PCA computation

Machine Learning for Marketing Analytics in R

Verena Pflieger

Data Scientist at INWT Statistics

Status quo

# Variances of all variables before any data preparation
lapply(dataCustomers, var)

$nOrders                        $salesOrdered
[1] 264.3989                           [1] 202384132

$nItemsOrdered                  $salesSold
[1] 506.5496                           [1] 9345112

$nItemsSold                     $returnRatio
[1] 56.35125                           [1] 0.0836261
...

Standardization

dataCustomers <- dataCustomers %>% scale() %>% as.data.frame()

# Check variances of all variables
lapply(dataCustomers, var)

$nOrders                        $salesOrdered
[1] 1                           [1] 1

$nItemsOrdered                  $salesSold
[1] 1                           [1] 1

$nItemsSold                     $returnRatio
[1] 1                           [1] 1
...

PCA computation

pcaCust <- prcomp(dataCustomers)
str(pcaCust, give.attr = FALSE)

List of 5
 $ sdev    : num [1:16] 2.1 1.84 1.3 1.2 1.12 ...
 $ rotation: num [1:16, 1:16] -0.439 -0.44 -0.33 -0.384 -0.352 ...
 $ center  : Named num [1:16] -4.66e-17 1.90e-17 -1.24e-18 ...
 $ scale   : logi FALSE
 $ x       : num [1:989, 1:16] -11.06 -1.67 0.53 -3.39 -3.81 ...

# Standard deviations
pcaCust$sdev %>% round(2)

 [1] 2.10 1.84 1.30 1.20 1.12 1.07 0.80 0.78 0.72 0.61 0.48 0.37 0.26
[14] 0.21 0.17 0.13

# Variances (Eigenvalues)
pcaCust$sdev ^ 2 %>% round(2)

 [1] 4.39 3.38 1.68 1.45 1.26 1.15 0.65 0.61 0.52 0.38 0.23 0.14 0.07
[14] 0.04 0.03 0.02

# Proportion of explained variance
(pcaCust$sdev ^ 2/length(pcaCust$sdev)) %>% round(2)

 [1] 0.27 0.21 0.10 0.09 0.08 0.07 0.04 0.04 0.03 0.02 0.01 0.01 0.00
[14] 0.00 0.00 0.00

Loadings and interpretation

# Loadings (correlations between original variables and components)
round(pcaCust$rotation[, 1:6], 2)

Values of the observations

# Value on 1st component for 1st customer
sum(dataCustomers[1,] * pcaCust$rotation[,1])

-11.05858

pcaCust$x[1:5, 1:6]

             PC1        PC2        PC3         PC4        PC5          PC6
[1,] -11.0585802  3.5750683 -4.1371495  0.28864769 -0.1045802  0.698612248
[2,]  -1.6734771 -1.6630208  0.9498452  0.14091195 -1.2760898 -0.006310673
[3,]   0.5303018 -0.4672193 -0.1918865  1.77466781  0.4623840 -0.037466682
[4,]  -3.3903118 -0.1274839  4.2217216  0.03710948 -0.1840454  0.164680941
[5,]  -3.8069613  5.3971530 -1.2241316 -0.38341585  0.9721412 -2.142731490

It's your turn!

Machine Learning for Marketing Analytics in R