Color Two-Dimensional Principal Component Analysis for Face Recognition Based on Quaternion Model

Jia, Zhigang; Ling, Sitao; Zhao, Mi

doi:10.1007/978-3-319-63309-1_17

Cited by 25 publications

(37 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It is obvious that the optimal problem of the row directional 2D-QPCA (R2D-QPCA) proposed in [13] is a special case of (II.7) with fixing U = I m . In this case, we only need to compute the eigenvalue problem of E 2 for solving (II.7) with fixing U = I m .…”

Section: D-qpcamentioning

confidence: 99%

“…Once the samples are represented by matrices instead of vectors, the two-dimensional PCA (2DPCA) [40] are in need to extract the spatial information and more essential features which can improve the performance of compressed samples, see 2DPCANet [44] for example. To implicitly utilize the cross-channel correlation and spatial structure of color images, the two-dimensional quaternion principal component analysis (2D-QPCA) in one direction was proposed to extract features of color image samples under quaternion representations in [13] (column direction) and [38] (row direction). In this paper, we present the improved 2D-QPCA with perfections in three aspects: abstracting the features of quaternion…”

Section: Introductionmentioning

confidence: 99%

“…Many quaternion-based methods, such as the quaternion PCA (QPCA) [3], the two-dimensional QPCA (2DQPCA), the bidirectional 2DQPCA [29], the kernel QPCA (KQPCA) and the two-dimensional KQPCA [5], have been proposed for color image processing, with generalizing the conventional PCA and 2DPCA [40]. Recently, Jia et al [13] proposed the 2D-QPCA approach based on quaternion models with reducing the feature dimension in row direction, which is a generalization of the 2DPCA method proposed by Yang et al [40]. Xiao and Zhou [38] proposed novel quaternion ridge regression models for 2D-QPCA with reducing the feature dimension in column direction and two-dimensional quaternion sparse principle component analysis.…”

Section: Introductionmentioning

confidence: 99%

“…With retaining the advantages of 2DPCA, 2D-QPCA recently proposed in [13] is based on quaternion matrices rather than quaternion vectors, and hence can fully utilize color information and the spatial structure of face images. In this method, the generated covariance matrix is Hermitian and low-dimensional.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Improved Two-Dimensional Quaternion Principal Component Analysis

2019

View full text Add to dashboard Cite

The two-dimensional quaternion principal component analysis (2D-QPCA) is first improved into abstracting the features of quaternion matrix samples in both row and column directions, being the generalization ability, and with the components weighted by corresponding eigenvalues. The main components of the 2D-QPCA in row and column directions are defined as the solution of one optimal problem with orthogonality constraints on two variables. In advance, 2D-QPCA is innovatively armed with the generalization ability by applying the label information (if known) to generate the weight of each class of training set. With such generalization ability, 2D-QPCA may enlarge the variance of all projections of known and unknown samples. Different from the well-known PCA-like methods, the improved 2D-QPCA prefers to the components that have larger variances of projected samples and weight them with larger factors. The improved versions of 2D-QPCA are applied to the color face recognition and image reconstruction. The numerical results based on the real face data sets validate that the newly proposed method performs better than the state-of-the-art ones.

show abstract

Section: D-qpcamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Improved Two-Dimensional Quaternion Principal Component Analysis

2019

View full text Add to dashboard Cite

show abstract

“…To directly deal with three channels of color image, the quaternion with zero real part was used to represent the color pixel consisting of three components [25]- [34]. Based on quaternion matrix theory, Jia et al [35] presented the color two-dimensional principal component analysis (2D-QPCA) method for color face recognition. With the aid of twodimensional quaternion matrices rather than one-dimensional quaternion vectors, 2D-QPCA utilizes the color information and the spatial characteristics simultaneously and mathematically.…”

Section: Introductionmentioning

confidence: 99%

F-2D-QPCA: A Quaternion Principal Component Analysis Method for Color Face Recognition

et al. 2020

View full text Add to dashboard Cite

Two-dimensional quaternion principal component analysis (2D-QPCA) is one of the successful dimensionality reduction methods for color face recognition. However, 2D-QPCA is sensitive to outliers. For solving this shortcoming, an efficient robust method(F-2D-QPCA) is presented by means of Frobenius norm(F-norm). The goal of F-2D-QPCA is to find the projection matrix such that the projected data has the maximum variance based on F-norm, and it is more robust to outliers and has higher recognition accuracy than other methods, such as 2D-QPCA,R 1-2-DPCA, F-norm 2DPCA and 2D-PCA, etc. Also, we study in detail a quaternion optimization problem, propose a nongreedy iterative algorithm and prove its convergence. Experiments on several color face databases illustrate the superiority of our proposed method.

show abstract

Relaxed 2-D Principal Component Analysis by Lp Norm for Face Recognition

Chen

Jia

Cai

et al. 2019

Intelligent Computing Theories and Application

View full text Add to dashboard Cite

A relaxed two dimensional principal component analysis (R2DPCA) approach is proposed for face recognition. Different to the 2DPCA, 2DPCA-L1 and G2DPCA, the R2DPCA utilizes the label information (if known) of training samples to calculate a relaxation vector and presents a weight to each subset of training data. A new relaxed scatter matrix is defined and the computed projection axes are able to increase the accuracy of face recognition. The optimal Lp-norms are selected in a reasonable range. Numerical experiments on practical face databased indicate that the R2DPCA has high generalization ability and can achieve a higher recognition rate than state-of-the-art methods.

show abstract

Color Two-Dimensional Principal Component Analysis for Face Recognition Based on Quaternion Model

Cited by 25 publications

References 17 publications

Improved Two-Dimensional Quaternion Principal Component Analysis

Improved Two-Dimensional Quaternion Principal Component Analysis

F-2D-QPCA: A Quaternion Principal Component Analysis Method for Color Face Recognition

Relaxed 2-D Principal Component Analysis by Lp Norm for Face Recognition

Contact Info

Product

Resources

About