An Adaptive Neighborhood Graph for LLE Algorithm without Free-Parameter

Locally Linear Embedding (LLE) algorithm is the first classic nonlinear manifold learning algorithm based on the local structure information about the data set, which aims at finding the low-dimension intrinsic structure lie in high dimensional data space for the purpose of dimensionality reduction. One deficiency appeared in this algorithm is that it requires users to give a free parameter k which indicates the number of nearest neighbors and closely relates to the success of unfolding the true intrinsic structure. Here, we present an adaptive neighborhood graph with respect to LLE algorithm for learning an adaptive local infrastructure in order to avoid the problem of how to automatically choosing nearest neighbors existed in manifold learning by making use of a novel concept: natural nearest neighbor (3N). Experiment results show that LLE algorithm without free parameter performs more practical and simple algorithm than LLE. General Terms Machine Learning; Pattern Recognition; Algorithm; Dimensionality Reduction;