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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 \(v_{1}\) = and the second principal component is \(v_{2}\) = . What is the new 2D coordinates (new features created by PCA) for the point \(x\) = ?