Sparse PCA on fixed-rank matrices

Asteris, M., Papailiopoulos, D., Karystinos, G.: Sparse principal component of a rank-deficient matrix. In: Proceedings of ISIT (2011)

Asteris, M., Papailiopoulos, D., Karystinos, G.: The sparse principal component of a constant-rank matrix. IEEE Trans. Inf. Theor. 60(4), 2281–2290 (2014)

Asteris, M., Papailiopoulos, D., Kyrillidis, A., Dimakis, A.: Sparse PCA via bipartite matchings. In: Proceedings of NIPS (2015)

Berk, L., Bertsimas, D.: Certifiably optimal sparse principal component analysis. Math. Progr. Comput. 11, 381–420 (2019)

Bertsimas, D., Tsitsiklis, J.: Introduction to Linear Optimization. Athena Scientific, Belmont (1997)

Boutsidis, C., Drineas, P., Magdon-Ismail, M.: Sparse features for PCA-like linear regression. In: Proceedings of NIPS, pp. 2285–2293 (2011)

Cadima, J., Jolliffe, I.: Loading and correlations in the interpretation of principle compenents. J. Appl. Stat. 22(2), 203–214 (1995)

Chan, S., Papailiopoulos, D., Rubinstein, A.: On the worst-case approximability of sparse PCA. Proceedings of COLT (2016)

d’Aspremont, A., Bach, F., Ghaoui, L.: Optimal solutions for sparse principal component analysis. J. Mach. Learning Res. 9, 1269–1294 (2008)

d’Aspremont, A., Bach, F., Ghaoui, L.: Approximation bounds for sparse principal component analysis. Mathematical Programming Series . 148(1), pp. 89–110

d’Aspremont, A., El Ghaoui, L., Jordan, M., Lanckriet, G.: A direct formulation for sparse PCA using semidefinite programming. SIAM Rev. 49(3), 434–448 (2007)

Dey, S., Mazumder, R., Wang, G.: A convex integer programming approach for optimal sparse PCA. arXiv preprint arXiv:1810.09062 (2018)

Edelsbrunner, H., O’Rourke, J., Seidel, R.: Constructing arrangements of lines and hyperplanes with applications. SIAM J. Comput. 15(2), 341–363 (1986)

Goldberg, A., Tarjan, R.: Finding minimum-cost circulations by canceling negative cycles. In: Proceedings of STOC, pp. 388–397 (1988)

Goldberg, A., Tarjan, R.: Finding minimum-cost circulations by canceling negative cycles. J. Assoc. Comput. Mach. 36, 873–886 (1989)

Hastie, T., Tibshirani, R., Wainwright, M.: Stat. learning Sparsity. CRC Press, Boca Raton (2015)

He, Y., Monteiro, R., Park, H.: An efficient algorithm for rank-1 sparse PCA. In: working paper (2010)

Jolliffe, I., Trendafilov, N., Uddin, M.: A modified principal component technique based on the lasso. J. Comput. Graph. Stat. 12(3), 531–547 (2003)

Journée, M., Nesterov, Y., Richtárik, P., Sepulchre, R.: Generalized power method for sparse principal component analysis. J. Mach. Learn. Res. 11, 517–553 (2010)

Karystinos, G., Liavas, A.: Efficient computation of the binary vector that maximizes a rank-deficient quadratic form. IEEE Trans. Inf. Theor. 56(7), 3581–3593 (2010)

Karystinos, G., Pados, D.: Rank-2-optimal adaptive design of binary spreading codes. IEEE Trans. Inf. Theor. 53(9), 3075–3080 (2007)

Mackenthun, K.: A fast algorithm for multiple-symbol differential detection of MPSK. IEEE Trans. Commun. 42(234), 1471–1474 (1994)

Mackey, L.: Deflation methods for sparse PCA. In: Proceedings of NIPS, vol. 21, pp. 1017–1024 (2009)

Magdon-Ismail, M.: NP-hardness and inapproximability of sparse PCA. Inf. Process. Lett. 126, 35–38 (2017)

Moghaddam, B., Weiss, Y., Avidan, S.: Spectral bounds for sparse PCA: exact and greedy algorithms. In: Proceedings of NIPS, vol. 18, p. 915 (2006)

Motedayen, I., Krishnamoorthy, A., Anastasopoulos, A.: Optimal joint detection/estimation in fading channels with polynomial complexity. IEEE Trans. Inf. Theor. 53(1), 209–223 (2007)

Papailiopoulos, D., Dimakis, A., Korokythakis, S.: Sparse PCA through low-rank approximations. In: Proceedings of ICML (2013)

Schrijver, A.: Combinatorial Optimization . Polyhedra and Efficiency. Springer-Verlag, Berlin (2003)

Shalev-Shwartz, S., Ben-David, S.: Understanding Machine Learning. Cambridge University Press, Cambridge (2014)

Sigg, C., Buhmann, J.: Expectation-maximization for sparse and non-negative PCA. In: Proceedings of ICML, pp. 960–967 (2008)

Sweldens, W.: Fast block noncoherent decoding. IEEE Commun. Lett. 5(4), 132–134 (2001)

Vu, V., Lei, J.: Minimax rates of estimation for sparse PCA in high dimensions. In: Proceedings of AIStats, pp. 1278–1286 (2012)

Yuan, X., Zhang, T.: Truncated power method for sparse eigenvalue problems. J. Mach. Learn. Res. 14, 899–925 (2013)

Zhang, Y., d’Aspremont, A., Ghaoui, L.E.: Sparse PCA: convex relaxations, algorithms and applications. In: Anjos, M., Lasserre, J. (eds.) Handbook on Semidefinite, Conic and Polynomial Optimization. International Series in Operations Research & Management Science, vol. 166, pp. 915–940. Springer, Boston, MA (2011). https://doi.org/10.1007/978-1-4614-0769-0_31

Zou, H., Hastie, T., Tibshirani, R.: Sparse principal component analysis. J. Comput. Graph. Stat. 15(2), 265–286 (2006)