How to improve RBF neural network interpolation ability?

Hi! There are 55 sampels, 2 inputs and 1 output. The predictions at samples are exellent, but the interpolation are very poor. How can I improve the RBF NN for interpolaion? Thanks!

clc,clear
  % samples
  data=[  550  50.9114   4.9195 
          550  53.9864   4.8926 
          550  56.3262   4.8658 
          550  58.5372   4.5436 
          550  59.9610   3.3356 
          525  46.3723   4.5689 
          525  50.6499   4.5638 
          525  52.6551   4.5607 
          525  53.6585   4.5168 
          525  54.0599   4.4899 
          525  55.1983   4.3624 
          525  56.7400   4.1007 
          525  57.6911   3.1812 
          500  42.2350   4.1678 
          500  47.3824   4.1141 
          500  49.3885   4.0604 
          500  52.0637   3.9597 
          500  54.0059   3.7248 
          500  54.6201   2.9664 
          475  38.7662   3.7584 
          475  43.1781   3.7248 
          475  45.1173   3.6711 
          475  47.5921   3.5638 
          475  50.0018   3.3557 
          475  50.6136   2.7383 
          450  34.8298   3.3423  
          450  37.0355   3.3356 
          450  40.7792   3.2886 
          450  43.9895   3.1678 
          450  45.7969   3.0000 
          450  46.3401   2.4899 
          400  28.0909   2.6476 
          400  31.3660   2.6376 
          400  33.3715   2.6107 
          400  35.9125   2.5436 
          400  37.9872   2.3826 
          400  38.5303   1.8792 
          350  19.5438   2.1477 
          350  24.2224   2.1544 
          350  27.0301   2.1208 
          350  29.2368   2.0604 
          350  31.1102   1.9463 
          350  31.7844   1.5973 
          300  14.3362   1.8054 
          300  19.3493   1.7852 
          300  21.4217   1.7651 
          300  23.4944   1.7181 
          300  25.2336   1.6376 
          300  26.5071   1.4228 
          250  11.1324   1.5369 
          250  15.6110   1.5101 
          250  17.2824   1.4832 
          250  18.3522   1.4631 
          250  19.2214   1.4430 
          250  21.8308   1.2819 ];

      p=data(:,[1 3])';
      t=data(:,2)';

      % input data for interpolation
      data1=[     425     2.3000
                  425     2.3500
                  425     2.4000
                  425     2.4500
                  425     2.5000
                  425     2.5500
                  425     2.6000
                  425     2.6500
                  425     2.7000
                  425     2.7500
                  425     2.8000
                  425     2.8500
                  425     2.9000
                  425     2.9500
                  425     3.0000  ];
       inputInterp=data1';

net=newrbe(p,t);
outTrain=sim(net,p);

% comparison of samples and predictions
plot(outTrain,p(2,:),'o',t,p(2,:),'r*')
hold on

% interpolation
% outInterp=sim(net,inputInterp);
% plot(outInterp,inputInterp(2,:),'o')

Answer 1

[Greg Heath]

1. Standarize the inputs to have zero-mean and unit-variance

2. Design two nets

    a. Odd indices  1:2:55
    b. Even indices 2:2:54

3. Determine good spread values

   a. Vary the spread on the odds and test with the evens
   b. Vary the spread on the evens and test with the odds
   c. Choose a good spread value for a combined data design

4. Test with the normalized non-design data1

Thank you for formally accepting my answer

Greg

[huan tu]

1. I have normalized the training data and the interpolation inputs, but the result is not as desired.
2. The variance in Guassian function is also called smoothing factor, is it the same meaning with 'spread' in function net=newrbe(P,T,spread)?
3. I don't understand how to design two nets to predict. Could you show me the codes if possible? Thank you very much!

