1 Peter Fox Data Analytics – ITWS-4963/ITWS-6965 Week 8b, March 21, 2014 Using the models, prediction, deciding

scatterplotMatrix 2

Hierarchical clustering 3 > dswiss <- dist(as.matrix(swiss)) > hs <- hclust(dswiss) > plot(hs)

ctree 4 require(party) swiss_ctree <- ctree(Fertility ~ Agriculture + Education + Catholic, data = swiss) plot(swiss_ctree)

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pairs(iris[1:4], main = "Anderson's Iris Data -- 3 species”, pch = 21, bg = c("red", "green3", "blue")[unclass(iris$Species)]) 6

splom extra! require(lattice) super.sym <- trellis.par.get("superpose.symbol") splom(~iris[1:4], groups = Species, data = iris, panel = panel.superpose, key = list(title = "Three Varieties of Iris", columns = 3, points = list(pch = super.sym$pch[1:3], col = super.sym$col[1:3]), text = list(c("Setosa", "Versicolor", "Virginica")))) splom(~iris[1:3]|Species, data = iris, layout=c(2,2), pscales = 0, varnames = c("Sepal\nLength", "Sepal\nWidth", "Petal\nLength"), page = function(...) { ltext(x = seq(.6,.8, length.out = 4), y = seq(.9,.6, length.out = 4), labels = c("Three", "Varieties", "of", "Iris"), cex = 2) }) 7

8 parallelplot(~iris[1:4] | Species, iris)

9 parallelplot(~iris[1:4], iris, groups = Species, horizontal.axis = FALSE, scales = list(x = list(rot = 90)))

hclust for iris 10

plot(iris_ctree) 11

Ctree > iris_ctree <- ctree(Species ~ Sepal.Length + Sepal.Width + Petal.Length + Petal.Width, data=iris) > print(iris_ctree) Conditional inference tree with 4 terminal nodes Response: Species Inputs: Sepal.Length, Sepal.Width, Petal.Length, Petal.Width Number of observations: 150 1) Petal.Length <= 1.9; criterion = 1, statistic = )* weights = 50 1) Petal.Length > 1.9 3) Petal.Width <= 1.7; criterion = 1, statistic = ) Petal.Length <= 4.8; criterion = 0.999, statistic = )* weights = 46 4) Petal.Length > 4.8 6)* weights = 8 3) Petal.Width > 1.7 7)* weights = 46 12

> plot(iris_ctree, type="simple”) 13

New dataset to work with trees fitK <- rpart(Kyphosis ~ Age + Number + Start, method="class", data=kyphosis) printcp(fitK) # display the results plotcp(fitK) # visualize cross-validation results summary(fitK) # detailed summary of splits # plot tree plot(fitK, uniform=TRUE, main="Classification Tree for Kyphosis") text(fitK, use.n=TRUE, all=TRUE, cex=.8) # create attractive postscript plot of tree post(fitK, file = “kyphosistree.ps", title = "Classification Tree for Kyphosis") # might need to convert to PDF (distill) 14

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16 > pfitK<- prune(fitK, cp= fitK$cptable[which.min(fitK$cptable[,"xerror"]),"CP"]) > plot(pfitK, uniform=TRUE, main="Pruned Classification Tree for Kyphosis") > text(pfitK, use.n=TRUE, all=TRUE, cex=.8) > post(pfitK, file = “ptree.ps", title = "Pruned Classification Tree for Kyphosis”)

17 > fitK <- ctree(Kyphosis ~ Age + Number + Start, data=kyphosis) > plot(fitK, main="Conditional Inference Tree for Kyphosis”)

18 > plot(fitK, main="Conditional Inference Tree for Kyphosis",type="simple")

randomForest > require(randomForest) > fitKF <- randomForest(Kyphosis ~ Age + Number + Start, data=kyphosis) > print(fitKF) # view results Call: randomForest(formula = Kyphosis ~ Age + Number + Start, data = kyphosis) Type of random forest: classification Number of trees: 500 No. of variables tried at each split: 1 OOB estimate of error rate: 20.99% Confusion matrix: absent present class.error absent present > importance(fitKF) # importance of each predictor MeanDecreaseGini Age Number Start Random forests improve predictive accuracy by generating a large number of bootstrapped trees (based on random samples of variables), classifying a case using each tree in this new "forest", and deciding a final predicted outcome by combining the results across all of the trees (an average in regression, a majority vote in classification).

