### Document

Lecture
Data Mining in R
732A44 Programming in R
Logistic regression: two classes
• Consider Logistic model with one predictor X=Price of the car
Y=Equipment
• Logistic model
P(Y  1 | X  x)
P(Y  1 | X  x)
 log
  0  1 x
P(Y  0 | X  x)
1  P(Y  0 | X  x)
exp(  0  1 x)
P(Y  1 | X  x) 
1  exp(  0  1 x)
log
• Use function glm(formula, family, data)
– Formula: Response~Model
• Model consists of a+b (addition), a:b (interaction terms, a*b (addition and
interaction) . All predictors
– Family: specify binomial
732A44 Programming in R
Logistic regression: two classes
reg<-glm(X3...Equipment~Price.in.SEK.,
family=binomial, data=mydata);
732A44 Programming in R
Logistic regression: several predictors
log
P(Y  1 | X  x)
  0   1T x
P(Y  0 | X  x)
P(Y  1 | X  x) 
exp(  0   1T x)
1  exp(  0   1T x)
– Several analysis plots can be
obtained by plot(lrfit)
– Response: matrix
success/failure
732A44 Programming in R
Logistic regression
• Nominal logistic regressions (library mlogit, function
mlogit)
• Stepwise model selection: step() function.
• Prediction: predict() function
732A44 Programming in R
Smoothing splines
Minimize a penalized sum of squared residuals
N
RSS f ,      yi  f xi      f t  dt
2
i 1
where λ is smoothing parameter.
λ=0 : any function interpolating data
λ=+ : least squares line fit
732A44 Programming in R
2
Smoothing splines
• smooth.spline(x, y, df, spar, cv,…)
– Df degrees of freedom
– Spar: penalty parameter
– CV=
plot(m2\$Kilometer,m2\$Price,
• TRUE=GCV
• FALSE=CV
• NA= no CV
main="df=40");
res<-smooth.spline(
m2\$Kilometer,
m2\$Price,df=40);
lines(res, col="blue");
732A44 Programming in R
A function
g ( E(Y | X1, ..., X n ))
of the expected response is additive in the set of inputs, i.e.,
g ( E(Y | X1, ..., X n ))    s1 ( X1 )  ...  s p ( X p )
Example: Nonlinear logistic regression of a binary response
log
E (Y | X  x)
P(Y  1 | X  x)
 log
  0  s ( x)
1  E (Y | X  x)
P(Y  0 | X  x)
732A44 Programming in R
GAM
• gam(formula,family=gaussian,data,method="GCV.Cp" select=FALSE, sp)
– Method: method for selection of smoothing parameters
– Select: TRUE – variable selection is performed
– Sp: smoothing parameters (maximal df)
– Formula: usual terms and spline terms s(…)
Library: mgcv
• Car properties
bp<-gam(MPG~s(WT, sp=2)+s(SP, sp=1),data=m3)
vis.gam(bp, theta=10, phi=30);
• Predict.gam() can be used for predictions
732A44 Programming in R
GAM
Smoothing components
plot(bp, pages=1)
732A44 Programming in R
Principal components analysis
15
PC1
X2
Idea: Introduce a new coordinate system (PC1,
PC2, …) where
• The first principal component (PC1) is the
direction that maximizes the variance of the
projected data
• The second principal component (PC2) is
the direction that maximizes the variance of
the projected data after the variation along
PC1 has been removed
• …
10
PC2
5
0
5
X1
In the new coordinate system, coefficients
corresponding to the last principal components
are very small  can take away this columns
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10
Principal components analysis
• princomp(x, ...)
m4<-m3;
m4\$MODEL<-c();
res<-princomp(m4);
plot(res);
biplot(res);
summary(res);
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Decision trees
20
X1
<9
>=9
X2
<16
0
10
0
10
20
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>=16
1
X2
<7
>=7
1
X1
<15
>=15
1
0
Regression tree example
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Training-validation-test
• Training-validation (60/40)
sub <- sample(nrow(m2), floor(nrow(m2) * 0.6))
training <- m2[sub, ]
validation <- m2[-sub, ]
• If training-validation-test is required, use similar
strategy
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Decision trees by CART
Growing a full tree
Library ”tree”.
• Create tree: tree(formula, data, subset, split = c("deviance", "gini"),…)
– Subset: if subset of cases needs to be used for training
– Split: splitting criterion
– More parameters with control parameter
• Prune tree with help of validation set: prune.tree(tree, newdata,
method = c("deviance", "misclass”),…)
• Prune tree with cross-validation: cv.tree(object, FUN = prune.tree, K = 10,
...)
