New Random Features Enhance Grassmannian Kernel Scalability

A novel approach has been introduced to make kernel machines on Grassmannian manifolds more scalable, particularly for datasets where data classes are best described by low-dimensional subspaces. Traditional Grassmannian kernels, such as projection and Binet-Cauchy kernels, demand extensive computational resources and memory due to their reliance on full Gram matrices, which becomes impractical for large, high-dimensional datasets. The proposed method utilizes random features derived from rank-one projections of subspace projection matrices, followed by bounded non-linear transformations. This technique effectively approximates well-defined, rotation-invariant Grassmannian kernels, with the approximation holding true for a sufficient number of features relative to the subspace dimension. Experimental results on synthetic data and classification tasks demonstrate that these random features accurately preserve Grassmannian geometry while significantly reducing computational and memory overhead, offering a practical and scalable alternative to existing methods.