gasdemo.m

模糊逻辑工具箱 模糊逻辑工具箱 模糊逻辑工具箱 模糊逻辑工具箱 模糊逻辑工具箱

function slide=gasdemo
% This is a slideshow file for use with playshow.m and makeshow.m
% Too see it run, type 'playshow gasdemo', 

% Copyright (c) 1994-98 by The MathWorks, Inc.
% $Revision: 1.3 $
if nargout<1,
  playshow gasdemo
else
  %========== Slide 1 ==========

  slide(1).code={
   'a=imread(''gascover.jpg'', ''jpg'');',
   'image(a); colormap(gray); axis image;',
   'axis off;' };
  slide(1).text={
   'This slide show addresses the use of ANFIS function in the Fuzzy Logic Toolbox for predicting the MPG (miles per gallon) of a given automobile.'};

  %========== Slide 2 ==========

  slide(2).code={
   'a=imread(''carbrand.jpg'', ''jpg'');',
   'image(a); colormap(gray); axis image',
   'axis off',
   '' };
  slide(2).text={
   'Automobile MPG (miles per gallon)  prediction is a typical nonlinear regression problem, in which several attributes of an automobile''s profile information are used to predict another continuous attribute, that is, the fuel consumption in MPG. The training data is available from the UCI (Univ. of California at Irvine) Machine Learning Repository (http://www.ics.uci.edu/~mlearn/MLRepository.html). It contains data collected from automobiles of various manufactures and models, as shown in the next slide.'};

  %========== Slide 3 ==========

  slide(3).code={
   'a=imread(''gasdata.jpg'', ''jpg'');',
   'image(a); colormap(gray); axis image;',
   'axis off',
   '[data, input_name] = loadgas;',
   'trn_data = data(1:2:end, :);',
   'chk_data = data(2:2:end, :);' };
  slide(3).text={
   'The table shown above is several tuples from the MPG data set.  The six input attributes are no. of cylinders, displacement, horsepower, weight, acceleration, and model year; the output variable to be predicted is the fuel consumption in MPG. (The automobile''s manufacturers and models in the first column of the table are not used for prediction.  The data set is obtained from the original data file ''auto-gas.dat''. Then we partition the data set into a training set (odd-indexed tuples) and a checking set (even-indexed tuples), and use the function ''exhsrch'' to find the input attributes that have better prediction power for ANFIS modeling.'};

  %========== Slide 4 ==========

  slide(4).code={
   'exhsrch(1, trn_data, chk_data, input_name);',
   'winH1 = gcf;'
   ''};
  slide(4).text={
   'To select the best input attribute, ''exhsrch'' constructs six ANFIS, each with a single input attribute. The popped figure displays the result after executing exhsrch(1, trn_data, chk_data, input_name). Obviously, ''Weight'' is the most influential input attribute and ''Disp'' is the second one, etc.  The training and checking errors are comparable in size, which implies that there is no overfitting and we can select more input variables. Intuitively, we can simply select ''Weight'' and ''Disp'' directly.  However, this will not necessarily lead to a two-ANFIS model with the minimal training error.  To verify this, we can issue the command exhsrch(2, trn_data, chk_data, input_name) to select the best two inputs from all possible combinations.'};

  %========== Slide 5 ==========

  slide(5).code={
   'input_index = exhsrch(2, trn_data, chk_data, input_name);',
   'winH2 = gcf;'
   'new_trn_data = trn_data(:, [input_index, size(trn_data,2)]);',
   'new_chk_data = chk_data(:, [input_index, size(chk_data,2)]);' };
  slide(5).text={
   'The popped figure demonstrates the result of selecting two inputs. ''Weight'' and ''Year'' are selected as the best two input variables, which is quite reasonable.  The training and checking errors are getting distinguished, indicating the outset of overfitting.  As a comparison, let us use exhsrch to select three inputs'};

  %========== Slide 6 ==========

  slide(6).code={
   'exhsrch(3, trn_data, chk_data, input_name);',
   'winH3 = gcf;'
   ''};
  slide(6).text={
   'The popped figure demonstrates the result of selecting three inputs, in which ''Weight'', ''Year'', and ''Acceler'' are selected as the best three input variables.  However, the minimal training (and checking) error do not reduce significantly from that of the best 2-input model, which indicates that the newly added attribute ''Acceler'' does not improve the prediction too much.  For better generalization, we always prefer a model with a simple structure. Therefore we will stick to the two-input ANFIS for further exploration'};