– K is number of folds in cross-validation
732A44 Programming in R
Classification trees: CART
Example: Olive oils in Italy
sub <- sample(nrow(m5), floor(nrow(m5) * 0.6))
training <- m5[sub, ]
validation <- m5[-sub, ]
mytree<-tree(Area~.-Region-X,data=training);
summary(mytree)
plot(mytree,type="uniform");
text(mytree,cex=0.5);
732A44 Programming in R
Classification trees: CART
• Dependence of the misclassification rate on the length of the
tree:
treeseq1<-prune.tree(mytree, newdata=validation,method="misclass")
plot(treeseq1);
title("Validation");
treeseq2<-cv.tree(mytree, method="misclass")
plot(treeseq2);
title("CV");
732A44 Programming in R
Regression trees: CART
mytree2<-tree(eicosenoic~linoleic+linolenic+palmitic+palmitoleic,data=training);
mytree3<-prune.tree(mytree2, best=4) #totally 4 leaves
print(mytree3)
summary(mytree3)
plot.tree(mytree3)
text(mytree3)
732A44 Programming in R
Decision trees: other techniques
• Conditional inference trees
Library: party
training\$X<-c();
training\$Area<-c();
mytree4<-ctree(Region~.,data=training);
print(mytree4)
plot(mytree4, type= "simple");# gives nice plots
• CART, another library ”rpart”
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Neural network
• Input nodes, input layer
• [Hidden nodes, Hidden
layer(s)]
• Output nodes, output layer
• Weights
• Activation functions
• Combination functions
z1
x1
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…
f1
z2
x2
fK
…
…
zM
xp
Neural networks
• Feed –forward NNs
Library: neuralnet
• neuralnet(formula, data, hidden = 1, rep = 1, startweights = NULL, algorithm =
"rprop+", err.fct = "sse", act.fct = "logistic", linear.output = TRUE,…)
–
–
–
–
–
–
–
•
•
•
Hidden: vector showing amount of hidden neurons at each layer
Rep: amount of runs of network
Startweights: starting weights
Algorithm: ”backprop”, ”rpprop+”, ”sag”, ”slr”
Err.fct: any function +”sse”+”ce” (cross-entropy)
Act.fct:any function+”logistic”+”tanh”
Linear.output: TRUE, if no activation at the output
confidence.interval(x, alpha = 0.05) Confidence intervals for weights
compute(x, covariate) Prediction
plot(x,…) plot given neural network
732A44 Programming in R
Neural networks
• Example
mynet<-neuralnet(
Region~eicosenoic+linoleic+linolenic+palmitic, data=training,
rep=5, hidden=c(2,2),act.fct="tanh")
plot(mynet);
mynet\$result.matrix
732A44 Programming in R
Neural networks
• Prediction with compute()
• Finding misclassification rate: table(true_values,predicted
values) – not only for neural networks
• Another package, ready for qualitative response (classical
nnet):
mynet1<-nnet( Region~eicosenoic+linoleic,
data=training, size=3);
coef(mynet1)
predict(mynet1, data=validation);
732A44 Programming in R
Clustering
• Purpose is to identify groups of observations into
intput space (separated)
– K-means
– Hierarchical
– Density-based
732A44 Programming in R
K-means
• Amount of seeds K should be given
• Starting seed positions needed
•
kmeans(x, centers, iter.max = 10, nstart = 1)
–
–
–
X: data frame
Centers: either ”K” value or set of initial cluster centers
Iter.max: maximum number of iterations
732A44 Programming in R
res<-kmeans(data.frame (m5\$linoleic,
m5\$eicosenoic),2);
K-means
• One way to visualize
plot(m5\$linoleic, m5\$eicosenoic, col=res\$cluster);
points(res\$centers[,1], res\$centers[,2], col = 1:2, pch = 8, cex=2)
732A44 Programming in R
Hierarchical clustering
• Agglomerative
– Place each point into a single cluster
– Merge nearest clusters until you get 1 cluster
• Meaning of ”two objects are close”?
– Measure of proximity (ex: quantiative vars, Euclidian distance)
• Similarity measure srs (=1 if same object, <1 otherwise)
– Ex: correlation
• Dissimilarity measure δrs (=0 if same object, >0 otherwise)
– Ex: euclidian distance
732A44 Programming in R
Hierarchical clustering
• hclust(d, method = "complete", members=NULL)
– D: dissimilarity measure
– Method: ”ward”, "single", "complete", "average",
"mcquitty", "median" or "centroid".
Returned: a tree showing merging sequence
• cutree(tree, k = NULL, h = NULL)
– K: number of clusters to make
– H: at which level to cut
Returned: cluster index
732A44 Programming in R
Hierarchical clustering
• Example
x<-data.frame(m5\$linolenic, m5\$eicosenoic);
m5_dist<-dist(x);
m5_dend<-hclust(m5_dist,
method="complete")
plot(m5_dend);
732A44 Programming in R
Hierarchical clustering
• Example
clust=cutree(m5_dend, k=2);
plot(m5\$linoleic, m5\$eicosenoic, col=clust);
 DO NOT forget to standardize!
732A44 Programming in R
Density-based clustering
• Kernel-based density estimation.
Library: pdfcluster
•
pdfCluster(x, h = h.norm(x), hmult = 0.75,…)
–
–
–
X: Data to be partitioned
h: a vector of smoothing parameters
Hmult: shrinkage factor
x<-data.frame(m5\$linolenic, m5\$eicosenoic);
res<-pdfCluster(x);
plot(res)
732A44 Programming in R
Reference
http://cran.r-project.org/doc/contrib/YanchangZhaorefcard-data-mining.pdf
732A44 Programming in R