Scilab Function
Last update : 19/6/2006

ANN_OIPDERIV - Function to estimate input variables influence on one output variable based on ANN partial derivative

Calling Sequence

[CI,[PD]]=ANN_OIPDERIV(IN,Nhid,W)

Parameters

Description

The activation function of the hidden layer is the hyperbolic tangent and the identity function for the output layer.

The network should have only ONE output.

The values of CI indicates the relative importance of inputs into output calculation.

Examples

    // INPUT
    t=1:0.03:10;
    // Two variables : first can explain output values, second is only a random sample : 
    IN  = [sin(t)./(t+%eps)+rand(1,size(t,2))/10;rand(1,size(t,2))/2];
    TARG= [sin(t)+rand(1,size(t,2))/20];
    
    // Network calibration (10 repetitions, 30 epochs, 4 hidden neurons)
    Nhid=4;
    ChemRAND  = 'C:\_JUL\!UTILS\sources\RAND.txt';
    [W,OUT,C,RMSE,IN_Stat,TARG_Stat]=ANN_REPET(IN,TARG,Nhid,ChemRAND,10,30);
    
    [CI,PD]=ANN_OIPDERIV(IN,Nhid,ANN_CONV_W(W(:,3),size(IN,1),Nhid,1,'vector'));
    // Here : 
    //  CI(1) = 857.57
    //  CI(2) = 1.16    >> Second variable has no impact on output variable 
    
    // Results
    subplot(2,1,1),plot2d(t,[TARG' OUT(:,3)]);legends(['Target' 'Network output'],1:2,'lr');
    subplot(2,1,2),plot2d(t,PD');legends(['Part. der. with resp. to 1st var.' 'Part. der. with resp. to 2nd var.'],1:2,'ul');
  

See Also

ANN_CONV_W ,   ANN_JACOB ,   ANN_NORM ,   ANN_LMBR ,   ANN_SIM ,  

Authors

Julien Lerat CEMAGREF Antony, HBAN Unit, julien.lerat@cemagref.fr

Bibliography

MacKay, Neural Computation, vol. 4, no. 3, 1992, pp. 415-447. Foresee and Hagan, Proceedings of the International Joint Conference on Neural Networks, June, 1997.