Optimal manifold neighborhood and kernel width for robust non-linear dimensionality reduction

A rotation based regularization method for semi-supervised learning

In manifold learning, the intrinsic geometry of the manifold is explored and preserved by identifying the optimal local neighborhood around each observation. It is well known that when a Riemannian manifold is unfolded correctly, the observations lying spatially near to the manifold, should remain near on the lower dimension as well. Due to the nonlinear properties of manifold around each observation, finding such optimal neighborhood on the manifold is a challenge. Thus, a sub-optimal neighborhood may lead to erroneous representation and incorrect inferences. In this paper, we propose a rotation-based affinity metric for accurate graph Laplacian approximation. It exploits the property of aligned tangent spaces of observations in an optimal neighborhood to approximate correct affinity between them. Extensive experiments on both synthetic and real world datasets have been performed. It is observed that proposed method outperforms existing nonlinear dimensionality reduction techniques in low-dimensional representation for synthetic datasets. The results on real world datasets like COVID-19 prove that our approach increases the accuracy of classification by enhancing Laplacian regularization.