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CSC3022H ML1-Principal Component Analysis (PCA) Solved

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thatFigure is, average 1 illustrates rainfall a  (scattermm) in plot July of  and64 pairs January of data-points for 64 selected for 2  places.variables See −  attached text file of raw data: 2018-AvgRainfall(mm).

Implement (in C++) a PCA algorithm [Lever et al., 2017], [Smith, 2002], to find the covariance matrix and two (2) principal components of this data-set. Results should answer the following questions:

  1. What are the Eigenvalues for the principal components 1 and 2?
  2. What are the Eigenvectors for the principal components 1 and 2 (showingJuly and January component values for each)?
  3. Compute the values for the covariance matrix.
  4. What is the total variance?
  5. What proportion (as a percentage) of total variance do principal components 1 and 2 ”explain”?

Figure 1: Average rainfall (mm) for selected places in January and July, 2018.

In a ZIP file, place the source code, makefile, and output text file (answers to questions 1 − 5). Upload the ZIP file to Vula before 10.00 AM, Monday, 5th of August.

References

[Lever et al., 2017] Lever, J., Krzywinski, M., and Altman, N. (2017). Points of significance: Principal component analysis. Nature Methods, 14(1):641–642.

[Smith, 2002] Smith, L. (2002). A tutorial on Principal Components Analysis. On Vula.

  • ML1-rwbesu.zip

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