Adaptive manifold regularized matrix factorization for data clustering

Data clustering is the task to group the data samples into certain clusters based on the relationships of samples and structures hidden in data, and it is a fundamental and important topic in data mining and machine learning areas. In the literature, the spectral clustering is one of the most popular approaches and has many variants in recent years. However, the performance of spectral clustering is determined by the affinity matrix, which is usually computed by a predefined model (e.g., Gaussian kernel function) with carefully tuned parameters combination, and may not optimal in practice. In this paper, we propose to consider the observed data clustering as a robust matrix factorization point of view, and learn an affinity matrix simultaneously to regularize the proposed matrix factorization. The solution of the proposed adaptive manifold regularized matrix factorization (AMRMF) is reached by a novel Augmented Lagrangian Multiplier (ALM) based algorithm. The experimental results on standard clustering datasets demonstrate the superior performance over the exist alternatives.