Clustering-based nonlinear dimensionality reduction on manifold

This paper proposes a clustering-based nonlinear dimensionality reduction approach. It utilizes the clustering approaches to form the clustering structure by which the distance between any two data points are rescaled to make data points from different clusters separated more easily. This rescaled distance matrix is then provided to improve the nonlinear dimensionality reduction approaches such as Isomap to achieve the better performance. Furthermore, the proposed approach also decreases the time complexity on the large data sets, as it provides good neighborhood structure that can speed up the subsequent dimensionality reducing process. Unlike the supervised approaches, this approach does not take the labelled data set as prerequisite, so that it is unsupervised. This makes it applicable to the broader domains. The conducted experiments by classification on benchmark data sets have validated the proposed approach.