2013 OntheEquivalentofLowRankLinearR

• (Cai et al., 2013) ⇒ Xiao Cai, Chris Ding, Feiping Nie, and Heng Huang. (2013). “On the Equivalent of Low-rank Linear Regressions and Linear Discriminant Analysis based Regressions.” In: Proceedings of the 19th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. ISBN:978-1-4503-2174-7 doi:10.1145/2487575.2487701

Subject Headings:

Cited By

• http://scholar.google.com/scholar?q=%222013%22+On+the+Equivalent+of+Low-rank+Linear+Regressions+and+Linear+Discriminant+Analysis+based+Regressions
• http://dl.acm.org/citation.cfm?id=2487575.2487701&preflayout=flat#citedby

Quotes

Author Keywords

• Learning; linear discriminant analysis; low-rank regression; low-rank ridge regression; sparse low-rank regression

Abstract

The low-rank regression model has been studied and applied to capture the underlying classes / tasks correlation patterns, such that the regression / classification results can be enhanced. In this paper, we will prove that the low-rank regression model is equivalent to doing linear regression in the linear discriminant analysis (LDA) subspace. Our new theory reveals the learning mechanism of low-rank regression, and shows that the low-rank structures exacted from classes / tasks are connected to the LDA projection results. Thus, the low-rank regression efficiently works for the high-dimensional data.

Moreover, we will propose new discriminant low-rank ridge regression and sparse low-rank regression methods. Both of them are equivalent to doing regularized regression in the regularized LDA subspace. These new regularized objectives provide better data mining results than existing low-rank regression in both theoretical and empirical validations. We evaluate our discriminant low-rank regression methods by six benchmark datasets. In all empirical results, our discriminant low-rank models consistently show better results than the corresponding full-rank methods.

References

;

	Author	volume	Date Value	title	type	journal	titleUrl	doi	note	year
2013 OntheEquivalentofLowRankLinearR	Chris Ding Feiping Nie Heng Huang Xiao Cai			On the Equivalent of Low-rank Linear Regressions and Linear Discriminant Analysis based Regressions				10.1145/2487575.2487701		2013