More on another dataset. # Regression Tree Example library(rpart) # build the tree fitM <- rpart(Mileage~Price + Country + Reliability + Type, method="anova", data=cu.summary) printcp(fitM) # display the results …. Root node error: /60 = n=60 (57 observations deleted due to missingness) CP nsplit rel error xerror xstd

Mileage… plotcp(fitM) # visualize cross-validation results summary(fitM) # detailed summary of splits 21

22 par(mfrow=c(1,2)) rsq.rpart(fitM) # visualize cross-validation results

# plot tree plot(fitM, uniform=TRUE, main="Regression Tree for Mileage ") text(fitM, use.n=TRUE, all=TRUE, cex=.8) # prune the tree pfitM<- prune(fitM, cp= ) # from cptable # plot the pruned tree plot(pfitM, uniform=TRUE, main="Pruned Regression Tree for Mileage") text(pfitM, use.n=TRUE, all=TRUE, cex=.8) post(pfitM, file = ”ptree2.ps", title = "Pruned Regression Tree for Mileage”) 23

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# Conditional Inference Tree for Mileage fit2M <- ctree(Mileage~Price + Country + Reliability + Type, data=na.omit(cu.summary)) 25

Enough of trees! 26

Bayes > cl <- kmeans(iris[,1:4], 3) > table(cl$cluster, iris[,5]) setosa versicolor virginica # > m <- naiveBayes(iris[,1:4], iris[,5]) > table(predict(m, iris[,1:4]), iris[,5]) setosa versicolor virginica setosa versicolor virginica pairs(iris[1:4],main="Iris Data (red=setosa,green=versicolor,blue=virginica)", pch=21, bg=c("red","green3","blue")[u nclass(iris$Species)])

Digging into iris classifier<-naiveBayes(iris[,1:4], iris[,5]) table(predict(classifier, iris[,-5]), iris[,5], dnn=list('predicted','actual')) actual predicted setosa versicolor virginica setosa versicolor virginica

Digging into iris > classifier$apriori iris[, 5] setosa versicolor virginica > classifier$tables$Petal.Length Petal.Length iris[, 5] [,1] [,2] setosa versicolor virginica

Digging into iris plot(function(x) dnorm(x, 1.462, ), 0, 8, col="red", main="Petal length distribution for the 3 different species") curve(dnorm(x, 4.260, ), add=TRUE, col="blue") curve(dnorm(x, 5.552, ), add=TRUE, col = "green") 30

ench/html/HouseVotes84.html > require(mlbench) > data(HouseVotes84) > model <- naiveBayes(Class ~., data = HouseVotes84) > predict(model, HouseVotes84[1:10,-1]) [1] republican republican republican democrat democrat democrat republican republican republican [10] democrat Levels: democrat republican 31

House Votes 1984 > predict(model, HouseVotes84[1:10,-1], type = "raw") democrat republican [1,] e e-01 [2,] e e-01 [3,] e e-01 [4,] e e-03 [5,] e e-02 [6,] e e-01 [7,] e e-01 [8,] e e-01 [9,] e e-01 [10,] e e-11 32

House Votes 1984 > pred <- predict(model, HouseVotes84[,-1]) > table(pred, HouseVotes84$Class) pred democrat republican democrat republican

So now you could complete this: > data(HairEyeColor) > mosaicplot(HairEyeColor) > margin.table(HairEyeColor,3) Sex Male Female > margin.table(HairEyeColor,c(1,3)) Sex Hair Male Female Black Brown Red Blond Construct a naïve Bayes classifier and test. 34

Assignments to come… Term project (A6). Due ~ week % (25% written, 5% oral; individual). Assignment 7: Predictive and Prescriptive Analytics. Due ~ week 9/10. 20% (15% written and 5% oral; individual); 35

Coming weeks I will be out of town Friday March 21 and 28 On March 21 you will have a lab – attendance will be taken – to work on assignments (term (6) and assignment 7). Your project proposals (Assignment 5) are on March 18. On March 28 you will have a lecture on SVM, thus the Tuesday March 25 will be a lab. Back to regular schedule in April (except 18 th ) 36

Admin info (keep/ print this slide) Class: ITWS-4963/ITWS 6965 Hours: 12:00pm-1:50pm Tuesday/ Friday Location: SAGE 3101 Instructor: Peter Fox Instructor contact: (do not leave a Contact hours: Monday** 3:00-4:00pm (or by appt) Contact location: Winslow 2120 (sometimes Lally 207A announced by ) TA: Lakshmi Chenicheri Web site: –Schedule, lectures, syllabus, reading, assignments, etc. 37