Robust multi-view locality preserving regression embedding

Feature extraction research has witnessed significant advancements in recent decades, particularly with single-view graph embedding (GE) methods that demonstrate clear advantages by incorporating structural information. However, multi-view data includes descriptions from various perspectives or sensors, offering richer and more comprehensive information compared to single-view data. Research interest in multi-view feature extraction is steadily increasing. Hence, there is a pressing need for a comprehensive framework that extends single-view methods, especially effective GE methods, into multi-view approaches. This article proposes three innovative multi-view feature extraction frameworks based on regression embedding. These frameworks extend single-view GE methods to the multi-view scenario. Our approach meticulously considers the consistency and complementarity of multi-view data, placing strong emphasis on robustness to noisy datasets. Additionally, the use of non-linear shared embedding helps prevent the loss of essential information that may occur with linear projection techniques. Through numerical experiments, we validate the effectiveness and robustness of our proposed frameworks on both real and noisy datasets.