1. Regression, classification and clustering - interpreting and exploring data
Peter Fox and Greg Hughes
Data Analytics – ITWS-4600/ITWS-6600
Group 2, Module 5, February 6, 2017

2. Regression Retrieve this dataset: dataset_multipleRegression.csv
Using the unemployment rate (UNEM) and number of spring high school graduates (HGRAD), predict the fall enrollment (ROLL) for this year by knowing that UNEM=9% and HGRAD=100,000.
Repeat and add per capita income (INC) to the model. Predict ROLL if INC=$30,000
Summarize and compare the two models.
Comment on significance

3. Object of class lm:
An object of class "lm" is a list containing at least the following components: coefficients a named vector of coefficients residuals the residuals, that is response minus fitted values. fitted.values the fitted mean values. rank the numeric rank of the fitted linear model. weights (only for weighted fits) the specified weights. df.residual the residual degrees of freedom. call the matched call. terms the terms object used. contrasts (only where relevant) the contrasts used. xlevels (only where relevant) a record of the levels of the factors used in fitting. offset the offset used (missing if none were used). y if requested, the response used. x if requested, the model matrix used. model if requested (the default), the model frame used.

4. Regression Exercises (lab2)
Using the EPI dataset find the single most important factor in increasing the EPI in a given region
Examine distributions across all the columns and build up an EPI “model”
We will be interpreting and discussing these models next module (week)!

5. Classification
abalone.csv dataset = predicting the age of abalone from physical measurements.
The age of abalone is determined by cutting the shell through the cone, staining it, and counting the number of rings through a microscope: a boring and time-consuming task.
Other measurements, which are easier to obtain, are used to predict the age.
Perform knn classification to get predictors for Age (Rings).

6. Clustering The Iris dataset (in R use data(“iris”) to load it)
The 5th column is the species and you want to find how many clusters without using that information
Create a new data frame and remove the fifth column
Apply kmeans (you choose k) with 1000 iterations
Use table(iris[,5],<your clustering>) to assess results

7. Return object
cluster A vector of integers (from 1:k) indicating the cluster to which each point is allocated. centers A matrix of cluster centres. totss The total sum of squares. withinss Vector of within-cluster sum of squares, one component per cluster. tot.withinss Total within-cluster sum of squares, i.e., sum(withinss). betweenss The between-cluster sum of squares, i.e. totss-tot.withinss. size The number of points in each cluster.

8. K-Means Algorithm: Example Output

9. Describe v. Predict

10. Predict = Decide

11. Contingency table

12. Classification or clustering on nyt dataset(s)
"Age","Gender","Impressions","Clicks","Signed_In"
36,0,3,0,1
73,1,3,0,1
30,0,3,0,1
49,1,3,0,1
47,1,11,0,1
47,0,11,1,1
(nyt datasets)
Model e.g.: If Age<45 and Impressions >5 then Gender=female (0)
Age ranges? 41-45, 46-50, etc?

13. Contingency tables
> table(nyt1$Impressions,nyt1$Gender) #
Contingency table - displays the (multivariate) frequency distribution of the variable.
Tests for significance (not now)
> table(nyt1$Clicks,nyt1$Gender)

14. Classification Exercises (group1/lab2_knn1.R)
> nyt1<-read.csv(“nyt1.csv") > nyt1<-nyt1[which(nyt1$Impressions>0 & nyt1$Clicks>0 & nyt1$Age>0),] > nnyt1<-dim(nyt1)[1] # shrink it down! > sampling.rate=0.9 > num.test.set.labels=nnyt1*(1.-sampling.rate) > training <-sample(1:nnyt1,sampling.rate*nnyt1, replace=FALSE) > train<-subset(nyt1[training,],select=c(Age,Impressions)) > testing<-setdiff(1:nnyt1,training) > test<-subset(nyt1[testing,],select=c(Age,Impressions)) > cg<-nyt1$Gender[training] > true.labels<-nyt1$Gender[testing] > classif<-knn(train,test,cg,k=5) # > classif > attributes(.Last.value) # interpretation to come!

15. K Nearest Neighbors (classification)
> nyt1<-read.csv(“nyt1.csv")
… from week 3 lab slides or scripts
> classif<-knn(train,test,cg,k=5) #
> head(true.labels)
[1]
> head(classif)
[1]
Levels: 0 1
> ncorrect<-true.labels==classif
> table(ncorrect)["TRUE"] # or > length(which(ncorrect))
> What do you conclude?

16. Weighted KNN…
require(kknn) data(iris) m <- dim(iris)[1] val <- sample(1:m, size = round(m/3), replace = FALSE, prob = rep(1/m, m)) iris.learn <- iris[-val,] iris.valid <- iris[val,] iris.kknn <- kknn(Species~., iris.learn, iris.valid, distance = 1, kernel = "triangular") summary(iris.kknn) fit <- fitted(iris.kknn) table(iris.valid$Species, fit) pcol <- as.character(as.numeric(iris.valid$Species)) pairs(iris.valid[1:4], pch = pcol, col = c("green3", "red”)[(iris.valid$Species != fit)+1])

17. summary
Call:
kknn(formula = Species ~ ., train = iris.learn, test = iris.valid, distance = 1, kernel = "triangular")
Response: "nominal"
fit prob.setosa prob.versicolor prob.virginica
1 versicolor
2 versicolor
3 versicolor
setosa
5 virginica
6 virginica
setosa
8 versicolor
9 virginica
10 versicolor
virginica
......

18. table
fit setosa versicolor virginica setosa versicolor virginica

19. pcol <- as.character(as.numeric(iris.valid$Species))
pairs(iris.valid[1:4], pch = pcol, col = c("green3", "red”)[(iris.valid$Species != fit)+1])

20. Ctrees?
We want a means to make decisions – so how about a “if this then this otherwise that” approach == tree methods, or branching.
Conditional Inference – what is that?
Instead of: if (This1 .and. This2 .and. This3 .and. …)

21. Decision tree classifier

22. Conditional Inference Tree
> require(party) # don’t get me started! > str(iris) 'data.frame': 150 obs. of 5 variables: $ Sepal.Length: num $ Sepal.Width : num $ Petal.Length: num $ Petal.Width : num $ Species : Factor w/ 3 levels "setosa","versicolor",..: > iris_ctree <- ctree(Species ~ Sepal.Length + Sepal.Width + Petal.Length + Petal.Width, data=iris)

23. Ctree
> 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

24. plot(iris_ctree)
> plot(iris_ctree, type="simple”) # try this

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

26. But the means for branching..
Do not have to be threshold based ( ~ distance)
Can be cluster based = I am more similar to you if I possess these attributes (in this range)
Thus: trees + cluster = hierarchical clustering
In R: hclust (and others) in stats package

27. Try hclust for iris

28. gpairs(iris)

29. Better scatterplots
install.packages("car") require(car) scatterplotMatrix(iris)

30. splom(iris) # default

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

34. Shift the dataset…

35. Hierarchical clustering
> d <- dist(as.matrix(mtcars)) > hc <- hclust(d) > plot(hc)

36. Data(swiss) - pairs
pairs(~ Fertility + Education + Catholic, data = swiss, subset = Education < 20, main = "Swiss data, Education < 20")

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

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

39. scatterplotMatrix

40. require(lattice); splom(swiss)

41. Start collecting Your favorite plotting routines
Get familiar with annotating plots

42. Assignment 3
Preliminary and Statistical Analysis. Due February % (written)
Distribution analysis and comparison, visual ‘analysis’, statistical model fitting and testing of some of the nyt2…31 datasets.
See LMS … for Assignment and details.