<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 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 -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 -norm based KM (KM clustering is proposed. Then, based on the equivalence of LDA and linear regression, a -norm based LDA LDA) is proposed, and an efficient Iteratively Reweighted Least Squares algorithm for-LDA is presented. Finally, KMp and -LDA are combined into a single framework to form an efficient generalized DSC algorithm: -norm based DSC clustering -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 -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.