l2,p-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 I
_2,p
-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
_p
-norm based KM (KM
_p
) clustering is proposed. Then, based on the equivalence of LDA and linear regression, a I
_2,p
-norm based LDA (I
_2,p
-LDA) is proposed, and an efficient Iteratively Reweighted Least Squares algorithm for I
_2,p
-LDA is presented. Finally, KMp and I
_2,p
-LDA are combined into a single framework to form an efficient generalized DSC algorithm: I
_2,p
-norm based DSC clustering (I
_2,p
-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
_2,p
-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.