Difference between revisions of "McCulloch-Pitts neuron"
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Revision as of 13:31, 22 April 2016
Definition
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| Diagram of a McCulloch-Pitts neuron |
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- Inputs: [ilmath](I_1,\ldots,I_n)\in\mathbb{R}^n[/ilmath]
- Usually each [ilmath]I_i[/ilmath] is confined to [ilmath][0,1]\subset\mathbb{R} [/ilmath] or [ilmath][-1,1]\subset\mathbb{R} [/ilmath]
- A set of weights, one for each input: [ilmath](w_1,\ldots,w_n)\in\mathbb{R}^n[/ilmath]
- A bias: [ilmath]\theta\in\mathbb{R} [/ilmath]
- An activation function, [ilmath]\mathcal{A}:\mathbb{R}\rightarrow\mathbb{R} [/ilmath]
- It is more common to see [ilmath]\mathcal{A}:\mathbb{R}\rightarrow[-1,1]\subset\mathbb{R} [/ilmath] or sometimes [ilmath]\mathcal{A}:\mathbb{R}\rightarrow[0,1]\subset\mathbb{R} [/ilmath] than the entire of [ilmath]\mathbb{R} [/ilmath]
The output of the neuron is given by:
- [math]\text{Output}:=\mathcal{A}\left(\sum_{i=1}^n(I_iw_i)+\theta\right)[/math]
References
- ↑ Neural Networks and Statistical Learning - Ke-Lin Du and M. N. S. Swamy
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