for the truncated power method, and this theory is our key motivation for developing the new algorithm. The proposed method is tested on applications such as sparse principal component analysis and the densest k-subgraph problem. Extensive experiments on several synthetic and real-world data sets demonstrate the competitive empirical performance of our method.