Robust Locality Preserving Projections With Cosine-Based Dissimilarity for Linear Dimensionality Reduction
Locality preserving projection (LPP) is a classical tool for dimensionality reduction problems. However, it is sensitive to outliers because of utilizing the ℓ<sub>2</sub>-norm-based distance criterion. In this paper, we propose a new approach, termed Euler-LPP, by preserving...
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| Format: | Article |
| Language: | English |
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IEEE
2017-01-01
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| Series: | IEEE Access |
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| Online Access: | https://ieeexplore.ieee.org/document/7604144/ |
| _version_ | 1818329600004980736 |
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| author | Qiang Yu Rong Wang Bing Nan Li Xiaojun Yang Minli Yao |
| author_facet | Qiang Yu Rong Wang Bing Nan Li Xiaojun Yang Minli Yao |
| author_sort | Qiang Yu |
| collection | DOAJ |
| description | Locality preserving projection (LPP) is a classical tool for dimensionality reduction problems. However, it is sensitive to outliers because of utilizing the ℓ<sub>2</sub>-norm-based distance criterion. In this paper, we propose a new approach, termed Euler-LPP, by preserving the local structures of data under the distance criterion of the cosine-based dissimilarity. Euler-LPP is robust to outliers in that the cosine-based dissimilarity suppresses the influence of outliers more efficiently than the ℓ<sub>2</sub> -norm. An explicit mapping, defined by a complex kernel (euler kernel) is adopted to map the data from the input space to complex reproducing kernel Hilbert spaces (CRKHSs), in which the distance of the data pairs under the ℓ<sub>2</sub>-norm is equal to that in the input space under the cosine-based dissimilarity. Thus, the robust dimensionality problem can be directly solved in CRKHS, where the solution is guaranteed to converge to a global minimum. In addition, Euler-LPP is easy to implement without significantly increasing computational complexity. Experiment results on several benchmark databases confirm the effectiveness of the proposed method. |
| first_indexed | 2024-12-13T12:50:38Z |
| format | Article |
| id | doaj.art-8bdb66f26ad64e32808fe14205468f2f |
| institution | Directory Open Access Journal |
| issn | 2169-3536 |
| language | English |
| last_indexed | 2024-12-13T12:50:38Z |
| publishDate | 2017-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj.art-8bdb66f26ad64e32808fe14205468f2f2022-12-21T23:45:20ZengIEEEIEEE Access2169-35362017-01-0152676268410.1109/ACCESS.2016.26165847604144Robust Locality Preserving Projections With Cosine-Based Dissimilarity for Linear Dimensionality ReductionQiang Yu0Rong Wang1https://orcid.org/0000-0001-9240-6726Bing Nan Li2Xiaojun Yang3Minli Yao4Xi’an Research Institute of Hi-Tech, Xi’an, ChinaXi’an Research Institute of Hi-Tech, Xi’an, ChinaHefei University of Technology, Hefei, ChinaXi’an Research Institute of Hi-Tech, Xi’an, ChinaXi’an Research Institute of Hi-Tech, Xi’an, ChinaLocality preserving projection (LPP) is a classical tool for dimensionality reduction problems. However, it is sensitive to outliers because of utilizing the ℓ<sub>2</sub>-norm-based distance criterion. In this paper, we propose a new approach, termed Euler-LPP, by preserving the local structures of data under the distance criterion of the cosine-based dissimilarity. Euler-LPP is robust to outliers in that the cosine-based dissimilarity suppresses the influence of outliers more efficiently than the ℓ<sub>2</sub> -norm. An explicit mapping, defined by a complex kernel (euler kernel) is adopted to map the data from the input space to complex reproducing kernel Hilbert spaces (CRKHSs), in which the distance of the data pairs under the ℓ<sub>2</sub>-norm is equal to that in the input space under the cosine-based dissimilarity. Thus, the robust dimensionality problem can be directly solved in CRKHS, where the solution is guaranteed to converge to a global minimum. In addition, Euler-LPP is easy to implement without significantly increasing computational complexity. Experiment results on several benchmark databases confirm the effectiveness of the proposed method.https://ieeexplore.ieee.org/document/7604144/Locality preserving projections (LPP)complex kerneldimensionality reductionrobusteuler mapping |
| spellingShingle | Qiang Yu Rong Wang Bing Nan Li Xiaojun Yang Minli Yao Robust Locality Preserving Projections With Cosine-Based Dissimilarity for Linear Dimensionality Reduction IEEE Access Locality preserving projections (LPP) complex kernel dimensionality reduction robust euler mapping |
| title | Robust Locality Preserving Projections With Cosine-Based Dissimilarity for Linear Dimensionality Reduction |
| title_full | Robust Locality Preserving Projections With Cosine-Based Dissimilarity for Linear Dimensionality Reduction |
| title_fullStr | Robust Locality Preserving Projections With Cosine-Based Dissimilarity for Linear Dimensionality Reduction |
| title_full_unstemmed | Robust Locality Preserving Projections With Cosine-Based Dissimilarity for Linear Dimensionality Reduction |
| title_short | Robust Locality Preserving Projections With Cosine-Based Dissimilarity for Linear Dimensionality Reduction |
| title_sort | robust locality preserving projections with cosine based dissimilarity for linear dimensionality reduction |
| topic | Locality preserving projections (LPP) complex kernel dimensionality reduction robust euler mapping |
| url | https://ieeexplore.ieee.org/document/7604144/ |
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