Dimension reduction of nonlinear manifolds by Kernel Graph Laplacian Features

Abstract

Spectral clustering is used for clustering nonlinear manifolds.The better the performance,the better the distance between the clusters.However,as the S/N ratio of the data decreases, spectral clustering does not work well. This is because the pre-processing in spectral clustering is based on the assumption that the clusters can be sufficiently separated from each other by parameter adjustment.Therefore, in this paper, we propose robust preprocessing to S/N ratio by kernelized graph Laplacian features(Kernel GLF).The GLF is a linear transformation that brings each other's data with high affinity closer and keeps each other's data with low affinity away. The results show that Kernel GLF can convert nonlinear manifold into linear structure. By clustering the pre-processed data with K-Means , it became a more robust algorithm for S/N ratio than Spectral Clustering.