Data-dependent nearest-neighbor and neighborhood-window bidirectionally constrained locality preserving projection
摘要
Manifold learning reveals the inherent low-dimensional manifold characteristics of high-dimensional data by analyzing the local structure of the data. Existing methods may encounter situations where the low-dimensional manifold structure is destroyed, and the smoothness and continuity between local neighborhoods are weak when only using nearest-neighbor or neighborhood-window to describe the local structure of the sample space. Consequently, a data-dependent nearest-neighbor and neighborhood-window bidirectionally constrained locality preserving projection algorithm (D2NBC-LPP) is proposed. The algorithm initially utilizes the statistical distribution information of the window corresponding to the nearest-neighbor sample to learn the range of the neighborhood-window. This process can obtain a neighborhood-window scale that reflects the potential structure by relying on the global information of the data. Subsequently, the centroid consistency measure based on the spatial distribution is utilized within the neighborhood-window to select an appropriate nearest-neighbor representation for each sample. The distribution of samples within the learned local neighborhood is more uniform, which is closer to the properties of Euclidean space. Ultimately, the low-dimensional manifold features that maintain the original local structure are learned through the learned neighborhood. Experimental results demonstrate that D2NBC-LPP achieves superior recognition performance through the nearest-neighbor and neighborhood-window bidirectional constraint, surpassing existing methods.