Problem Description
Figure 1 illustrates a scatter plot of 64 pairs of data-points for 2 variables that is, average rainfall (mm) in July and January for 64 selected places. See attached text le of raw data: 2018-AvgRainfall(mm).
Implement (in C++) a PCA algorithm [Lever et al., 2017], [Smith, 2002], to nd the two (2) principal components of this data-set. Results should answer the following questions:
What are the Eigenvalues for the principal components 1 and 2?
What are the Eigenvectors for the principal components 1 and 2 (showing July and January component values for each)?
What is the total variance?
What proportion (as a percentage) of total variance do principal compo-nents 1 and 2 "explain"?
Figure 1: Average rainfall (mm) for selected places in January and July, 2018.
In a ZIP le, place the source code, make le, and output text le (answers to questions 1 4). Upload the ZIP le to Vula before 10.00 AM, Friday, 24 August.
References
[Lever et al., 2017] Lever, J., Krzywinski, M., and Altman, N. (2017). Points of signi cance: Principal component analysis. Nature Methods, 14(1):641{642.
[Smith, 2002] Smith, L. (2002). A tutorial on Principal Components Analysis.
On Vula.
