Unsupervised feature selection with adaptive residual preserving

Abstract

Many feature selection approaches are proposed in recent years. Most approaches utilize graph-based methods in studying the structure and relationship among data. However, many data relationships may loss during the graph construction, such as the residual relationships. To better preserve the relationships between data, in this paper, we propose a novel unified learning framework - unsupervised feature selection with adaptive residual preserving (UFSARP). The framework unifies feature selection, data reconstruction, and local residual preserving into one unified process, in which these tasks are completed simultaneously. We use the distance of projected data to learn the similarity matrix and simultaneously impose it on the data representation term to enforce that similar samples have similar reconstruction residuals. The use of such learning way has three-fold advantages: (1) The reconstruction residuals aim to maintain the residual relationships between data samples, namely, similar samples have similar residuals, and this helps to reconstruct the original data better; (2) Imposing the similarity matrix on the data representation term encourages similar samples not only have similar reconstruction residuals but also have similar reconstruction coefficients; (3) The similarity matrix and the reconstruction coefficient can be promoted by each other during the learning process. The experimental results show that the proposed algorithm is superior to other similar researches.