Question 1

Figure from the original question paper The covariance matrix of a mean centered dataset in $\mathbb{R}^3$ is: $$\mathbf{C} = \begin{bmatrix} 2.5 & 0 & 0.5 \\ 0 & 1 & 0 \\ 0.5 & 0 & 2.5 \end{bmatrix}$$ Standard PCA is performed on this dataset. If the first principal component is $\mathbf{w}_1 = \begin{bmatrix} -1/\sqrt{2} \\ 0 \\ -1/\sqrt{2} \end{bmatrix}$, which of the following is the variance along $\mathbf{w}_1$? Figure from the original question paper