Difference between revisions of "Perceptron"
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== Definition == | == 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 with weights <math>w_i</math> and threshold <math>t</math> is defined as | + | 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 \\ | <math> f(x) = \begin{cases} 1, & \text{if} ~ \sum_i w_i x_i \geq t \\ | ||
Revision as of 07:28, 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.
Depending on the choice of weights and threshold, the perceptron may be symmetric, balanced, or monotone.
Properties
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