Nonlinear projection for the display of high dimensional distance data

Display and visualization of high dimensional data are typically performed with a well-chosen linear projection of the data or by displaying many linear projections to form an animation. This study presents an evolutionary algorithm for producing nonlinear projections of high dimensional data with cues, in the drawing of the projection, as to the types of distortions introduced. Such projections can provide drawings closer to the true high dimensional distances of the displayed data than any single linear drawing. This permits a researcher to view a good analog to a scatter plot for high dimensional data. The system is demonstrated on a synthetic four dimensional fitness landscape and on distance data derived from RNA folds. Because fitness landscapes often have more dimensions than can be easily visualized it is difficult to gain an intuitive understanding of a fitness landscape. The nonlinear projection algorithm is applied to an abstraction of the fitness landscape called a fitness web. Fitness webs can be used to display the relative quality of optima, the frequency with which they were found by different evolutionary runs, or other factors of interest. In addition to displaying the relative position of optima in a fitness landscape, a graph of the fitness function along the edges a fitness web displays important slices of the fitness landscape. Called fitness morphs these plots can provide intuition about the fitness landscapes as well as direction for subsequent evolutionary searches. The second demonstration of the nonlinear projection algorithm is to data generated from an ad hoc metric on RNA folds. The algorithm yields drawings that permit a researcher to correctly distinguish two different types of folds for iron response elements.