Using the Euclidean norm, compute a fairly dense sample of points on the unit sphere S =
Question:
Using the Euclidean norm, compute a fairly dense sample of points on the unit sphere S = {x ∈ R3 | ΙΙxΙΙ = 1}.
(a) Set μ = .95 in (8.78), and then find the principal components of your data set. Do they indicate the two-dimensional nature of the sphere? If not, why not?
(b) Now look at the subset of your data that is within a distance r > 0 of the north pole, i.e., ΙΙx − ( 0, 0, 1 )TΙΙ ≤ r, and compute its principal components. How small does r need to be to reveal the actual dimension of S? Interpret your calculations.
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Related Book For
Question Posted: