Linear Regression Classification in the Quaternion and Reduced Biquaternion Domains

El-Melegy, Moumen T.; Kamal, Aliaa T.

doi:10.1109/lsp.2022.3140682

Cited by 11 publications

(9 citation statements)

References 18 publications

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“…In this section, the proposed methods are evaluated on two color face recognition benchmark databases: the GATech database [24] and the FERET database [25]. We compare the proposed CbPCR, Q-CbPCR, and RB-CbPCR methods with LRC [1], the quaternion-based QLRC method [9,12], the RB-based RBLRC method [12], IPCRC [2,3], and the CLRC method [5]. Note that LRC, IPCRC and CbPCR work on grayscale images, while the other methods operate on color images.…”

Section: Methodsmentioning

confidence: 99%

“…where ̈ is the mean of the l-th class, and ̈ represents the eigenvectors of the RB scatter matrix ̈ ̈ corresponding to the t largest eigenvalues in terms of the RB norm as obtained via our efficient RBbased PCA algorithm [8]. By Lemma 2 in [12], it can be proved that ( 20) is equivalent to:…”

Section: Reduced Biquaternion-based Cbpcrmentioning

confidence: 99%

“…To that end, we exploit an efficient algorithm we derive in [8] for computing the principal components (eigenvectors) of an RB matrix by casting it into an x + y selection problem [14,15]. In our experimental results on public benchmark databases for color face recognition, we demonstrate the better performances of the new quaternion and RB-based CbPCR algorithms over existing and competing ones [5,9,12].…”

Section: Introductionmentioning

confidence: 98%

“…Some methods (e.g., [5]) apply LRC to every color channel separately, then select the class having the smallest total prediction error over all color channels. Unlike all those methods, several studies [6]- [12], have suggested the use of 4D hypercomplex numbers to represent color images. This depends on treating the color components of each image pixel as one entity thus considering the correlation between color components.…”

Section: Introductionmentioning

confidence: 99%

“…QLRC relies on converting the quaternion quantities to real ones to circumvent using quaternion derivatives. In our recent paper [12], we develop closed-form solutions of QLRC from the principles of quaternion calculus. In addition, we propose new solutions based on reduced biquaternions (RBs), which represent another hypercomplex space with 3 imaginary components and one real.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Face Recognition by Principal Component Regression using Hypercomplex Numbers

Kamal

El-Melegy

ElHawary

et al. 2022

Assiut University Journal of Multidisciplinary Scientific Resea

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In this paper, we propose a classification by principal component regression (CbPCR) strategy, which depends on performing regression of each data class in terms of its principal components. This CbPCR formulation leads to a novel formulation of the Linear Regression Classification (LRC) problem that keeps the key information of the data classes while providing more compact closed-form solutions. We also extend this strategy to the 4D hypercomplex domains to take into account the color information of the image. Our experiments on two color face recognition benchmark databases prove the efficacy of the proposed strategy.

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Section: Methodsmentioning

confidence: 99%

Section: Reduced Biquaternion-based Cbpcrmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Face Recognition by Principal Component Regression using Hypercomplex Numbers

Kamal

El-Melegy

ElHawary

et al. 2022

Assiut University Journal of Multidisciplinary Scientific Resea

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Three minimal norm Hermitian solutions of the reduced biquaternion matrix equation EM+M˜F=G$$ EM+\tilde{M}F=G $$

Han,

Song

2024

Math Methods in App Sciences

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In this paper, we investigate the minimal norm Hermitian solution, pure imaginary Hermitian solution and pure real Hermitian solution of the reduced biquaternion matrix equation. We introduce the new real representation of the reduced biquaternion matrix and the special properties of . We present the sufficient and necessary conditions of three solutions and the corresponding numerical algorithms for solving the three solutions. Finally, we show that our method is better than the complex representation method in terms of error and CPU time in numerical examples.

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Classification by Principal Component Regression in the Real and Hypercomplex Domains

et al. 2022

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Linear regression is a simple and widely used machine learning algorithm. It is a statistical approach for modeling the relationship between a scalar variable and one or more variables. In this paper, a classification by principal component regression (CbPCR) strategy is proposed. This strategy depends on performing regression of each data class in terms of its principal components. This CbPCR formulation leads to a new formulation of the Linear Regression Classification (LRC) problem that preserves the key information of the data classes while providing more compact closed-form solutions. For the sake of image classification, this strategy is also extended to the 4D hypercomplex domains to take into account the color information of the image. Quaternion and reduced biquaternion CbPCR strategies are proposed by representing each channel of the color image as one of the imaginary parts of a quaternion or reduced biquaternion number. Experiments on two color face recognition benchmark databases show that the proposed methods achieve better accuracies by a margin of about 3% over the original LRC and like methods.

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Linear Regression Classification in the Quaternion and Reduced Biquaternion Domains

Cited by 11 publications

References 18 publications

Face Recognition by Principal Component Regression using Hypercomplex Numbers

Face Recognition by Principal Component Regression using Hypercomplex Numbers

Three minimal norm Hermitian solutions of the reduced biquaternion matrix equation EM+M˜F=G$$ EM+\tilde{M}F=G $$

Classification by Principal Component Regression in the Real and Hypercomplex Domains

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