Abstract
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.