Manifold NMF with L21 norm for clustering

Nonnegative matrix factorization has been widely used in data mining and machine learning fields as a clustering algorithm. The standard nonnegative matrix factorization algorithm utilizes the sum of squared error to measure the quality of factorization, however, the noise and outliers in the dataset will reduce the performance of algorithm significantly. This paper proposes a robust manifold nonnegative matrix factorization algorithm based on L21 norm, and the projected gradient method is utilized to obtain the updating rules. The proposed algorithm utilizes the L21 norm to measure the quality of factorization, which is insensitive to the noise and outliers, also it utilizes the geometrical structure of the dataset and considers the local invariance. The experimental results on several data sets and the comparison with other clustering algorithms demonstrate the effectiveness of the proposed algorithm.