Edge colourings of graphs by Fiorini, Stanley; Wilson, Robin J

By Fiorini, Stanley; Wilson, Robin J

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16. } m- for c ranging over all real numbers and m = 21. 2) was used, and the final tree selected by means of pruning and cross-validation. 17. It has 11 terminal nodes. 28. 17 is the population, by class, of the node. Underneath each node is the question producing the split. To illustrate how the splitting mechanism works, examine the first few splits. (t) superim] posed. 0. The sixth coordinate is nearly at the peak of the first waveform. 'ill be high for these two, except when the proportion is small or s6 is large and negative.

J class problem, let N. /N}. But the learning sample ] proportions may not reflect the proportions expected in future cases. In the mass spectra problem, only one-tenth of the com- 28 Introduction to Tree Classification pounds in the data base contained chlorine. But since the unknowns the classifier would face were those already suspected of containing chlorine, the priors [}, } J were used. /N} or supplied by the analyst. {t) the number of class j cases in t. (t)/N .. For a given Xp ] ] set of priors, nCj) is interpreted as the probability that a class j case will be presented to the tree.

In later work, other definitions of i(t) became preferable. Ol? 53]? 53J? This gave a total of 100 • 101 '" 5000 2 questions, so that S contained a similar number of candidate splits. l*, t 1 ) = max bi (J.. ,ES 1 ). , E S repeated on both t2 and t3 separately. To terminate the tree growing, a heuristic rule was designed. When a node t was reached such that no significant decrease in im- purity was possible, then t was not split and became a terminal node. The class character of a terminal node was determined by the plurality rule.

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