k-nearest neighbor normalized error for visualization and reconstruction - A new measure for data visualization performance

It can be very difficult to automatically determine the hyperparameter values of nonlinear data visualization methods. In this study, a new measure called the k-nearest neighbor normalized error for visualization and reconstruction (k3n-error) is developed to compare the visualization performance and automatically optimize the hyperparameters of nonlinear visualization methods using only unsupervised data. For a given sample, the k3n-error approach is based on the standardized errors between the Euclidean distances to neighboring samples before and after projection onto the latent space. Case studies are conducted using two numerical simulation datasets and four quantitative structure-activity/property relationship datasets. The results confirm that, for each nonlinear visualization method, samples can be mapped to the two-dimensional space while maintaining their proximity relationship from the original space by selecting the hyperparameters using the proposed k3n-error.