Optimize parameter K in locally linear embedding based on spatial distributions

Data in a high-dimensional data space may reside a low-dimensional manifold embedded within the high-dimensional space. Manifold learning discovers intrinsic manifold data structures to facilitate dimensionality reductions. We propose a novel manifold learning technique called fast optimal locally linear embedding, which judiciously chooses an appropriate number (i.e., parameter K) of neighbouring points where the local geometric properties are maintained by the locally linear embedding (LLE) criterion. To measure the spatial distribution of a group of neighbouring points, our schema relies on relative variance and mean difference to form a spatial correlation index characterizing the neighbours' data distribution. The goal of our schema is to quickly identify the optimal value of parameter K, which aims at minimizing the spatial correlation index. our schema optimizes parameter K by making use of the spatial correlation index to discover intrinsic structures of a data point's neighbours. After implementing our schema, we conduct extensive experiments to validate the correctness and evaluate the performance of our schema. Our experimental results show that our schema outperforms the existing solutions (i.e., LLE and ISOMAP) in manifold learning and dimension reduction.