Difference between revisions of "Perceptron"
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The [[majority]] function is a special case of the perceptron, with threshold <math>t=0</math> and all weights <math>w_i</math> equal to each other. | The [[majority]] function is a special case of the perceptron, with threshold <math>t=0</math> and all weights <math>w_i</math> equal to each other. | ||
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== Properties == | == Properties == | ||
| + | * If all weights are equal to each other, the function is [[:Category:symmetric function | symmetric]]. | ||
| + | * If all weights are non-negative, or all weights are non-positive, the function is [[:Category:monotone function | monotone]]. | ||
| + | * The weights and threshold may be chosen so that the function is [[:Category:balanced function | balanced]]. | ||
* TODO | * TODO | ||
== References == | == References == | ||
<references/> | <references/> | ||
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| + | [[Category:symmetric function]] [[Category:balanced function]] [[Category:monotone function]] | ||
Revision as of 07:37, 1 October 2018
Definition
Let [math]n[/math] be a positive integer and let [math]t, \{w_i\}_{i=1}^n[/math] be real numbers. The perceptron function, or linear threshold function [math]f:\{-1,1\}^n \to \{-1,1\}[/math] with weights [math]w_i[/math] and threshold [math]t[/math] is defined as
[math] f(x) = \begin{cases} 1, & \text{if} ~ \sum_i w_i x_i \geq t \\ -1 & \text{otherwise} \end{cases}[/math]
The majority function is a special case of the perceptron, with threshold [math]t=0[/math] and all weights [math]w_i[/math] equal to each other.
Properties
- If all weights are equal to each other, the function is symmetric.
- If all weights are non-negative, or all weights are non-positive, the function is monotone.
- The weights and threshold may be chosen so that the function is balanced.
- TODO
