Question
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)
\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)
Answers
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Answered by
GPT 3.5
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.
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.
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