Unsupervised Feature Selection via Nonlinear Representation and Adaptive Structure Preservation

Aihong Yuan, Lin Lin, Peiqi Tian, Qinrong Zhang

Abstract: Unsupervised feature selection has attracted increasing attention for its promising performance on high dimensional data with higher dimensionality and more expensive labeling costs. Existing unsupervised feature selection methods mostly assume that linear relationships can interpret all feature associations. However, data with exclusively linear relationships are rare and impractical. Moreover, the quality of the similarity matrix significantly affects the effectiveness of conventional spectral-based methods. Real-world data contains lots of noise and redundancy, making the similarity matrix built using the raw data unreliable. To address these problems, we propose a novel and robust method for feature selection over a novel nonlinear mapping function, aiming to mine the nonlinear relationships among features. Furthermore, we incorporated manifold learning into our training process, embedded with adaptive graph constraints based on the principle of maximum entropy, to maintain the intrinsic structure of the data and simultaneously capture more accurate information. An efficient and effective algorithm was designed to perform our method. Experiments with eight benchmark datasets from face images, biology, and time series outperformed nine state-of-the-art algorithms, validating the superiority and effectiveness of our method. The source code is available at https://github.com/aasdlaca/NRASP.