Question-7

Consider the dataset made up of blue data-points in \(\displaystyle \mathbb{R}^{2}\) as given below. Four lines are drawn passing through the center of this dataset.

Which of the following are directions associated with the principal components (PCs) that result from performing PCA?

• \(\displaystyle ( 2)\) corresponds to the first PC and \(\displaystyle ( 4)\) corresponds to the second PC
• \(\displaystyle ( 4)\) corresponds to the first PC and \(\displaystyle ( 2)\) corresponds to the second PC
• \(\displaystyle ( 3)\) corresponds to the first PC and \(\displaystyle ( 1)\) corresponds to the second PC
• \(\displaystyle ( 1)\) corresponds to the first PC and \(\displaystyle ( 3)\) corresponds to the second PC

Answer

• \(\displaystyle ( 2)\) corresponds to the first PC and \(\displaystyle ( 4)\) corresponds to the second PC
• \(\displaystyle ( 4)\) corresponds to the first PC and \(\displaystyle ( 2)\) corresponds to the second PC
• \(\displaystyle ( 3)\) corresponds to the first PC and \(\displaystyle ( 1)\) corresponds to the second PC
• \(\displaystyle ( 1)\) corresponds to the first PC and \(\displaystyle ( 3)\) corresponds to the second PC

Solution

The direction of maximum variance is \(\displaystyle ( 2)\). This is the first PC. \(\displaystyle ( 4)\) is orthogonal to it and is the second PC.