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| + | [[Category:decision theory]] | ||
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| + | [[Category:pattern recognition]] | ||
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| + | =Decision Surfaces= | ||
| + | from [[Lecture_1_-_Introduction_OldKiwi|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?' | * The primary question that we must ask when working with decision surfaces is 'which line are we going to draw?' | ||
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** [[Varieties_OldKiwi]] are often used to define Decision Surfaces. A [[hyperplane_OldKiwi]] is an example of a variety. | ** [[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_OldKiwi]]s. For example, hyperplanes are defined by a linear combination of the parameters. | ** Decision Surfaces are defined by [[discriminant function_OldKiwi]]s. For example, hyperplanes are defined by a linear combination of the parameters. | ||
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== Algebraic Geometry == | == Algebraic Geometry == | ||
* Studies the geometry of zero set polynomials | * Studies the geometry of zero set polynomials | ||
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== See Also == | == See Also == | ||
| − | * [[Discriminant function_OldKiwi]] | + | * [[Discriminant function_OldKiwi|Discriminant Functions]] |
| + | ---- | ||
| + | [[Lecture_1_-_Introduction_OldKiwi|Back to Lecture 1, ECE662, Spring 2010]] | ||
Latest revision as of 10:43, 10 June 2013
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.
- Hyperplane surfaces
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
