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

Source: [1]

Global behavior

The global behavior of each layer of a neural network is to produce a linear combination of the weights its nodes produced. These weights model the connections between neurons, using an activation function, as detailled in the activation function section. Then all incoming weights to a node are summed, hence resulting in a linear combination of its inputs. Often, positive contributions are labelled "excitatory" and negative ones, "inhibitory".

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

Download: [2]

Get level 1 MERIS satellite data from [3] : filename = *.N1 (Uncompress the .bz2 file!)

BEAM > Processing > Water > Meris case 2 [Run]

In SeaDAS > File > Open… *.N1_C2IOP.dim