l2,p-Norm Based Discriminant Subspace Clustering Algorithm

• Published in: IEEE access Vol. 8; pp. 76043 - 76055
• Main Authors: Zhi, Xiaobin, Bi, Longtao, Fan, Jiulun
• Format: Journal Article
• Language: English
• Published: IEEE 2020
• Subjects: <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 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 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 -norm; <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 -norm; Clustering algorithms; Dimensionality reduction; Feature extraction; iterative reweighted least squares; Linear discriminant analysis; Linear regression; Robustness; Subspace clustering; Telecommunications
• ISSN: 2169-3536; 2169-3536
• DOI: 10.1109/ACCESS.2020.2988821

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 <inline-formula> <tex-math notation="LaTeX">l_{2, p} </tex-math></inline-formula>-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 <inline-formula> <tex-math notation="LaTeX">l_{p} </tex-math></inline-formula>-norm based KM (KM<inline-formula> <tex-math notation="LaTeX">_{\mathrm {p}} </tex-math></inline-formula>) clustering is proposed. Then, based on the equivalence of LDA and linear regression, a <inline-formula> <tex-math notation="LaTeX">l_{\mathrm {2,}p} </tex-math></inline-formula>-norm based LDA (<inline-formula> <tex-math notation="LaTeX">l_{\mathrm {2,}p} </tex-math></inline-formula>-LDA) is proposed, and an efficient Iteratively Reweighted Least Squares algorithm for <inline-formula> <tex-math notation="LaTeX">l_{\mathrm {2,}p} </tex-math></inline-formula>-LDA is presented. Finally, KM p and <inline-formula> <tex-math notation="LaTeX">l_{2, p} </tex-math></inline-formula>-LDA are combined into a single framework to form an efficient generalized DSC algorithm: <inline-formula> <tex-math notation="LaTeX">l_{2,{p}} </tex-math></inline-formula>-norm based DSC clustering (<inline-formula> <tex-math notation="LaTeX">l_{2,{p}} </tex-math></inline-formula>-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 <inline-formula> <tex-math notation="LaTeX">l_{2,{p}} </tex-math></inline-formula>-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.