Details of Research Outputs

This paper introduces a robust bi-orthogonal projection (RBOP) learning method for dimensionality reduction (DR). The proposed RBOP enhances the flexibility, robustness, and sparsity of the embedding framework, extending beyond traditional DR methods such as principal component analysis (PCA), neighborhood preserving embedding (NPE), and locality preserving projection (LPP). Unlike conventional approaches that rely on a single type of projection, RBOP innovates by employing two types of projections: the "true" projection and the "counterfeit" projection. These projections are crafted to be orthogonal, offering enhanced flexibility for the "true" projection and facilitating more precise data transformation in the process of subspace learning. By utilizing sparse reconstruction, the acquired true projection has the capability to map the data into a low-dimensional subspace while efficiently maintaining sparsity. Observing that the two projections share many similar data structures, the method aims to maintain the similarity structure of the data through distinct reconstruction processes. Additionally, the incorporation of a sparse component allows the method to address noise-corrupted data, compensating for noise during the DR process. Within this framework, a number of new unsupervised DR techniques have been developed, such as RBOP_PCA, RBOP_NPE, and RBO_LPP. Experimental results from both natural and synthetic datasets indicate that these proposed methods surpass existing, well-established DR techniques.