Self-representation with adaptive loss minimization via doubly stochastic graph regularization for robust unsupervised feature selection

Unsupervised feature selection (UFS), which involves selecting representative features from unlabeled high-dimensional data, has attracted much attention. Numerous self-representation-based models have been recently developed successfully for UFS. However, these models have two main problems. First, existing self-representation-based UFS models cannot effectively handle noise and outliers. Second, many graph-regularized self-representation-based UFS models typically construct a fixed graph to maintain the local structure of data. To overcome the above shortcomings, we propose a novel robust UFS model called self-representation with adaptive loss minimization via doubly stochastic graph regularization (SRALDS). Specifically, SRALDS uses an adaptive loss function to minimize the representation residual term, which may enhance the robustness of the model and diminish the effect of noise and outliers. Besides, rather than utilizing a fixed graph, SRALDS learns a high-quality doubly stochastic graph that more accurately captures the local structure of data. Finally, an efficient optimization algorithm is designed to obtain the optimal solution for SRALDS. Extensive experiments demonstrate the superior performance of SRALDS over several well-known UFS methods.