Answers.Body: <p>It depends on the accuracy you want. If you had 1 neuron, it could discern things across a line, if you have 2, you could solve things across 2 lines, etc. As you increase the number of neurons, you are increasing the number of discernible areas. As you increase the number of lines you can use to break up the input space, the lines can be placed to approximate any curve (sinusoidal) As the number of neurons approaches infinity, the accuracy of categorizing different inputs across this curve increases. </p>
  
  <p>Interestingly enough, if one graphed "Number of Neurons (x) vs Accuracy (y)", it would look sinusoidal. </p>
  
Answers.ContentLicense: CC BY-SA 3.0
Answers.CreationDate: 2016-12-24T19:17:32.087Z
Answers.LastActivityDate: 2017-01-28T04:43:31.133Z
Answers.LastEditDate: 2017-01-28T04:43:31.133Z
Answers.UserDisplayName: Jaden Travnik
Body: <p>A single neuron is capable of forming a decision boundary between linearly seperable data. Is there any intuition as to how many, and in what configuration, would be necessary to correctly approximate a sinusoidal decision boundary?</p>
  
  <p>Thanks</p>
  
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2017-01-25T04:08:25.933Z
Comments.Text: You can read about [ANFIS](ftp://ftp.unicauca.edu.co/Documentos_Publicos/Facultades/FIET/DEIC/Materias/Control%20Inteligente/clases_2006a/Parte%20III/clase%2023%20int/FVAnfis2.pdf).
Comments.UserDisplayName: kiner_shah
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2017-01-30T16:08:39.257Z
Comments.Text: Please consider to use radial basis neurons, instead of linear ones. They looks more accurate to your challenge. https://en.m.wikipedia.org/wiki/Radial_basis_function_network?wprov=sfla1
Comments.UserDisplayName: Szymon Dudziak
Tags: <neural-networks><hidden-layers><neurons><artificial-neuron>
Title: How many nodes/hidden layers are required to solve a classification problem where the boundary is a sinusoidal function?
UserDisplayName: Ian Larson
ThreadText: # How many nodes/hidden layers are required to solve a classification problem where the boundary is a sinusoidal function?
  
  (Asked by: username_0 on 2016-11-28)
  
  A single neuron is capable of forming a decision boundary between linearly seperable data. Is there any intuition as to how many, and in what configuration, would be necessary to correctly approximate a sinusoidal decision boundary?
  
  Thanks
  
  **Tags:** neural-networks, hidden-layers, neurons, artificial-neuron
  > **Comments:**
  > **username_1**: You can read about [ANFIS](ftp://ftp.unicauca.edu.co/Documentos_Publicos/Facultades/FIET/DEIC/Materias/Control%20Inteligente/clases_2006a/Parte%20III/clase%2023%20int/FVAnfis2.pdf).  
  > **username_2**: Please consider to use radial basis neurons, instead of linear ones. They looks more accurate to your challenge. https://en.m.wikipedia.org/wiki/Radial_basis_function_network?wprov=sfla1  
  
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  ## 1 answers
  
  ### Answer by username_3 on 2016-12-24. Score: 3
  
  It depends on the accuracy you want. If you had 1 neuron, it could discern things across a line, if you have 2, you could solve things across 2 lines, etc. As you increase the number of neurons, you are increasing the number of discernible areas. As you increase the number of lines you can use to break up the input space, the lines can be placed to approximate any curve (sinusoidal) As the number of neurons approaches infinity, the accuracy of categorizing different inputs across this curve increases.
  
  Interestingly enough, if one graphed "Number of Neurons (x) vs Accuracy (y)", it would look sinusoidal.
  
  
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