Quiz4

1.

Your dataset has d binary attributes. Which of the following best describe the points?

  • ☐ The origin in d-dimensions
  • ☑ The corners of a d-dimensional hypercube
  • ☐ The surface of a d-dimensional hypershere
  • ☐ The shell of a d-dimensional hypersphere

2.

As \(d \rightarrow \infty,\) the volume of a unit hypershere goes to

  • ☐ \(\infty\)
  • ☐ 1
  • ☐ Correct!
  • ☐ 0

3.

As \(d \rightarrow \infty\), which of the following is false?

  • ☑ The probability of sampling points near the origin is high
  • ☐ The volume of a unit hypercube is 1
  • ☐ The volume of a hypercube with sides of length 2 goes to ∞
  • ☐ The "corners" of a hypercube occupies more space than the inscribed hypercube

4.

In d-dimensional space, how many orthogonal axes do we have in addition to the major axes?

  • ☐ \(\mathcal{O}(d)\)
  • ☐ \(\mathcal{O}(d^2)\)
  • ☑ \(\mathcal{O}(2^d)\)
  • ☐ \(\mathcal{O}(d^3)\)

5.

A unit hypercube in 2D is best described as:

  • ☐ a line with length = 1
  • ☐ a circle with radius = 1
  • ☑ a square with side = 1
  • ☐ a circle with diameter = 1