Mathematics of neural networks in machine learning: Difference between revisions

Revision as of 18:42, 18 August 2019

Revision as of 18:50, 18 August 2019

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{{Main|Artificial neural network}}

An artificial neural network (ANN) combines biological principles with advanced statistics to solve problems in domains such as pattern recognition and game-play. ANNs adopt the basic model of neuron analogues connected to each other in a variety of ways.

== Structure ==

=== Neuron ===

A neuron with label <math>j</math> receiving an input <math>p_j(t)</math> from predecessor neurons consists of the following components:<ref name="Zell1994ch5.2">{{Cite book|url=http://worldcat.org/oclc/249017987|title=Simulation neuronaler Netze|last=Zell|first=Andreas|date=2003|publisher=Addison-Wesley|isbn=978-3-89319-554-1|edition=1st|language=German|trans-title=Simulation of Neural Networks|chapter=chapter 5.2|oclc=249017987}}</ref>

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An ''input neuron'' has no predecessor but serves as input interface for the whole network. Similarly an ''output neuron'' has no successor and thus serves as output interface of the whole network.

==== Propagation function ====

The ''propagation function'' computes the ''input'' <math>p_j(t)</math> to the neuron <math>j</math> from the outputs <math>o_i(t)</math>and typically has the form<ref name="Zell1994ch5.22">{{Cite book|url=http://worldcat.org/oclc/249017987|title=Simulation neuronaler Netze|last=Zell|first=Andreas|date=2003|publisher=Addison-Wesley|isbn=978-3-89319-554-1|edition=1st|language=German|trans-title=Simulation of Neural Networks|chapter=chapter 5.2|oclc=249017987}}</ref>

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=== Neural networks as functions ===

{{See also|Graphical models}}Neural network models can be viewed as defining a function that takes an input (observation) and produces an output (decision).