Selection of the Optimal Parameter value for the Locally Linear Embedding Algorithm

The locally linear embedding (LLE) algorithm has recently emerged as a promising technique for nonlinear dimensionality reduction of high-dimensional data. One of its advantages over many similar methods is that only one parameter has to be defined, but no guidance was yet given how to choose it. We propose a hierarchical method for automatic selection of an optimal parameter value. Our approach is experimentally verified on two large data sets of real-world images and applied to visualization of multidimensional data.