An evaluated model based on the variance of distance ratios for nonlinear dimensionality reduction algorithms

We analyze and compare three evaluation models for nonlinear dimensionality reduction algorithms including the evaluation model based on the stress function, the evaluation model based on the residual variance and the evaluation model based on the dy-dx representation. On the base of the dy-dx representation, we propose an evaluation model base on the variance of distance ratios. The model is on the assumption that a good dimensionality reduction technique should best preserve the proportion between distances in the original space and corresponding distances in the embedding space. Experiments illustrate that the model not only can evaluate results from the same algorithm with various parameters, but also can compare results from different methods.