Performing PCA in R
Linear Algebra for Data Science in R
Eric Eager
Data Scientist at Pro Football Focus
NFL Combine Data
head(select(combine, height:shuttle))
height weight forty vertical bench broad_jump three_cone shuttle
1 71 192 4.38 35.0 14 127 6.71 3.98
2 73 298 5.34 26.5 27 99 7.81 4.71
3 77 256 4.67 31.0 17 113 7.34 4.38
4 74 198 4.34 41.0 16 131 6.56 4.03
5 76 257 4.87 30.0 20 118 7.12 4.23
6 78 262 4.60 38.5 18 128 7.53 4.48
NFL Combine Data
prcomp(A)
Standard deviations (1, .., p=8):
[1] 46.7720885 6.6356959 4.7108443 2.2950226 1.6430770 0.2513368 0.1216908 0.1143365
Rotation (n x k) = (8 x 8):
PC1 PC2 PC3 PC4 PC5 PC6 PC7 PC8
height 0.042047079 -0.061885367 0.1454490039 -0.1040556410 -0.980792060 0.020679696 -6.155636e-03 0.0008055445
weight 0.980711529 -0.130912788 0.1270100265 0.0193388930 0.066908382 -0.008423587 6.988341e-04 0.0036087841
forty 0.006112061 0.012525260 0.0025260713 -0.0021291637 0.004096693 0.152469227 -2.539868e-01 -0.9549983725
vertical -0.062926466 -0.333556369 0.0398922845 0.9366594549 -0.074901137 0.012214516 7.045063e-03 -0.0070051256
bench 0.088291423 -0.313533433 -0.9363461471 -0.0745692157 -0.107188391 0.009167322 -8.604309e-05 -0.0048308793
broad_jump -0.156742686 -0.876925849 0.2904565302 -0.3252903706 0.126494599 0.013753112 -2.187651e-03 -0.0076907609
three_cone 0.007468520 0.014691994 0.0009057581 0.0003320888 0.020902644 0.894560357 -3.743559e-01 0.2427137770
shuttle 0.004518826 0.009863931 0.0023111814 -0.0094052914 0.004010629 0.419039274 8.917710e-01 -0.1700673446
NFL Combine Data
summary(prcomp(A))
Importance of components:
PC1 PC2 PC3 PC4 PC5 PC6 PC7 PC8
Standard deviation 46.7721 6.63570 4.71084 2.29502 1.64308 0.25134 0.12169 0.11434
Proportion of Variance 0.9672 0.01947 0.00981 0.00233 0.00119 0.00003 0.00001 0.00001
Cumulative Proportion 0.9672 0.98663 0.99644 0.99877 0.99996 0.99999 0.99999 1.00000
head(prcomp(A)$x[, 1:2])
PC1 PC2
[1,] -62.005067 -2.654645
[2,] 48.123290 6.693433
[3,] 3.732016 1.283046
[4,] -56.823742 -9.764098
[5,] 4.213670 -3.779862
[6,] 6.924978 -15.530509
head(cbind(combine[, 1:4], prcomp(A)$x[, 1:2]))
player position school year PC1 PC2
1 Jaire Alexander CB Louisville 2018 -62.005067 -2.654645
2 Brian Allen C Michigan St. 2018 48.123290 6.693433
3 Mark Andrews TE Oklahoma 2018 3.732016 1.283046
4 Troy Apke S Penn St. 2018 -56.823742 -9.764098
5 Dorance Armstrong EDGE Kansas 2018 4.213670 -3.779862
6 Ade Aruna DE Tulane 2018 6.924978 -15.530509
Things to Do After PCA
- Data wrangling/quality control
- Data visualization
- Unsupervised learning (clustering)
- Supervised learning (for prediction or explanation)
- Much more!
Example - Data Visualization
Let's practice!
Linear Algebra for Data Science in R
