Locally Multidimensional Scaling for Nonlinear Dimensionality Reduction

A data embedding method is introduced to configure global coordinates of data using local distances as input. The method applies classical multidimensional scaling within a neighborhood of each data point. The local models are then aligned to derive global coordinates in order to minimize a residual measure. The residual measure has a quadratic form of resulting global coordinates, which makes the alignment problem solved analytically by using an eigensolver. Experiments show that the method produces less deformed embedding results than locally linear embedding. Variations of the method and possible extensions are also discussed