Fuzzy nonlinear projection

The objective functions for nonlinear projection and clustering are combined and lead to the definition of fuzzy nonlinear projection. Conventional nonlinear projection preserves topologies well, but produces bad results for multiple manifolds. Conventional clustering can discover complex cluster shapes, but the geometry has to be specified in advance. Fuzzy nonlinear projection avoids these drawbacks of projection and clustering methods. It produces both good projections and good partitions for data sets that contain arbitrarily shaped multiple nonlinear manifolds.