Manifold Regularized Principal Component Analysis Method Using L2,p-Norm
The main idea of principal component analysis (PCA) is to transform the problem of high-dimensional space into low-dimensional space, and obtain the output sample set after a series of operations on the samples. However, the accuracy of the traditional principal component analysis method in dimensio...
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MDPI AG
2022-12-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/23/4603 |
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| author | Minghua Wan Xichen Wang Hai Tan Guowei Yang |
| author_facet | Minghua Wan Xichen Wang Hai Tan Guowei Yang |
| author_sort | Minghua Wan |
| collection | DOAJ |
| description | The main idea of principal component analysis (PCA) is to transform the problem of high-dimensional space into low-dimensional space, and obtain the output sample set after a series of operations on the samples. However, the accuracy of the traditional principal component analysis method in dimension reduction is not very high, and it is very sensitive to outliers. In order to improve the robustness of image recognition to noise and the importance of geometric information in a given data space, this paper proposes a new unsupervised feature extraction model based on <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>l</mi><mrow><mn>2</mn><mo>,</mo><mi>p</mi></mrow></msub></mrow></semantics></math></inline-formula>-norm PCA and manifold learning method. To improve robustness, the model method adopts <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>l</mi><mrow><mn>2</mn><mo>,</mo><mi>p</mi></mrow></msub></mrow></semantics></math></inline-formula>-norm to reconstruct the distance measure between the error and the original input data. When the image is occluded, the projection direction will not significantly deviate from the expected solution of the model, which can minimize the reconstruction error of the data and improve the recognition accuracy. To verify whether the algorithm proposed by the method is robust, the data sets used in this experiment include ORL database, Yale database, FERET database, and PolyU palmprint database. In the experiments of these four databases, the recognition rate of the proposed method is higher than that of other methods when <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>p</mi><mo>=</mo><mn>0.5</mn></mrow></semantics></math></inline-formula>. Finally, the experimental results show that the method proposed in this paper is robust and effective. |
| first_indexed | 2024-03-09T17:40:45Z |
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| language | English |
| last_indexed | 2024-03-09T17:40:45Z |
| publishDate | 2022-12-01 |
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| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-7892e96b320d407689660558c77a569c2023-11-24T11:36:19ZengMDPI AGMathematics2227-73902022-12-011023460310.3390/math10234603Manifold Regularized Principal Component Analysis Method Using L2,p-NormMinghua Wan0Xichen Wang1Hai Tan2Guowei Yang3School of Information Engineering, Nanjing Audit University, Nanjing 211815, ChinaSchool of Information Engineering, Nanjing Audit University, Nanjing 211815, ChinaSchool of Information Engineering, Nanjing Audit University, Nanjing 211815, ChinaSchool of Information Engineering, Nanjing Audit University, Nanjing 211815, ChinaThe main idea of principal component analysis (PCA) is to transform the problem of high-dimensional space into low-dimensional space, and obtain the output sample set after a series of operations on the samples. However, the accuracy of the traditional principal component analysis method in dimension reduction is not very high, and it is very sensitive to outliers. In order to improve the robustness of image recognition to noise and the importance of geometric information in a given data space, this paper proposes a new unsupervised feature extraction model based on <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>l</mi><mrow><mn>2</mn><mo>,</mo><mi>p</mi></mrow></msub></mrow></semantics></math></inline-formula>-norm PCA and manifold learning method. To improve robustness, the model method adopts <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>l</mi><mrow><mn>2</mn><mo>,</mo><mi>p</mi></mrow></msub></mrow></semantics></math></inline-formula>-norm to reconstruct the distance measure between the error and the original input data. When the image is occluded, the projection direction will not significantly deviate from the expected solution of the model, which can minimize the reconstruction error of the data and improve the recognition accuracy. To verify whether the algorithm proposed by the method is robust, the data sets used in this experiment include ORL database, Yale database, FERET database, and PolyU palmprint database. In the experiments of these four databases, the recognition rate of the proposed method is higher than that of other methods when <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>p</mi><mo>=</mo><mn>0.5</mn></mrow></semantics></math></inline-formula>. Finally, the experimental results show that the method proposed in this paper is robust and effective.https://www.mdpi.com/2227-7390/10/23/4603principal component analysismanifold learningfeatures extracting<i>l</i><sub>2,<i>p</i></sub>-normneighborhood preserving embedding |
| spellingShingle | Minghua Wan Xichen Wang Hai Tan Guowei Yang Manifold Regularized Principal Component Analysis Method Using L2,p-Norm Mathematics principal component analysis manifold learning features extracting <i>l</i><sub>2,<i>p</i></sub>-norm neighborhood preserving embedding |
| title | Manifold Regularized Principal Component Analysis Method Using L2,p-Norm |
| title_full | Manifold Regularized Principal Component Analysis Method Using L2,p-Norm |
| title_fullStr | Manifold Regularized Principal Component Analysis Method Using L2,p-Norm |
| title_full_unstemmed | Manifold Regularized Principal Component Analysis Method Using L2,p-Norm |
| title_short | Manifold Regularized Principal Component Analysis Method Using L2,p-Norm |
| title_sort | manifold regularized principal component analysis method using l2 p norm |
| topic | principal component analysis manifold learning features extracting <i>l</i><sub>2,<i>p</i></sub>-norm neighborhood preserving embedding |
| url | https://www.mdpi.com/2227-7390/10/23/4603 |
| work_keys_str_mv | AT minghuawan manifoldregularizedprincipalcomponentanalysismethodusingl2pnorm AT xichenwang manifoldregularizedprincipalcomponentanalysismethodusingl2pnorm AT haitan manifoldregularizedprincipalcomponentanalysismethodusingl2pnorm AT guoweiyang manifoldregularizedprincipalcomponentanalysismethodusingl2pnorm |