Contextual self-organizing maps for visual design space exploration

Visualization of an optimization problem (i.e the “design space”) becomes complex when the number of independent variables of the problem increases beyond two. Unfortunately, realistic optimization problems and their design spaces are often greater than two dimensions and therefore difficult to visualize. In order to create and display in greater than three dimensions it is necessary to use color, size, or symbols to show added dimensions. With the complexity in a visualization that uses these extra dimensional features, an observer is often overloaded with data and it can be difficult to grasp a firm understanding of the relationships therein. Furthermore, this solution of adding dimensions greater than three can only increment to a few dimensions beyond three and cannot achieve higher dimensions. There are currently two general areas for visualizing a higher dimensional design space: dimensional reduction, and individual variable comparison. With either of these methods, it is possible to display the resulting design space, or portion thereof, in a viewable dimensionality such as two or three dimensions. Self-organizing contextual maps provide a solution to this visualization problem by utilizing the dimensionality reduction capability of self-organizing maps and the display capability of the contextual map. Self-organizing maps (SOMs) are able to map a design space of varying dimensionality to a two dimensional neuron lattice. The SOM can then be provided contextual information to display the similarities between areas of the design space either in terms of alphanumerical labels or visuals. This method will organize the numerical objective values associated with a design space to apply labels to the contextual SOMs. These