Abstract: Clustering is to divide a given sample into several different clusters,which is a widely used tool,has been applied in machine learning,data mining and so on,and has received extensive concern by researchers.However,there are still three main limitations.Firstly,usually there are noises and outliers in the data,which will bring about significant errors in the clustering results.Secondly,traditional clustering methods do not use supervision information to guide the construction of similarity matrices.Finally,in the graph-based clustering method,when constructing graphs,the neighbor relationship is determined.Once the calculation is wrong, it will result in poor quality of the constructed graph,which will affect the clustering performance.Therefore,a semi-supervised clustering model based on Gaussian field and adaptive graph regularization (SCGFAG) is proposed in this paper. In this model,supervised information is introduced by gaussian field and harmonic function to guide the construction of similarity matrix to realize semi-supervised learning.Sparse error matrix is introduced to represent sparse noise,such as impulse noise,dead line,stripes,and l₁ norm is introduced to alleviate the sparse noise.In addition,the l_2,1 norm is also introduced by the proposed model to mitigate the effects of outliers.Therefore,our SCGFAG is insensitive to data noise and outliers.More importantly,the regularization of adaptive graph is introduced into SCGFAG to improve the clustering performance.In order to realize the goal of optimization clustering,an iterative updating algorithm-Augmented Lagrangian Method (ALM) is proposed to update the optimization variables respectively.Experimental results on four datasets show that the proposed method is superior to the eight classical clustering methods,and has better clustering performance.

Key words: Adaptive graph regularization, Augmented Lagrangian method, Noise and outliers, Rotation invariance property of l_2,1, Semi-supervised clustering