Sparse quadratic classification rules via linear dimension reduction

Gaynanova, Irina; Wang, Tianying

doi:10.1016/j.jmva.2018.09.011

Cited by 13 publications

(7 citation statements)

References 46 publications

(113 reference statements)

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“…In the conventional classification problem where m 0 " 1, a special case of the proposed CLIPS classifier becomes a new sparse quadratic discriminant analysis (QDA) method (cf. Fan et al, 2015Li and Shao, 2015;Jiang et al, 2018;Qin, 2018;Zou, 2019;Gaynanova and Wang, 2019;Cai and Zhang, 2019;Pan and Mai, 2020). As a byproduct of our theoretical study, we show that the new QDA method enjoys better theoretical properties compared to some of the state-of-the-art sparse QDA methods such as Fan et al (2015).…”

Section: Introductionsupporting

confidence: 54%

Covariance-engaged Classification of Sets via Linear Programming

Ren¹,

Jung²,

Qiao³

2022

STAT SINICA

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Section: Introductionsupporting

confidence: 54%

Covariance-engaged Classification of Sets via Linear Programming

Ren¹,

Jung²,

Qiao³

2022

STAT SINICA

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“…In this section, we compare our method, Algorithm 1 (QDAP), with LDA, DSDA (Clemmensen et al, 2011), QDA, DAP (Gaynanova & Wang, 2019), and RDA (Guo et al, 2007) by both simulated and real data examples. Besides the classical methods LDA and QDA, RDA is a well known regularization approach which works well for moderate and high dimensional data.…”

Section: Methods For Comparisonmentioning

confidence: 99%

“…A majority of these works are based on various sparsity assumptions. See Mai (2013) for a review and Gaynanova & Wang (2019) for recent progresses. In contrast, we do not impose sparsity assumptions and our method shares invariance property with the classical LDA and QDA methods.…”

Section: Introductionmentioning

confidence: 99%

Quadratic Discriminant Analysis by Projection

Wu¹,

Hao²

2021

Preprint

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Discriminant analysis, including linear discriminant analysis (LDA) and quadratic discriminant analysis (QDA), is a popular approach to classification problems. It is well known that LDA is suboptimal to analyze heteroscedastic data, for which QDA would be an ideal tool. However, QDA is less helpful when the number of features in a data set is moderate or high, and LDA and its variants often perform better due to their robustness against dimensionality. In this work, we introduce a new dimension reduction and classification method based on QDA. In particular, we define and estimate the optimal one-dimensional (1D) subspace for QDA, which is a novel hybrid approach to discriminant analysis. The new method can handle data heteroscedasticity with number of parameters equal to that of LDA. Therefore, it is more stable than the standard QDA and works well for data in moderate dimensions. We show an estimation consistency property of our method, and compare it with LDA, QDA, regularized discriminant analysis (RDA) and a few other competitors by simulated and real data examples.

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“…Then the same formulation as (8), with Γ replaced by Γ, follows. Alternatively, we can consider the two-dimensional projection approach for quadratic discriminant analysis proposed by Gaynanova and Wang (2019) in the multivariate setting. In our functional framework, we would optimize the following two objective functions…”

Section: Properties Of the Regularized Classifier In The Population Modelmentioning

confidence: 99%

Sparse functional linear discriminant analysis

2021

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Functional linear discriminant analysis offers a simple yet efficient method for classification, with the possibility of achieving a perfect classification. Several methods are proposed in the literature that mostly address the dimensionality of the problem. On the other hand, there is a growing interest in interpretability of the analysis, which favors a simple and sparse solution. In this work, we propose a new approach that incorporates a type of sparsity that identifies nonzero sub-domains in the functional setting, offering a solution that is easier to interpret without compromising performance. With the need to embed additional constraints in the solution, we reformulate the functional linear discriminant analysis as a regularization problem with an appropriate penalty. Inspired by the success of ℓ1-type regularization at inducing zero coefficients for scalar variables, we develop a new regularization method for functional linear discriminant analysis that incorporates an L1-type penalty, ∫ |f|, to induce zero regions. We demonstrate that our formulation has a well-defined solution that contains zero regions, achieving a functional sparsity in the sense of domain selection. In addition, the misclassification probability of the regularized solution is shown to converge to the Bayes error if the data are Gaussian. Our method does not presume that the underlying function has zero regions in the domain, but produces a sparse estimator that consistently estimates the true function whether or not the latter is sparse. Numerical comparisons with existing methods demonstrate this property in finite samples with both simulated and real data examples.

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Sparse quadratic classification rules via linear dimension reduction

Cited by 13 publications

References 46 publications

Covariance-engaged Classification of Sets via Linear Programming

Covariance-engaged Classification of Sets via Linear Programming

Quadratic Discriminant Analysis by Projection

Sparse functional linear discriminant analysis

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