Generative Topographic Mapping Visualization Performance allied to Root Mean Square Error of Midpoint among Nearest Neighbors

Abstract

In the realm of data visualization, reducing complex data sets to 2-D maps is a common practice used for reconciling information and for identifying meaningful patterns and clusters. Within the plethora of different methodologies and criteria for defining optimal maps, however, one must be aware on how to assess the performance of such visualization. This work focuses on Generative Topographic Mapping, a well-known nonlinear visualization methodology, to investigate and propose different indexes used for defining optimal latent 2-D maps. More specifically, this work focuses on criteria used for obtaining optimal hyperparameters used for map training. Common criterion such as RMSE is used, but also a new strategy relying on Root Mean Square Error of Midpoint (RMSEM) and its association with Nearest Neighbors (NN) is proposed. In order to evaluate their performance, an artificial data set and Tennessee Eastman Process (TEP) were used as case studies, highlighting the potential of the proposed criterion for defining more reliable and meaningful data visualization.