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