2013 OntheEquivalentofLowRankLinearR

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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

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 AuthorvolumeDate ValuetitletypejournaltitleUrldoinoteyear
2013 OntheEquivalentofLowRankLinearRXiao Cai
Chris Ding
Feiping Nie
Heng Huang
On the Equivalent of Low-rank Linear Regressions and Linear Discriminant Analysis based Regressions10.1145/2487575.24877012013
AuthorXiao Cai +, Chris Ding +, Feiping Nie + and Heng Huang +
doi10.1145/2487575.2487701 +
proceedingsProceedings of the 19th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining +
titleOn the Equivalent of Low-rank Linear Regressions and Linear Discriminant Analysis based Regressions +
year2013 +