Data Structures & Algorithms
Homework 5: Data Reduction: PCA in R
To complete this homework you will have to use R and R-Studio. If you do not already have them, they are available at no charge from the following links:
R download: –
R-Studio download (choose the free desktop version: –
In this exercise we will build on the R skills you learned in Week 2 to perform a data reduction analysis using PCA. Recall that PCA tries to find the axes that contribute the most to the variation in the data – in this case, which axes best separate malignant from benign tumors.
IN ORDER TO RECEIVE FULL CREDIT you are expected to comment each code block, describing what it does in detail. You will have to research some of the R commands we use on your own so that you understand what they are doing. You will receive 40 pts for running the exercise and 60 pts for answering the questions at the bottom of the assignment. You must also submit your R script along with these answers!
Let’s get started!
- Launch R Studio. From the FILE menu choose NEW FILE -> RSCRIPT.
- Using the hashtag comment indicator, put your name and the date at the top of your script.
- The PCA plots we will generate require the factoextra package, so you should install it the same way you have installed R packages previously. Then add this line to your script to make sure it is loaded into memory for this analysis:
library(factoextra)
- Now let’s load the data set. We will be using the Wisconsin Breast Cancer Data Set from the UCI Machine Learning repository; this dataset contains 30 columns of numerical data that has been extracted from breast cancer slide images. In order to simplify the exercise, the data has been combined into a single .csv file (wcbd.csv) and is in the CLASS RESOURCES section of the classroom. Download it and put it on your desktop, then load it into R:
wbcd <- read.csv(‘~/Desktop/wcbd.csv’)
Also, you should understand what each of the commands here is doing – for example, what is read.csv doing?
HINT: if you type a command into the console window, RStudio will try to autocomplete the command and offer you guidance on what parameters the command needs – including a link to the built-in help. Try this out by typing just the first three letters of the order command into the console.
- Take a look at the data set. Notice that the first two columns are not “data” but are descriptive information which we will exclude from the analysis. That leaves 30 columns of data to reduce down to the most meaningful two which we can plot on a 2D plot.
Now let’s proceed. To make things easier we’ll create a new matrix, removing the ID column from the original data set, and then add that column back in but as the row names:
wbcd.data <- wbcd[,c(2:32)]
row.names(wbcd.data) <- wbcd$id
- To run the PCA we will invoke the prcomp function on the data:
wbcd.pca <- prcomp(wbcd.data[c(2:31)], center = TRUE, scale = TRUE)
- We now have our principal components. To display them you can enter this command:
summary(wbcd.pca)
- Plotting the data is a simple matter of feeding the PCA into factoextra along with some parameters. This works particularly well for this type of data; for general purpose plotting you should explore ggplot2, which is probably the most popular plotting package available for R. Go ahead
fviz_pca_ind(wbcd.pca, geom.ind = “point”, pointshape = 21,
pointsize = 2,
fill.ind = wbcd$diagnosis,
col.ind = “black”,
palette = “jco”,
addEllipses = TRUE,
label = “var”,
col.var = “black”,
repel = TRUE,
legend.title = “Diagnosis”) +
ggtitle(“2D PCA-plot from 30 feature dataset”) +
theme(plot.title = element_text(hjust = 0.5))
QUESTIONS TO ANSWER:
- (10 pts) How many dimensions are in the original dataset? How do you know?
- (10 pts) What the the “center = true” and “scale = true” flags tell prcomp to do?
- (10 pts) We used the statement wbcd.data[c(2:31)] in the PCA command. What does this command do? Why was it necessary?
- (10 pts) How many principle components did you find in total?
- (10 pts) How much variation do the first and second component combined account for?
- (10 pts) Does the plot you generated show a good separation of malignant from benign cases? Why or why not?
