#reconstruction

Question 1: Select all that apply

mediumAI-checkedDimensionality Reduction

PCA reduces data $X$ with $d$ features to $Z = XW^\top$ with $k$ components and reconstructs $\hat{X} = ZW$ . Which statements are true? Select all that apply.

Each principal component is a $d$ -dimensional vector1
The first principal component is the direction with the highest variance in the data2
With $k = d$ , the transformed data $Z$ is exactly the same as $X$ 3
With $k = d$ , the reconstruction $\hat{X}$ is exactly the same as $X$ 4
It is best to pick $k$ as large as possible, so that most of the variance is kept5

Timed test