2. Social Media Application

4. Goal: Data Reduction for Data Visualization

5. People Variables CLUSTER ANALYSIS FACTOR ANALYSIS Variable/Dimension Reduction Cluster and Factor Analysis

6. For car buying, what matters to customers?

7. Brainstorm: Car Purchase

8. Surveys

9. QRate on a scale of 1-Low to 9-High (randomized list) Shopper#1New BMW 1971 Olds 442 Conv. 1Initial Price934 2Style789 3# of Miles on Car794 4Reliability762 5Color579 6Comfort675 7Horsepower269 8Safety671 9Financing Terms752 10Country Origin177 11Drive Type (Front, 4WD)446 12Miles Per Gallon (MPG)675 13Warranty Coverage452 Survey: Attribute Ratings Many more features, options….

10. QRate on a sale of 1- 9 1Initial Price 2Style 3# of Miles on Car 4Reliability 5Color 6Comfort 7Horsepower 8Safety 9Financing Terms 10Country Origin 11Drive Type (Front, 4WD) 12Miles Per Gallon (MPG) 13Warranty Coverage Survey: Attribute Ratings 12345678910101 1212 1313

11. cor(data, digits=2) Correlation Matrix

13. install.packages("corrgram") library(corrgram) corrgram(data)

14. Factor Analysis / Variable Reduction Correlation Matrix Correlated variables are grouped together and separated from other variables with low or no correlation Factor Analysis

15. F1 Factor Analysis F2FN …. F3

16. First & Second Principal Components Z 1 and Z 2 are two linear combinations. Z 1 has the highest variation (spread of values) Z 2 has the lowest variation 16

17. F1 b’s  Factor Loadings Factor Analysis F2FN …. F3

19. Packages LibraryPC MethodRotationPlot psychfa()YesNo principal() princomp()NoYes

20. Principal Components Analysis

21. Model model <- princomp(data, cor=TRUE) summary(model) biplot(model)

22. Output # scree plot plot(fit,type="lines")

23. Psych Package

24. Psych Package – fa library(psych) rmodel <- fa(r = corMat, nfactors = 3, rotate = “none", fm = "pa")

25. Each variable (circle) loads on both factors and there is no clarity about separating the variables into different factors, to give the factors useful names. Factor 2 Factor 1 Rotation Rotations Courtesy of Professor Paul Berger

26. 26 “CLASSIC CASE” After rotation of ~45 0 NOW, all variables are loading on one factor and not at all the other; This is an overly “dramatic” case. Not Correlated  Orthogonal Varimax = Orthogonal Rotation Rotation Rotations Courtesy of Professor Paul Berger

27. Psych Package – fa library(psych) rmodel <- fa(r = corMat, nfactors = 3, rotate = "oblimin", fm = "pa")

28. Psych Package – principal library(psych) fit <- principal(ratings6, nfactors=4, rotate=“null")

29. Psych Package – principal library(psych) fit <- principal(ratings6, nfactors=4, rotate="varimax“) corrgram(ratings6[,(1,2,9,12,3,4,6,8,10,5,11,7,13)]) Orthogonal / No Correlation

30. 3 Factor vs. 4 Factor

31. Style Comfort Color Upgrade Packages Reliability Safety Country Origin Horsepower Nice Dash Miles Per Gallon Initial Price # of Miles on Car Financing Options Aaahh!!! Factor Money

32. Perceptual Map Factor Loadings Brand Ratings Weights Average Variance

33. Which One? Which Car? Price $$$ $ Sweet!!!BORING Aaaah factor…

34. Factor Analysis Recap

35. Dimensionality Reduction Applications Algorithms