Quality Assessment for Nonlinear Dimensionality Reduction using Procrustes Analysis

In order to achieve of PNL-ICA (Post-Nonlinear Independent Component Analysis) by using Dimensionality Reduction [1] the data set has to be embedded in a hyperplane, i.e. linear combination of the latent variables. This condition must be fulfilled in order to ensure that there is an unique solution to the problem. This article describes a new quality measure for Nonlinear Dimensionality Reduction based on Procrustes Analysis. This approach aims to solve the question of how to evaluate if a low-dimensional embedding (outcome of the process of dimensional reduction) can be used to recover data by using ICA methods.