1. Interpreting: MDS, DR, SVM Factor Analysis
Peter Fox
Data Analytics – ITWS-4600/ITWS-6600/MATP-4450
Group 3 Module 10, March 29, 2018

2. MDS lab3_mds1.R lab3_mds2.R lab3_mds3.R

3. Eurodist

4. You worked on these… lab3_svm1.R –> lab3_svm11.R lab3_svm_rpart1.R
Karatzoglou et al
Who worked on this starting from page 9 (bottom)?

5. Ozone > library(e1071) > library(rpart)
> data(Ozone, package=“mlbench”)
> # # for field codes
> ## split data into a train and test set
> index <- 1:nrow(Ozone)
> testindex <- sample(index, trunc(length(index)/3))
> testset <- na.omit(Ozone[testindex,-3])
> trainset <- na.omit(Ozone[-testindex,-3])
> svm.model <- svm(V4 ~ ., data = trainset, type=“C-classification”,cost = 1000, gamma = )
> svm.pred <- predict(svm.model, testset[,-3])
> crossprod(svm.pred - testset[,3]) / length(testindex)
See:

6. Glass
library(e1071) library(rpart) data(Glass, package="mlbench") index <- 1:nrow(Glass) testindex <- sample(index, trunc(length(index)/3)) testset <- Glass[testindex,] trainset <- Glass[-testindex,] svm.model <- svm(Type ~ ., data = trainset, cost = 100, gamma = 1) svm.pred <- predict(svm.model, testset[,-10])

7. > table(pred = svm.pred, true = testset[,10]) true pred

8. Example lab3_svm1.R
n <- 150 # number of data points p <- 2 # dimension sigma <- 1 # variance of the distribution meanpos <- 0 # centre of the distribution of positive examples meanneg <- 3 # centre of the distribution of negative examples npos <- round(n/2) # number of positive examples nneg <- n-npos # number of negative examples # Generate the positive and negative examples xpos <- matrix(rnorm(npos*p,mean=meanpos,sd=sigma),npos,p) xneg <- matrix(rnorm(nneg*p,mean=meanneg,sd=sigma),npos,p) x <- rbind(xpos,xneg) # Generate the labels y <- matrix(c(rep(1,npos),rep(-1,nneg))) # Visualize the data plot(x,col=ifelse(y>0,1,2)) legend("topleft",c('Positive','Negative'),col=seq(2),pch=1,text.col=seq(2))

9. Example 1

10. Train/ test
ntrain <- round(n*0.8) # number of training examples tindex <- sample(n,ntrain) # indices of training samples xtrain <- x[tindex,] xtest <- x[-tindex,] ytrain <- y[tindex] ytest <- y[-tindex] istrain=rep(0,n) istrain[tindex]=1 # Visualize plot(x,col=ifelse(y>0,1,2),pch=ifelse(istrain==1,1,2)) legend("topleft",c('Positive Train','Positive Test','Negative Train','Negative Test'),col=c(1,1,2,2), pch=c(1,2,1,2), text.col=c(1,1,2,2))

11. Comparison of test classifier

12. Example ctd
svp <- ksvm(xtrain,ytrain,type="C-svc", kernel='vanilladot', C=100,scaled=c()) # General summary svp # Attributes that you can access attributes(svp) # did you look? # For example, the support vectors alpha(svp) alphaindex(svp) b(svp) # remember b? # Use the built-in function to pretty-plot the classifier plot(svp,data=xtrain)
> # For example, the support vectors
> alpha(svp)
[[1]]
[1]
> alphaindex(svp)
[1]
> b(svp)
[1]

14. SVM for iris

15. SVM for Swiss

16. e.g. Probabilities…
library(kernlab) data(promotergene) ## create test and training set ind <- sample(1:dim(promotergene)[1],20) genetrain <- promotergene[-ind, ] genetest <- promotergene[ind, ] ## train a support vector machine gene <- ksvm(Class~.,data=genetrain,kernel="rbfdot",\ kpar=list(sigma=0.015),C=70,cross=4,prob.model=TRUE) ## predict gene type probabilities on the test set genetype <- predict(gene,genetest,type="probabilities")

17. Result
> genetype + - [1,] [2,] [3,] [4,] [5,] [6,] [7,] [8,] [9,] [10,] [11,] [12,] [13,] [14,] [15,] [16,] [17,] [18,] [19,] [20,]

18. kernlab http://aquarius.tw.rpi.edu/html/DA/svmbasic_notes.pdf
Some scripts: lab1_svm12.R, lab1_svm13.R

19. These
example_exploratoryFactorAnalysis.R on dataset_exploratoryFactorAnalysis.csv (on website)
(this was the example skipped over in the lecture)
Do these – lab2_fa{1,2,4,5}.R

20. Factor Analysis
data(iqitems) # data(ability) ability.irt <- irt.fa(ability) ability.scores <- score.irt(ability.irt,ability) data(attitude) cor(attitude) # Compute eigenvalues and eigenvectors of the correlation matrix. pfa.eigen<-eigen(cor(attitude)) pfa.eigen$values # set a value for the number of factors (for clarity) factors<-2 # Extract and transform two components. pfa.eigen$vectors [ , 1:factors ] %*% + diag ( sqrt (pfa.eigen$values [ 1:factors ] ),factors,factors )

21. Glass
index <- 1:nrow(Glass) testindex <- sample(index, trunc(length(index)/3)) testset <- Glass[testindex,] trainset <- Glass[-testindex,] Cor(testset) Factor Analysis?