  %========== Slide 7 ==========

  slide(7).code={
   'close(winH1); close(winH2); close(winH3);',
   'in_fis=genfis1(new_trn_data);',
   'mf_n = 2;',
   'mf_type = ''gbellmf'';',
   'epoch_n = 1;',
   'ss = 0.01;',
   'ss_dec_rate = 0.5;',
   'ss_inc_rate = 1.5;',
   'in_fismat = genfis1(new_trn_data, mf_n, mf_type);',
   '[trn_out_fismat trn_error step_size chk_out_fismat chk_error] = anfis(new_trn_data, in_fismat, [epoch_n nan ss ss_dec_rate ss_inc_rate], nan, new_chk_data, 1);',
   'for i=1:length(input_index),',
   'chk_out_fismat = setfis(chk_out_fismat, ''input'', i, ''name'', deblank(input_name(input_index(i), :)));',
   'end',
   'chk_out_fismat = setfis(chk_out_fismat, ''output'', 1, ''name'', deblank(input_name(size(input_name, 1), :)));',
   'gensurf(chk_out_fismat); colormap(''default'');',
   'set(gca, ''box'', ''on'');',
   'view(-22, 36);',
   'fprintf(''\nLinear regression with parameters:\n'');',
   'param= size(trn_data,2)',
   'A_trn = [trn_data(:, 1:size(data,2)-1) ones(size(trn_data,1), 1)];', 
   'B_trn = trn_data(:, size(data,2));',
   'coef = A_trn\B_trn;',
   'trn_error = norm(A_trn*coef-B_trn)/sqrt(size(trn_data,1));',
   'A_chk = [chk_data(:, 1:size(data,2)-1) ones(size(chk_data,1), 1)];', 
   'B_chk = chk_data(:, size(data,2));',
   'chk_error = norm(A_chk*coef-B_chk)/sqrt(size(chk_data,1));',
   'fprintf(''\nRMSE for training data: '');',
   'RMSE=trn_error', 
   'fprintf(''\nRMSE for checking data: '');',
   'RMSE = chk_error'
   };
  slide(7).text={
   'The input-output surface of the best two-input ANFIS model for MPG prediction is shown above. It is a nonlinear and monotonic surface, in which the predicted MPG increases with the increase in ''Weight'' and decrease in ''Year''. The training RMSE (root mean squared error) is 2.766; the checking RMSE is 2.995. In comparison, a simple linear regression using all input candidates results in a training RMSE of 3.452, and a checking RMSE of 3.444.'};

  %========== Slide 8 ==========

  slide(8).code={
   'watchon;',
   'epoch_n = 100;',
   '[trn_out_fismat trn_error step_size chk_out_fismat chk_error] = anfis(new_trn_data, in_fismat, [epoch_n nan ss ss_dec_rate ss_inc_rate], nan, new_chk_data, 1);',
   '[a, b] = min(chk_error);',
   'plot(1:epoch_n, trn_error, ''g-'', 1:epoch_n, chk_error, ''r-'', b, a, ''ko'');',
   'axis([-inf inf -inf inf]);',
   'title(''Training (green) and checking (red) error curve'');',
   'xlabel(''Epoch numbers'');',
   'ylabel(''RMS errors'');',
   'watchoff;'};
  slide(8).text={
   'The function exhsrch only trains each ANFIS for a single epoch in order to be able to find the right inputs shortly.  Now that the inputs are fixed, we can spend more time on ANFIS training.  The above plot is the error curves for 100 epochs of ANFIS training.  The green curve is the training errors; the red one is the checking errors. The minimal checking error occurs at about epoch 45, which is indicated by a circle.  Notice that the checking error curve is going up after 50 epochs, indicating that further training overfits the data and produce worse generalization'};

  %========== Slide 9 ==========

  slide(9).code={
   'gensurf(chk_out_fismat);',
   'set(gca, ''box'', ''on'');',
   'view(-22, 36);',
   ''};
  slide(9).text={
   'The snapshot of the two-input ANFIS at the minimal checking error has the above input-output surface. Both the training and checking errors are lower than before, but we can see some spurious effects at the far-end corner of the surface.  The elevated corner says that the heavier an automobile is, the more gas-efficient it will be. This is totally counter-intuitive, and it is a direct result from lack of data.'};

  %========== Slide 10 ==========
  slide(10).code={
   'plot(new_trn_data(:,1), new_trn_data(:, 2), ''go'', new_chk_data(:,1), new_chk_data(:, 2), ''rx'');',
   'axis([-inf inf -inf inf]);',
   'xlabel(deblank(input_name(input_index(1), :)));',
   'ylabel(deblank(input_name(input_index(2), :)));',
   'title(''Training (o) and checking (x) data'');',
   ''};
  slide(10).text={
   'This plot shows the data distribution. The lack of training data at the upper right corner causes the spurious ANFIS surface mentioned earlier.  Therefore the prediction by ANFIS should always be interpreted with the data distribution in mind.'};
end