Abstract
This chapter provides an introduction to our main contributions concerning the development of the novel methods of CoCoSSC.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
S. Boyd, N. Parikh, E. Chu, B. Peleato, J. Eckstein, Distributed optimization and statistical learning via the alternating direction method of multipliers. Found. Trends Mach. Learn. 3(1), 1–122 (2011)
C.M. Carvalho, M.S. Johannes, H.F. Lopes, N.G. Polson, Particle learning and smoothing. Stat. Sci. 25, 88–106 (2010)
Z. Charles, A. Jalali, R. Willett, Sparse subspace clustering with missing and corrupted data. arXiv preprint: arXiv:1707.02461 (2017)
E.J. Candes, T. Tao, Decoding by linear programming. IEEE Trans. Inf. Theory 51(12), 4203–4215 (2005)
E. Candes, T. Tao, The Dantzig selector: statistical estimation when p is much larger than n. Ann. Stat. 35(6), 2313–2351 (2007)
A. Datta, H. Zou, Cocolasso for high-dimensional error-in-variables regression. Ann. Stat. 45(6), 2400–2426 (2017)
P. Hartman, The stable manifold of a point of a hyperbolic map of a banach space. J. Differ. Equ. 9(2), 360–379 (1971)
J.D. Lee, I. Panageas, G. Piliouras, M. Simchowitz, M.I. Jordan, B. Recht, First-order methods almost always avoid saddle points. arXiv preprint arXiv:1710.07406 (2017)
J.D. Lee, M. Simchowitz, M.I. Jordan, B. Recht, Gradient descent only converges to minimizers, in Conference on Learning Theory (2016), pp. 1246–1257
Y. Nesterov, Introductory Lectures on Convex Optimization: A Basic Course, vol. 87 (Springer, Berlin, 2013)
M. O’Neill, S.J. Wright, Behavior of accelerated gradient methods near critical points of nonconvex problems. arXiv preprint arXiv:1706.07993 (2017)
I. Panageas, G. Piliouras, Gradient descent only converges to minimizers: non-isolated critical points and invariant regions. arXiv preprint arXiv:1605.00405 (2016)
C. Qu, H. Xu, Subspace clustering with irrelevant features via robust dantzig selector, in Advances in Neural Information Processing Systems (2015), pp. 757–765
M. Soltanolkotabi, E. Elhamifar, E.J. Candes, Robust subspace clustering. Ann. Stat. 42(2), 669–699 (2014)
Y. Shen, B. Han, E. Braverman, Stability of the elastic net estimator. J. Complexity 32(1), 20–39 (2016)
M. Shub, Global Stability of Dynamical Systems (Springer, Berlin, 2013)
M.C. Tsakiris, R. Vidal, Theoretical analysis of sparse subspace clustering with missing entries. arXiv preprint arXiv:1801.00393 (2018)
Y.-X. Wang, H. Xu, Noisy sparse subspace clustering. J. Mach. Learn. Res. 17(12), 1–41 (2016)
H. Zou, T. Hastie, Regularization and variable selection via the elastic net. J. R. Stat. Soc. Ser. B Stat Methodol. 67(2), 301–320 (2005)
C. Zeng, Q. Wang, W. Wang, T. Li, L. Shwartz, Online inference for time-varying temporal dependency discovery from time series, in 2016 IEEE International Conference on Big Data (Big Data) (IEEE, Piscataway, 2016), pp. 1281–1290
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Shi, B., Iyengar, S.S. (2020). Development of Novel Techniques of CoCoSSC Method. In: Mathematical Theories of Machine Learning - Theory and Applications. Springer, Cham. https://doi.org/10.1007/978-3-030-17076-9_4
Download citation
DOI: https://doi.org/10.1007/978-3-030-17076-9_4
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-17075-2
Online ISBN: 978-3-030-17076-9
eBook Packages: EngineeringEngineering (R0)