Linear Algebra: Principal Component Analysis Example Step-by-Step Explanation (2024)

Principal Component Analysis Example-Linear Algebra 2024

Principal component analysis is potentially valuable for applications in which most of
the variation, or dynamic range, in the data is due to variations in only a few of the new
variables, y1,.......;yp.
It can be shown that an orthogonal change of variables, X=PY, does not change
the total variance of the data. (Roughly speaking, this is true because left-multiplication
by P does not change the lengths of vectors or the angles between them. This means that if S=PDP^T , then 'total variance of {x1,.........,xp}= total variance of {y1,.......,yp}= tr(D)
The variance of yj is Λj , and the quotient Λj = tr.(S) measures the fraction of the total
variance that is “explained” or “captured” by yj.

For detailed description of how to find the mean and covariance matrix:

https://www.youtube.com/watch?v=4dzf-mccH6w
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https://eevibes.com/mathematics/linear-algebra/principal-component-analysis-dimensionality-reduction-with-examples/

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