📗 The quizzes must be completed during the lectures and submitted on TopHat: Link. No Canvas submissions are required. The grades will be updated by the end of the week on Canvas.
📗 Please submit a regrade request if (i) you missed a few questions because you are late or have to leave during the lecture; (ii) you selected obviously incorrect answers by mistake (one or two of these shouldn't affect your grade): Link
The following questions may appear as quiz questions during the lecture. If the questions are not generated correctly, try refresh the page using the button at the top left corner.
📗 [4 points] What is the projected variance of and onto the principal component ? Use the MLE (Maximum Likelihood Estimate) formula for the variance: \(\sigma^{2} = \dfrac{1}{n} \displaystyle\sum_{i=1}^{n} \left(x_{i} - \mu\right)^{2}\) with \(\mu = \dfrac{1}{n} \displaystyle\sum_{i=1}^{n} x_{i}\).
📗 Answer: .
📗 [2 points] You performed PCA (Principal Component Analysis) in \(\mathbb{R}^{3}\). If the first principal component is \(u_{1}\) = \(\approx\) and the second principal component is \(u_{2}\) = \(\approx\) . What is the new 2D coordinates (new features created by PCA) for the point \(x\) = ?
📗 In the diagram, the black axes are the original axes, the green axes are the PCA axes, the red vector is \(x\), the red point is the reconstruction \(\hat{x}\) using the PCA axes.