Figure 2:

Examples of model fitting using augmented variables. The data are synthetic, for the purposes of illustration only.

(A) An example of a model-fitting problem in which desirable outcomes (represented by green circles) are clustered around a mean point, and adverse outcomes (represented by red crosses) are associated with deviations from that point. For clinical correlation, one might imagine that the data represent favorable or unfavorable ICU outcomes based on rigorous control of potassium (Feature K) and glucose (Feature G).

(B) Rather than attempting to fit outcomes solely to the variables K and G, the variable space can be augmented by also fitting to K² and G². This example demonstrates that the fitting of a perimeter around a mean value is easily accomplished by a linear fitting within the augmented space of K² and G². The linear discriminant of (K²) + (G²) – 9 = 0 as shown produces a circular boundary of radius 3 in the K,G space.