3(a). Consider the two-dimensional dataset of size 4 consisting of 21 = (+3,0) r2 = (-3,0) x3 = (0, +1) 24 = (0,-1). %3D %3D Show how we could use PCA to reduce this to a one-dimensional dataset. What would the dimension-reduced versions of r1, 12, 23, and r4 be?

Computer Networking: A Top-Down Approach (7th Edition)
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ISBN:9780133594140
Author:James Kurose, Keith Ross
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Chapter1: Computer Networks And The Internet
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3(a). Consider the two-dimensional dataset of size 4 consisting of
21 = (+3,0)
x2 = (-3,0)
23 = (0, +1)
= (0,-1).
%3D
T4
Show how we could use PCA to reduce this to a one-dimensional dataset. What would the
dimension-reduced versions of r1, r2, x3, and r4 be?
3(b). Your friend Claudio claims that dimension reduction via PCA is continuous everywhere:
that is, that no matter what the dataset looks like, a small change in the input dataset can't result
in a large change in the subspace selected by PCA or the output of PCA. Is Claudio correct?
Explain.
Transcribed Image Text:3(a). Consider the two-dimensional dataset of size 4 consisting of 21 = (+3,0) x2 = (-3,0) 23 = (0, +1) = (0,-1). %3D T4 Show how we could use PCA to reduce this to a one-dimensional dataset. What would the dimension-reduced versions of r1, r2, x3, and r4 be? 3(b). Your friend Claudio claims that dimension reduction via PCA is continuous everywhere: that is, that no matter what the dataset looks like, a small change in the input dataset can't result in a large change in the subspace selected by PCA or the output of PCA. Is Claudio correct? Explain.
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