Structure Preserving Dimensionality Reduction : A Fuzzy Logic Approach

We propose a fuzzy rule based method for structure preserving dimensionality reduction. This method selects a small representative sample and applies Sammon's method to project it. The input data points are then augmented by the corresponding projected(output) data points. The augmented data set thus obtained is clustered with the fuzzy c-means(FCM) clustering algorithm. Each cluster is then translated into a fuzzy rule for projection. Our rule based system is computationally very efficient compared to Sammon's method and is quite effective to project new points, i.e., it has good predictability.