High-dimensional data is characterized by its sparsity and noise, which can increase the likelihood of overfitting and compromise the model’s generalizability performance. In this paper, a novel robust subspace learning method based on stable adaptive spectral clustering is put forward for dimensionality reduction. Firstly, a robust estimator is used to distinguish the role of normal and abnormal samples in constructing the model, thereby small values are assigned to the outliers, then the influence of outliers on the construction of the learning models will be reduced. Secondly, the p-order of \(L_{2}\) -norm distance is applied as the distance metric, replacing the square of \(L_{2}\) -norm distance metric. The \(L_{2,p}\) -norm often commendably tolerates the biases caused by the outliers in sample data, especially when the outliers are away from the normal data distributions. Thirdly, the adaptive stable spectral clustering based on the \(L_{2,p}\) -norm is proposed to construct similarity matrix of the novel robust subspace to carry out reflexive embedding learning to learn the local and globe features of the raw data. In the subspace, the data is reconstructed to reduce the influence of noise and outliers, and the similarity matrix is structured by the new features, that is more conducive to subspace learning. Three main roles of the objective function of our model are: (1) preserving the consistency between the original data and the estimation; (2) achieving a "clean" subspace and further removing the outliers; (3) avoiding the trivial solution for each node in the graph. Finally, the random forest algorithm is used to classify and predict the learned subspace with different feature selections. Experimental results show that the proposed method is superior to other subspace learning methods in classification performance. The results of noise experiment and statistical analysis demonstrate the effectiveness of the proposed method once again.
