Adaptive graph regularization and self-expression for noise-aware feature selection

Abstract

Many traditional unsupervised feature selection algorithms utilize manifold information to mine the local structure of the data. However, the noise existing in the raw data reduces the accuracy of the manifold information of data, which affects the learning effect of the entire algorithm. In order to solve the above problems and more fully find the internal structure inside the data, this paper proposes an adaptive graph regularization and self-expression for noise-aware feature selection (ASNFS). Firstly, the algorithm adopts non-negative matrix factorization to decompose the raw data matrix, and utilizes the low-dimensional matrix generated after decomposition to replace the raw high-dimensional data matrix. This allows the algorithm to reveal some internal structural information of the raw data while reducing the dimensionality of the data. ASNFS also introduces the orthogonal basis clustering with excellent clustering effect, and the interpretability of the algorithm is enhanced. Secondly, in addition to preserving the manifold information in the low-dimensional projection subspace, the algorithm also preserves the manifold information in the non-negative matrix factorization subspace. Meanwhile, the adaptive graph regularization term added to the objective function enables the algorithm to continuously update the similarity matrix. It can effectively remove the noise inside the raw data, and prevent the occurrence of over-fitting phenomenon of the experimental results caused by the fixed similarity matrix. Finally, the similarity matrix retains the local structure information of the data with each iteration, and the results of the feature selection are reused for the construction of the similarity matrix. ASNFS adopts an alternate iterative method to optimize the objective function, which is simple and effective. Then, the algorithm complexity and convergence are analyzed. ASNFS is compared with seven feature selection algorithms on nine datasets, and the experimental results reflect the effectiveness of ASNFS in feature selection.