Local and Global Structures Preserving Projection

In this paper, we propose Local and Global Structures Preserving Projection (LGSPP), which is to find a small set of projection directions so as to properly preserve the local and global structures for a given set of data. Specifically, for each point in the dataset, its local neighborhood is extracted as well as a set of sampled points far away from this point, which characterize the global structure. The embedding minimizes the distances of the points in each local neighborhood while dispersing them far apart from their corresponding remote points. In this way, the local-global relationships between data points are well kept.