A$.1$ A$.$IE$333$ Data Science and Analytics $-$ Fall $2023$

Principal Component Analysis

Exercise:

Let's apply the Principal Component Analysis $($PCA$)$ on the

dataset with $10$ datapoints and $6$ columns given below. Since

the data has $6$ columns PCA will produce $6$ component vectors

each having $6$ columns. The component vectors given on the

right where each row corresponds to one vector. Scores are also

given on the right below the component vectors which we will

use in the example calculations below.

Dataset

$-31?$

$-10\mathrm{.}1$

Scores

PCA yields the following cumulative Explained Variance Ratio values:

Explained Variance Ratio measures how close we get to the original datapoints when we recreate them from the

component vectors. For example the second entry in the cumulative EVR table, $88\mathrm{.}59\%,$ means that if we use only

Question $2$

$2=|[40,,80],[20]|$ and

er$.$