clc,clear
% samples
data=[  550  50.9114   4.9195 
        550  53.9864   4.8926 
        550  56.3262   4.8658 
        550  58.5372   4.5436 
        550  59.9610   3.3356 
        500  42.2350   4.1678 
        500  47.3824   4.1141 
        500  49.3885   4.0604 
        500  52.0637   3.9597 
        500  54.0059   3.7248 
        500  54.6201   2.9664 
        475  38.7662   3.7584 
        475  43.1781   3.7248 
        475  45.1173   3.6711 
        475  47.5921   3.5638 
        475  50.0018   3.3557 
        475  50.6136   2.7383 
        450  34.8298   3.3423  
        450  37.0355   3.3356 
        450  40.7792   3.2886 
        450  43.9895   3.1678 
        450  45.7969   3.0000 
        450  46.3401   2.4899 
        400  28.0909   2.6476
        400  31.3660   2.6376 
        400  33.3715   2.6107 
        400  35.9125   2.5436 
        400  37.9872   2.3826 
        400  38.5303   1.8792 
        350  19.5438   2.1477 
        350  24.2224   2.1544 
        350  27.0301   2.1208 
        350  29.2368   2.0604 
        350  31.1102   1.9463 
        350  31.7844   1.5973 
        300  14.3362   1.8054 
        300  19.3493   1.7852 
        300  21.4217   1.7651 
        300  23.4944   1.7181 
        300  25.2336   1.6376 
        300  26.5071   1.4228 ];

    data=[data(:,1) data(:,3) data(:,2)];   
    p=data(:,[1 3])';
    t=data(:,2)';

      % interpolation validation
      data1=   [525.0000       46.3723
                525.0000       50.6499
                525.0000       52.6551
                525.0000       53.6585
                525.0000       54.0599
                525.0000       55.1983
                525.0000       56.7400
                525.0000       57.6911];
       dataInterp=data1';

[normInput,ps]=mapminmax(p);
[normTarget,ts]=mapminmax(t);

normInterp=mapminmax('apply',dataInterp,ps);

net=newrbe(normInput,normTarget);

normTrainOutput=sim(net,normInput);
normInterpOutput=sim(net,normInterp);

TrainOutput=mapminmax('reverse',normTrainOutput,ts);
InterpOutput=mapminmax('reverse',normInterpOutput,ts);

figure(1)
% plot predictions at samples
plot(p(2,:),TrainOutput,'o',...
     p(2,:),t,'r*',...
     dataInterp(2,:),InterpOutput,'o')
hold on 

% plot interpolation
plot(dataInterp(2,:),InterpOutput,'o')

     refInterp=[525.0000    4.5638   46.3723
                525.0000    4.5705   50.6499
                525.0000    4.5638   52.6551
                525.0000    4.5168   53.6585
                525.0000    4.4899   54.0599
                525.0000    4.3624   55.1983
                525.0000    4.1007   56.7400
                525.0000    3.1812   57.6911]';

plot(refInterp(3,:),refInterp(2,:),'rd','MarkerFaceColor','r')

Answer 2

[Greg Heath]

%1. I have normalized the training data and the interpolation inputs, but the result is not as desired.

That is no help. Show your new code.

% 2. The variance in Guassian function is also called smoothing factor, is it the same meaning with 'spread' in function net=newrbe(P,T,spread)?

No. Unfortunately, the help documentation on newrbe stinks. Try the doc command

doc newrbe

Maybe help and doc on the other rbf functions will help ... See Also

newgrnn | newpnn | newrb |

%3. I don't understand how to design two nets to predict. Could you show me the codes if possible? Thank you very much!

Very simple.

Just divide the data in half (odd/even). 

Loop over spread values
   Design a  net with the evens 
   Test with the odds 
   Choose the best spread value

 Repeat with evens and odds reversed in design and test roles.

 Combine those 2 "best" spread values

 Use the combined value to design a net with all of the data.

 Now test all 3 nets on data1.

Thank you for formally accepting my answer

Greg

[huan tu]

I found following describtion by searching 'rbf spread' in matlab help browser: All of the radial basis functions also have an associated width parameter 'sigma',which is related to the spread of the function around its center. Selecting the box in the model setup provides a default setting for the width. The default width is the average over the centers of the distance of each center to its nearest neighbor. This is a heuristic given in Hassoun (see References) for Gaussians, but it is only a rough guide that provides a starting point for the width selection algorithm.

Does it mean 'spread' is start value for training the 'variance' in RBF learning algorithm? Or something else?

[Greg Heath]

No. Spread stays constant. I vary it ( and most trial and error searches) by using a geometric grid [ ... 0.25, 0.5, 1, 2, 4, ...] for multipliers of the default value given in the documentation.

For each value I create 10 designs by using different random initial weights.

After debugging, the code should run in less than a few minutes.

You can probably find something useful by searching on

   greg spread

HTH

Greg