Statistics for CSQuestion 5 Consider another dataset {x} consisting of 4-dimensional vectors. Given below are mean({x}) and thenormalized eigenvectors u; of Covmat({x}), arranged in order of decreasing eigenvalue. Also given is an item x₁ from thedataset.mean({x})=1111U₁-+0.5+0.5+0.5+0.5U₂ =+0.5-0.5-0.5+0.5U3 =+0.5+0.5-0.5-0.5U4 =+0.5-0.5+0.5-0.5X13357Suppose you project the dataset onto its first two principal components and plot the resulting projection on a pair of axes.What are the coordinates of the projected point that represents x₁?

Given the mean and the normalized eigenvectors of Covmat, arranged in order of decreasing eigenvalue. Given data set Here, as the eigenvectors are typically arranged in order of decreasing eigenvalues, they represent the principal components of the data.Now, the required principal components have 2nd and 3rd values as follows The formula to find the 2nd principal component is and 3rd principal is Hence the required 2nd and 3rd principal components are (1,-3).The plot is as followsThe coordinates of the projected point that represents the required 2nd and 3rd principal components are (1, -3)

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Statistics

Consider another dataset {x} consisting of 4-dimensional vectors. Given below are mean({x}) and the normalized eigenvectors u; of Covmat({x}), arranged in order of decreasing eigenvalue. Also given is an item x₁ from the dataset. mean({x}) u₁ +0.5 +0.5 +0.5 +0.5 U2 = +0.5 -0.5 -0.5 +0.5] U3 = +0.5 +0.5 -0.5 -0.5 U4 = +0.5 -0.5 +0.5 -0.5 X1 = 3 5 7 Suppose you project the dataset onto its first two principal components and plot the resulting projection on a pair of axes. What are the coordinates of the projected point that represents x₁?

Consider another dataset {x} consisting of 4-dimensional vectors. Given below are mean({x}) and the normalized eigenvectors u; of Covmat({x}), arranged in order of decreasing eigenvalue. Also given is an item x₁ from the dataset. mean({x}) u₁ +0.5 +0.5 +0.5 +0.5 U2 = +0.5 -0.5 -0.5 +0.5] U3 = +0.5 +0.5 -0.5 -0.5 U4 = +0.5 -0.5 +0.5 -0.5 X1 = 3 5 7 Suppose you project the dataset onto its first two principal components and plot the resulting projection on a pair of axes. What are the coordinates of the projected point that represents x₁?

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Author:Amos Gilat

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Question

Statistics for CS

Question 5

Consider another dataset {x} consisting of 4-dimensional vectors. Given below are mean({x}) and the
normalized eigenvectors u; of Covmat({x}), arranged in order of decreasing eigenvalue. Also given is an item x₁ from the
dataset.
mean({x})
=
1
1
1
1
U₁
-
+0.5
+0.5
+0.5
+0.5
U₂ =
+0.5
-0.5
-0.5
+0.5
U3 =
+0.5
+0.5
-0.5
-0.5
U4 =
+0.5
-0.5
+0.5
-0.5
X1
3
3
5
7
Suppose you project the dataset onto its first two principal components and plot the resulting projection on a pair of axes.
What are the coordinates of the projected point that represents x₁?

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