Choosing the split classi cation trees in .NET Render PDF-417 2d barcode in .NET Choosing the split classi cation trees

11.3.3 Choosing the split classi cation trees use .net framework pdf417 integrating toconnect pdf-417 2d barcode in .net interleaved 2 of 5 To request a cl .net framework barcode pdf417 assi cation tree, include the argument method="class" in the rpart() call. This setting is the default when the outcome is a factor, but it is best to state it explicitly.

The classes (indexed by k) are the categories of the classi cation. Then nik is the number of observations at the ith leaf that are assigned to class k. The nik are used to estimate the proportions pik .

Each leaf becomes, in turn, a candidate to be the node for a new split.. 11.3 Terminology and methodology Miles per gallon 20 2000. 3000 Weight Figure 11.5 Mil eage versus Weight, for cars described in US April 1990 Consumer Reports. A loess curve is overlaid.

. For classi cati PDF 417 for .NET on trees, several different splitting criteria may be used, with different software programs offering different selections of criteria. In rpart, the default is gini, which uses a modi ed version of the Gini index pij pik = 1 .

j =k k 2 pik as its default Visual Studio .NET PDF 417 measure of error , or impurity . An alternative is information, or deviance.

The rpart documentation and output use the generic term error for whatever criterion is used. The information criterion, or deviance, is Di =. classes k nik log(pik ).. This differs on ly by a constant from the entropy measure that is used elsewhere, and thus would give the same tree if the same stopping rule were used. For the two-class problem (a binary classi cation), the Gini index and the deviance will almost always choose the same split as the deviance or entropy. The splitting rule, if speci ed, is set by specifying, e.

g., parms=list(split=gini) or parms=list(split=information)..

11.3.4 Tree-based regression versus loess regression smoothing The scatterplot of gas mileage versus vehicle weight in Figure 11.5 suggests a nonlinear relationship. Useful insights may be gained from the comparison of predictions from treebased regression with predictions from the more conventional and (for these data) more appropriate use of a loess() or similar regression smoothing approach.

. Tree-based classi cation and regression Wt>=2568 Wt>=2568 Wt>=3088 Wt>=2280 Wt>=3638 Wt>=2748 28.9 n=9 34 n=6 Wt>=3088 Wt>=2748 30.9 n=15 Wt< 3322 18.7 n=6 20.5 n=10 22 n=6 Wt< 2882 25.6 n=8 23.3 n=6 24.1 n=9 20.4 n=22 23.8 n=15. 25.6 n=8. Figure 11.6 Tre e-based model for predicting Mileage given Weight, for cars described in US April 1990 Consumer Reports. In panel A, split criteria have for illustrative purposes been changed from the rpart defaults, to increase the number of splits.

This plot has used uniform vertical spacing between levels of the tree. Panel B used the rpart default split criteria, and vertical spacing was set to re ect the change in residual sum of squares. In panel A, such non-uniform spacing would have given splits that were bunched up at the lower nodes.

. The code for Figure 11.5 is:. ## loess fit to Mileage vs Weight: data frame car.test.frame (rpart) with(car.

test.frame, scatter.smooth(Mileage Weight)).

To t a regress .net vs 2010 pdf417 2d barcode ion tree to the car mileage data shown in Figure 11.5, the model formula is Mileage Weight, i.

e., predict Mileage given Weight, just as for the use of lm() or loess(). The code is:.

car.tree <- rpart(Mileage Weight, data=car.test.

frame, control = list(minsplit = 10, minbucket = 5, cp = 0.0001), method="anova") plot(car.tree, uniform = TRUE) text(car.

tree, digits = 3, use.n = TRUE). Setting minspli .NET PDF 417 t=10 (the default is 20) allows splitting at any node that has at least ten observations, while minbucket=5 has reduced to 5 the minimum number of observations at a terminal node. See help(rpart.

control) for further details. Figure 11.6A shows the tted regression decision tree.

Table 11.3 compares the predictions of Figure 11.6 with predicted values from the use of loess in Figure 11.

5. Notice how the tree-based regression has given several anomalous predictions. Later splits have relied on information that is too local to improve predictive ability.

Figure 11.6B is the plot that results when the split criteria are left at their defaults. It used the simpler code:.

car.tree <- rpart(Mileage Weight, data = car.test.

frame) plot(car.tree, uniform = FALSE) text(car.tree, digits = 3, use.

n = TRUE). Prediction is m pdf417 2d barcode for .NET uch coarser. Table 11.

4 compares the predictions for this less ambitious tree with the predictions from the loess regression. Beyond a certain point, adding additional leaves reduces genuine predictive power, even though the t to the data used to develop the predictive model must continue to improve..

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