A new quality assessment criterion for nonlinear dimensionality reduction

A new quality assessment criterion for evaluating the performance of the nonlinear dimensionality reduction (NLDR) methods is proposed in this paper. Differing from the current quality assessment criteria focusing on the local-neighborhood-preserving performance of the NLDR methods, the proposed criterion capitalizes on a new aspect, the global-structure-holding performance, of the NLDR methods. By taking both properties into consideration, the intrinsic capability of the NLDR methods can be more faithfully reflected, and hence more rational measurement for the proper selection of NLDR methods in real-life applications can be offered. The theoretical argument is supported by experiment results implemented on a series of benchmark data sets.