Numerical study of learning algorithms on Stiefel manifold

Absil P-A, Mahony R, Sepulchre R (2008) Optimization algorithms on matrix manifolds. Princeton University Press, Princeton

An LTH, Minh LH, Phuc NT, Tao PD (2008) Noisy image segmentation by a robust clustering algorithm based on dc programming and dca. In: Proceedings of the 8th industrial conference on advances in data mining: medical applications, E-commerce, marketing, and theoretical aspects. pp 72–86

Ben-Tal A, El-Ghaoui L, Nemirovski A (2009) Robust optimization. Princeton University Press, Princeton

Bishop CM (2006) Pattern recognition and machine learning. Springer, New York

Boyd S, Parikh N, Chu E, Peleato B, Eckstein J (2011) Distributed optimization and statistical learning via the alternating direction method of multipliers. Found Trends Mach Learn 3(1):1–124

Boyd S, Vandenberghe L (2004) Convex optimization. Cambridge University Press, New York

Caramanis C, Mannor S, Xu H (2011) Robust optimization in machine learning. In: Nowozin S, Sra S, Wright S (eds) Optimization for machine learning. MIT press, Cambridge

Demmel JW (1997) Applied numerical linear algebra. Soc Ind Appl Math

Edelman A, Arias TA, Smith ST (1998) The geometry of algorithms with orthogonality constraints. SIAM J Matrix Anal Appl 20(2):303–353

Hastie T, Tibishirani R, Friedman J (2001) The elements of statistical learning. Springer, New York

Kanamori T, Suzuki T, Sugiyama M (2012) Statistical analysis of kernel-based least-squares density-ratio estimation. Mach Learn 86(3):335–367

Krause A, Guestrin C (2008) Beyond convexity: submodularity in machine learning. http://www.select.cs.cmu.edu/tutorials/icml08submodularity.html

Luenberger D, Ye Y (2008) Linear and nonlinear programming. Springer, Berlin

Nishimori Y, Akaho S (2005) Learning algorithms utilizing quasi-geodesic flows on the Stiefel manifold. Neurocomputing 67:106–135

Perez-Cruz F, Weston J, Hermann DJL, Schölkopf B (2003) Extension of the $$\nu $$ ν -SVM range for classification. In: Suykens JAK, Horvath G, Basu S, Micchelli C, Vandewalle J (eds) Advances inlearning theory: methods, models and applications, vol 190. IOS Press, Amsterdam, pp 179–196

R Development Core Team (2012) R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna. ISBN 3-900051-07-0

Schölkopf B, Smola AJ (2002) Learning with Kernels. MIT Press, Cambridge

Sra S, Nowozin S, Wright SJ (eds) (2011) Optimization for machine learning. MIT Press, Cambridge

Sugiyama M, Suzuki T, Kanamori T (2012) Density ratio estimation in machine learning. Cambridge University Press, Cambridge

Sugiyama M, Yamada M, von Bünau P, Suzuki T, Kanamori T, Kawanabe M (2011) Direct density-ratio estimation with dimensionality reduction via least-squares hetero-distributional subspace search. Neural Netw 24(2):183–198

Takeda A, Mitsugi H, Kanamori T (2012) A unified robust classification model. In: Proceedings of 29th international conference on machine learning (ICML2012). (in press)

Xanthopoulos P, Pardalos PM, Trafalis TB (2012) Robust Data Mining. In: Springer briefs in optimization. Springer, Berlin

Zhang Y (2010) Recent advances in alternating direction methods: theory and practice. IPAM workshop: numerical methods for continuous optimization. UCLA. Los Angeles, California, Oct 2010

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