2. [Prompt 2] Consider a dataset with n points and p=4 features which has a covariance matrix, Ex. The eigenvalues of Ex are given by A₁ = X₂ = 3 and A3 = A4 = 1. The associated eigenvectors are: $1 x1 O || 2 1 [1] 2 Using the top two principal components, which is a 2-dimensional reduction of the following data point: 1,42 = √/2 ° [3] 03 = 04 = √/2 0
2. [Prompt 2] Consider a dataset with n points and p=4 features which has a covariance matrix, Ex. The eigenvalues of Ex are given by A₁ = X₂ = 3 and A3 = A4 = 1. The associated eigenvectors are: $1 x1 O || 2 1 [1] 2 Using the top two principal components, which is a 2-dimensional reduction of the following data point: 1,42 = √/2 ° [3] 03 = 04 = √/2 0
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![2. [Prompt 2] Consider a dataset with n points and p = 4 features which has a covariance matrix, Ex. The eigenvalues of Ex are
given by A₁ = ₂ = 3 and X3 = A4 = 1. The associated eigenvectors are:
x1 =
O
1
0
0
O
121
[4]
H
O
° [1]
, 02
7/2
1
, Ф3
Using the top two principal components, which is a 2-dimensional reduction of the following data point:
=
0
,04 = √/2₂
>
0
0](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2dc327ef-0392-462a-929f-8eafe4e0a9fa%2F607ae8af-0e61-4147-93cd-b23b7c732831%2F5gyxboh_processed.png&w=3840&q=75)
Transcribed Image Text:2. [Prompt 2] Consider a dataset with n points and p = 4 features which has a covariance matrix, Ex. The eigenvalues of Ex are
given by A₁ = ₂ = 3 and X3 = A4 = 1. The associated eigenvectors are:
x1 =
O
1
0
0
O
121
[4]
H
O
° [1]
, 02
7/2
1
, Ф3
Using the top two principal components, which is a 2-dimensional reduction of the following data point:
=
0
,04 = √/2₂
>
0
0
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