Discriminative and Robust Autoencoders for Unsupervised Feature Selection

Many recent research works on unsupervised feature selection (UFS) have focused on how to exploit autoencoders (AEs) to seek informative features. However, existing methods typically employ the squared error to estimate the data reconstruction, which amplifies the negative effect of outliers and can lead to performance degradation. Moreover, traditional AEs aim to extract latent features that capture intrinsic information of the data for accurate data recovery. Without incorporating explicit cluster structure-detecting objectives into the training criterion, AEs fail to capture the latent cluster structure of the data which is essential for identifying discriminative features. Thus, the selected features lack strong discriminative power. To address the issues, we propose to jointly perform robust feature selection and $k$ -means clustering in a unified framework. Concretely, we exploit an AE with a $l_{2,1}$ -norm as a basic model to seek informative features. To improve robustness against outliers, we introduce an adaptive weight vector for the data reconstruction terms of AE, which assigns smaller weights to the data with larger errors to automatically reduce the influence of the outliers, and larger weights to the data with smaller errors to strengthen the influence of clean data. To enhance the discriminative power of the selected features, we incorporate $k$ -means clustering into the representation learning of the AE. This allows the AE to continually explore cluster structure information, which can be used to discover more discriminative features. Then, we also present an efficient approach to solve the objective of the corresponding problem. Extensive experiments on various benchmark datasets are provided, which clearly demonstrate that the proposed method outperforms state-of-the-art methods.