An Efficient Algorithm of Learning the Parametric Map of Locally Linear Embedding

A method is presented to obtain maps between the high-dimensional data and the low-dimensional space deduced by locally linear embedding (LLE). Since LLE does not provide a parametric function that build maps between the image space and the low-dimensional manifold. In this paper, multivariate linear regression is applied to deduce the maps. It can successfully project a new data point onto the embedded space. Also it can be extended to supervised LLE. The performance analysis on the obtained experimental results demonstrated that the proposed method is effective and efficient.