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Sample Essay on Multilayer Perceptron

Author: Bernard Sanchez
by Bernard Sanchez
Posted: Aug 09, 2014

Multilayer perceptron refers to a network model of a feed-forward artificial neural that maps input data sets into a set of the right outputs. A multilayer perceptron is made of multiple nodes’ layers in directed graph that has every layer connected to the adjacent one. Every node is a processing element or neuron except the input nodes. Their activation function is nonlinear.

Supervised learning method is used by multilayer perception. This method is called backpropagation and it is used in network training. This model is a modification of a linear perceptron in its standard form and it is possible to differentiate non-linearly separable data.

Basically, multilayer perceptron is a definition of a family of several functions. The most classical instance of multilayer perceptron is the hidden layer of neural network that maps a d-vector to m-vector. An example of this is in regression where:

g (x) =b + W tanh (c+ V x)

  • x us the d-vector (input)
  • V is the k X d matrix (known as the input to the hidden weights)
  • C is k-vector (known as the hidden unit bias or offsets)
  • b is m-vector (known as the output bias or offset)
  • W is the m X h matrix (known as the hidden to the output weights)

If the activation function of a multilayer perceptron is linear in all the neurons meaning that a linear function maps weighted inputs to output in the neuron, then proving it using linear algebra is easy. This is because it is easy to prove that any number of the layers is possible to reduce to a standard input-output model with two layers.

Multiple layer perceptron is made different by the fact that the activation function used by a nonlinear is designed to model the action potentials frequency or biological neurons found in the brain or firing. Different ways are used in modeling the function.

Each multilayer perceptron has three or even more layers. These are the output and input layer with a single hidden layer or even more. The layers have nonlinearly activating nodes. This makes them to be considered as deep neural networks. Every node in the layers connects with some weight to the node in the adjacent layer. In some cases, input layer may not be included in counting the layers’ number. Nevertheless, this has led to a disagreement on whether the input layer should be included or not and the weight interpreted.

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Sources

http://www.iro.umontreal.ca/~bengioy/ift6266/H12/html/mlp_en.html

http://en.wikipedia.org/wiki/Multilayer_perceptron

http://www.hiit.fi/u/ahonkela/dippa/node41.html

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Author: Bernard Sanchez

Bernard Sanchez

Member since: Aug 08, 2014
Published articles: 5

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