Utilisateur:Arbg0002/brouillons/réseaux de neurones

Neural networks

Pre-processing

• Data exploration (clean-up)
• Data transformation
• Outlier detection and removal
• Data normalization, one of:
  • Min-Max normalization: linear scaling into a data range, typically [0,1]
  • Zscore normalization: input variable data is converted into zero mean and unit variance
  • Sigmoidal normalization: nonlinear transformation of the input data into the range [-1,1], with a sigmoid function
  • Other normalization: e.g. if a variable is exponentially distributed, take the logarithm
• Data analysis
• Validation of results

Activation function

The activation function is alike <math>\phi(v_i)=U(v_i)</math>, where <math>U</math> is the Heaviside step function.

• normalizable sigmoid activation function <math>\phi(v_i)=U(v_i)\tanh(v_i)</math>, where the hyperbolic tangent function can be replaced by a sigmoid function
• gaussian function: <math>\,\phi(v_i)=\exp\left(-\frac{\|v_i-c_i\|^2}{2\sigma^2}\right)</math>
• multiquadratic function: <math>\,\phi(v_i)=\sqrt{\|v_i-c_i\|^2 + a^2}</math>
• inverse multiquadratic function: <math>\,\phi(v_i)=(\|v_i-c_i\|^2 + a^2)^{-1/2}</math> where <math>c_i</math> is the vector representing the function center and <math>a</math> and <math>\sigma</math> are parameters affecting the spread of the radius

Example: BEAM

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