Decision Surfaces

from Lecture 1, ECE662, Spring 2010

• The primary question that we must ask when working with decision surfaces is 'which line are we going to draw?'
  • Hyperplane surfaces
    • They are the easiest surfaces to draw
    • Reasonably 'easy' to define mathematically
    • May not be the best solution to the problem because of limitations to flexibility
    • 2D: straight lines
    • 3D: planes
    • ND: "Linear subspace of dimension n-1 in an d-dim space"
  • Curved decision surfaces
    • Defined by higher dim polynomials
    • The greater the degree, the greater the freedom
    • Harder to define mathematically
  • More realistic cases than simply defining gender based on hair length
    • It is difficult to define straight lines because a binary option does not exist
    • To truly understand this, learn about algebraic geometry (see the section on this topic below)
  • Varieties_OldKiwi are often used to define Decision Surfaces. A hyperplane_OldKiwi is an example of a variety.
  • Decision Surfaces are defined by discriminant function_OldKiwis. For example, hyperplanes are defined by a linear combination of the parameters.

Algebraic Geometry

• Studies the geometry of zero set polynomials
• This means that the set of all points that simultaneously satisfy one or more polynomial equations.
• Uses geometry of separation or surfaces described by polynomials
• Leads to the discussion of variety below

See Also

• Discriminant Functions

Back to Lecture 1, ECE662, Spring 2010