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

Abstract The graph Laplacian approximation of the Laplace–Beltrami operator on the Riemann manifold requires estimation of the kernel width and the neighborhood which is usually obtained through cross-validation. In this work, we propose a method based on local tangent space alignment to determine the optimal neighborhood. The method works by selecting the most distant point with minimum acceptable misalignment in every local region to define the neighborhood size. The work also proposes to use local kernel width which is represented as a function of the number of data points in the optimal neighborhood and maximum neighborhood distance. Extensive experiments on synthetic and real-world data including brain computer interface readings confirm that the proposed method is able to extract the intrinsic representation and outperforms the related existing state-of-the-art methods in the area.