Fig. 5

a Estimation of the minimum size of training set required for classification of truncated polyhedra. Each line in the graph represents a polyhedron from the family \( \mathcal{P} \). Only polyhedra with ≤ 20 vertices are shown (55 such). Each solid is randomly rotated n times and truncated by parallel planes to achieve 20 % truncation. For each truncated solid so obtained, a truncated topological profile (TTP) is created. Due to internal symmetries in the polyhedron, many of these topological profiles are identical. The y-axis counts the number of unique topological profiles obtained from these n truncated solids. b Misclassification error of the Bayes classifier as a function of the percent polyhedron truncated. The misclassification error was calculated using a test set of 500 randomly selected TTPs from each of 115 solids with unique complete topological profiles. c Comparison of topological feature subset specific misclassification errors for the Bayes classifier (115 solids). Regret is defined as the difference in misclassification errors achieved when classifying using just the features in the named subset versus using all features. See Table 1 for definition of subsets. d Comparison of topological feature subset specific misclassification errors for the SVM classifier (54 solids). See Table 1 for definition of subsets. Note that the test set polyhedral graphs is mis-specified for this calculation