Visualization of pattern data through learning of non-linear variance-conserving dimension-reduction mapping

摘要

A new approach to reduced-dimension mapping of multi-dimensional pattern data is described. It consists of learning a mapping from the original pattern space to a reduced-dimension space in an unsupervised non-linear manner but with the constraint that the overall variance in the representation of the data be conserved. The motivation for this work is to provide a method for “visualizing” complex large bodies of multidimensional data in terms of low-dimension entities. This approach relates to but is different from both the Karhunen-Loeve (K-L) and auto-associative approaches which emphasize feature extraction, and also from the ART and feature mapping approaches which emphasize category formation based on similarity in the original representation. This new method is highly efficient computationally. Basic characteristics of this new approach are described in this discussion. Application of the procedure to a body of gasoline blending data resulted in a mapping which can be used to guide future blending formulations. Application to sensor data resulted in the discovery of a rule for distinguishing between fault and no fault conditions. Visual monitoring of the evolution of a system can also be realized in this manner. This variance-conserving mapping is learned in a computationally efficient manner.