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05-student-guide.Rmd

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 The first PCs will capture most heterogeneity (and thus most of the signal) in our high-dimensional dataset by definition, while the variation in later PCs will mostly represent noise. Thus, we can use the first PCs to both examine structure in our dataset as well as for downstream analyses to reduce computational work and improve the fit of our statistical models.
 
 
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 GOING DEEPER: The math behind PCA
 
 PCA is a method of matrix factorization. Essentially, the PCA approach allows a researcher to break down (or decompose) a large data matrix into smaller constituent parts (similar to the way we can break the number 30 into the factors 5 and 6). Each smaller matrix can be summarized by a vector, called the eigenvector. This vector can be resized; how much it is resized can be summarized by a number called the eigenvalue. You can also think of the eigenvalue as the variance of the eigenvector.