<italic>l</italic><sub>2,<italic>p</italic></sub>-Norm Based Discriminant Subspace Clustering Algorithm
Discriminative subspace clustering (DSC) combines Linear Discriminant Analysis (LDA) with clustering algorithm, such as K-means (KM), to form a single framework to perform dimension reduction and clustering simultaneously. It has been verified to be effective for high-dimensional data. However, most...
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| Format: | Article |
| Language: | English |
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IEEE
2020-01-01
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| Series: | IEEE Access |
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| Online Access: | https://ieeexplore.ieee.org/document/9072148/ |
| _version_ | 1818616667971780608 |
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| author | Xiaobin Zhi Longtao Bi Jiulun Fan |
| author_facet | Xiaobin Zhi Longtao Bi Jiulun Fan |
| author_sort | Xiaobin Zhi |
| collection | DOAJ |
| description | Discriminative subspace clustering (DSC) combines Linear Discriminant Analysis (LDA) with clustering algorithm, such as K-means (KM), to form a single framework to perform dimension reduction and clustering simultaneously. It has been verified to be effective for high-dimensional data. However, most existing DSC algorithms rigidly use the Frobenius norm (F-norm) to define model that may not always suitable for the given data. In this paper, DSC is extended in the sense of I<sub>2,p</sub>-norm, which is a general form of the F-norm, to obtain a family of DSC algorithms which provide more alternative models for practical applications. In order to achieve this goal. Firstly, an efficient algorithm for the I<sub>p</sub>-norm based KM (KM<sub>p</sub>) clustering is proposed. Then, based on the equivalence of LDA and linear regression, a I<sub>2,p</sub>-norm based LDA (I<sub>2,p</sub>-LDA) is proposed, and an efficient Iteratively Reweighted Least Squares algorithm for I<sub>2,p</sub>-LDA is presented. Finally, KMp and I<sub>2,p</sub>-LDA are combined into a single framework to form an efficient generalized DSC algorithm: I<sub>2,p</sub>-norm based DSC clustering (I<sub>2,p</sub>-DSC). In addition, the effects of the parameters on the proposed algorithm are analyzed, and based on the theory of robust statistics, a special case of I<sub>2,p</sub>-DSC, which can show better robustness on the data sets with noise and outlier, is studied. Extensive experiments are performed to verify the effectiveness of our proposed algorithm. |
| first_indexed | 2024-12-16T16:53:27Z |
| format | Article |
| id | doaj.art-0efd9a2dc48847a09ab0af4285831fbf |
| institution | Directory Open Access Journal |
| issn | 2169-3536 |
| language | English |
| last_indexed | 2024-12-16T16:53:27Z |
| publishDate | 2020-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj.art-0efd9a2dc48847a09ab0af4285831fbf2022-12-21T22:23:57ZengIEEEIEEE Access2169-35362020-01-018760437605510.1109/ACCESS.2020.29888219072148<italic>l</italic><sub>2,<italic>p</italic></sub>-Norm Based Discriminant Subspace Clustering AlgorithmXiaobin Zhi0https://orcid.org/0000-0001-7396-5928Longtao Bi1Jiulun Fan2https://orcid.org/0000-0002-7553-204XSchool of Science, Xi’an University of Posts and Telecommunications, Xi’an, ChinaSchool of Communications and Information Engineering, Xi’an University of Posts and Telecommunications, Xi’an, ChinaSchool of Communications and Information Engineering, Xi’an University of Posts and Telecommunications, Xi’an, ChinaDiscriminative subspace clustering (DSC) combines Linear Discriminant Analysis (LDA) with clustering algorithm, such as K-means (KM), to form a single framework to perform dimension reduction and clustering simultaneously. It has been verified to be effective for high-dimensional data. However, most existing DSC algorithms rigidly use the Frobenius norm (F-norm) to define model that may not always suitable for the given data. In this paper, DSC is extended in the sense of I<sub>2,p</sub>-norm, which is a general form of the F-norm, to obtain a family of DSC algorithms which provide more alternative models for practical applications. In order to achieve this goal. Firstly, an efficient algorithm for the I<sub>p</sub>-norm based KM (KM<sub>p</sub>) clustering is proposed. Then, based on the equivalence of LDA and linear regression, a I<sub>2,p</sub>-norm based LDA (I<sub>2,p</sub>-LDA) is proposed, and an efficient Iteratively Reweighted Least Squares algorithm for I<sub>2,p</sub>-LDA is presented. Finally, KMp and I<sub>2,p</sub>-LDA are combined into a single framework to form an efficient generalized DSC algorithm: I<sub>2,p</sub>-norm based DSC clustering (I<sub>2,p</sub>-DSC). In addition, the effects of the parameters on the proposed algorithm are analyzed, and based on the theory of robust statistics, a special case of I<sub>2,p</sub>-DSC, which can show better robustness on the data sets with noise and outlier, is studied. Extensive experiments are performed to verify the effectiveness of our proposed algorithm.https://ieeexplore.ieee.org/document/9072148/Subspace clusteringlinear discriminant analysis<italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">l</italic>₂,<italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">ₚ</italic>-normiterative reweighted least squaresrobustness |
| spellingShingle | Xiaobin Zhi Longtao Bi Jiulun Fan <italic>l</italic><sub>2,<italic>p</italic></sub>-Norm Based Discriminant Subspace Clustering Algorithm IEEE Access Subspace clustering linear discriminant analysis <italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">l</italic>₂,<italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">ₚ</italic>-norm iterative reweighted least squares robustness |
| title | <italic>l</italic><sub>2,<italic>p</italic></sub>-Norm Based Discriminant Subspace Clustering Algorithm |
| title_full | <italic>l</italic><sub>2,<italic>p</italic></sub>-Norm Based Discriminant Subspace Clustering Algorithm |
| title_fullStr | <italic>l</italic><sub>2,<italic>p</italic></sub>-Norm Based Discriminant Subspace Clustering Algorithm |
| title_full_unstemmed | <italic>l</italic><sub>2,<italic>p</italic></sub>-Norm Based Discriminant Subspace Clustering Algorithm |
| title_short | <italic>l</italic><sub>2,<italic>p</italic></sub>-Norm Based Discriminant Subspace Clustering Algorithm |
| title_sort | italic l italic sub 2 italic p italic sub norm based discriminant subspace clustering algorithm |
| topic | Subspace clustering linear discriminant analysis <italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">l</italic>₂,<italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">ₚ</italic>-norm iterative reweighted least squares robustness |
| url | https://ieeexplore.ieee.org/document/9072148/ |
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