We can determine the direction of largest variance without computation by visually inspecting the data points.
In this case, the two data points are (0,1) and (0,-1), which lie on a vertical line. Since the points are symmetric about the x-axis, the direction of largest variance is also vertical, along the y-axis.
Therefore, the direction of largest variance (PC1) is (0,1), which is the second option.
Given two data points in 2 dimensions:
\displaystyle \displaystyle \mathbf{x}^{(1)} \displaystyle = \displaystyle (x^{(1)}, y^{(1)})= (0,1)
\displaystyle \mathbf{x}^{(2)} \displaystyle = \displaystyle (x^{(2)}, y^{(2)})=(0,-1)
Notice that this sample is already centered, with sample mean 0 in both x- and y- coordinates.
Without computation, find the direction of largest variance. (This is the first principal component \text {PC1}.
(1,0)
(0,1)
(1,1)
1 answer
1 answer