1. ) ( : - : . 1

2. - - - - - - - - 2

3. : 3

4. - Expert Systems . ) ( Expert Systems . - . : . . . . . . . . . . . . . . . . : . . : 4

5. . . . ) (classification : . . . . : . : . . . . . : Eliza : . . 5

6. . back tracking . :- . fever . cough . conjuctvitis . runny_nose . rash . measles :- . fever . headache . runny_nose . rash . german_measles 6

7. :- . fever . headache . body_ache . conjuctvitis . chills . sore_throat . cough . . flu :- . headache . sneezing . sore_throat . chills . runny_nose . common_cold :- . fever . swollen_glands . mumps 7

8. :- . fever . rash . body_ache . chills . chiken_pox 8

9. 9

10. prolog %MEDICAL DIAGNOSTIC SYSTEM %CHILDHOOD DISEASES %EXAMPLE ONLY NOT FOR MEDICAL USE domains disease=symbol symptom=symbol query=symbol replay=symbol database xpositive(symptom) xnegative(symptom) predicates nondeterm hypothesis(disease) nondeterm symptom(disease) go positive(query,symptom) clear_facts remember(symptom,replay) ask(query,symptom,replay) clauses go:%clearwindow, hypothesis(Disease),!, write("the patient probably has ",Disease), clear_facts. positive(_,Symptom):xpositive(Symptom),!. positive(Query,Symptom):not(xnegative(Symptom)), ask(Query,Symptom,Replay), Replay="y". 10

11. ask(Query,Symptom,Replay):write(Query), readln(Replay), remember(Symptom,Replay). remember(Symptom,"y"):asserta(xpositive(Symptom)). remember(Symptom,"n"):asserta(xnegative(Symptom)). clear_facts:retract(xpositive(_)),fail. clear_facts:retract(xnegative(_)),fail. clear_facts. symptom(fever):positive("Dos the patient have the fever (y/n)",fever). symptom(headache):positive("Dos the patient have the headache (y/n)",headache). symptom(body_ache):positive("Dos the patient have the body_ache (y/n)",body_ache). symptom(conjuctvitis):positive("Dos the patient have the conjuctvitis (y/n)",conjuctvitis). symptom(chills):positive("Dos the patient have the chills (y/n)",chills). symptom(sore_throat):positive("Dos the patient have the throat (y/n)",throat). symptom(couph):positive("Dos the patient have the couph (y/n)",couph). symptom(runny_nose):positive("Dos the patient have the runny_nose (y/n)",runny_nose). symptom(rash):positive("Dos the patient have the rash (y/n)",rash). 11

12. symptom(sneezing):positive("Dos the patient have the sneezing (y/n)",sneezing). %************************************************************ hypothesis(measles):symptom(fever), symptom(cough), symptom(conjuctvitis), symptom(runny_nose), symptom(rash). hypothesis(german_measles):symptom(fever), symptom(headache), symptom(runny_nose), symptom(rash). hypothesis(flu):symptom(fever), symptom(headache), symptom(body_ache), symptom(conjuctvitis), symptom(chills), symptom(sore_throat), symptom(couph), symptom(runny_nose). hypothesis(common_cold):symptom(headache), symptom(sneezing), symptom(sore_throat), symptom(chills), symptom(runny_nose). hypothesis(mumps):symptom(fever), symptom(swollen_glands). 12

13. hypothesis(chiken_pox):symptom(fever), symptom(rash), symptom(body_ache), symptom(chills). goal go. 13

14. : OR & NOR 41

15. . . . . . . . )( . )( . . . . fire pattern. . 51

16. firing rule . . . . . . . ) axon ( . . : 61

17. : . : the neuron as simple computing element . . . : sign function step function Hard limit function sigmoid function linear function soft limit function . ]5.0,5.0-[ 71

18. . . ) Yd(p : ,3,2,1=e(p) = Yd(p) Y(p) where p p p ) e(p ) Y(p ) .Y(p ) xi(p)* wi(p ) x(p ) xi(p ) wi(p ) . Y(p )xi(p ) wi(p . :Preceptron learning rule )Wi(p+1)= wi(p) +xi(p) e(p , learning rate : : w1,w2,,wn ]5.0,5.0-[ : ) x1(p),x2(p),xn(p ) . Yd(p 1=p n y sign xi wi 1i n step 81

19. : : )Wi(p+1)= wi(p) +Wi(p )Wi(p)= xi(p) e(p ) Wi(p p : p . 91

20. OR . 02

21. xor . . or or . 12

22. : NOR 22

23. Multilayer neural networks ) . (Perceptron multicouche : ) Input (layer ) .(Output layer . ) (Weight . . . . . . 32

24. . . : ,[-2.4/Fi ]2.4/Fi Fi i . . : ) x1(p),x2(p),xn(p )Yd,1(p) , Yd,2(p) ,.,Yd,n(p : n y ( p ) sigmoid xi ( p) wij ( p ) j j 1i n j sigmoid : m y ( p ) sigmoid x jk ( p) w jk ( p) k k 1i 42

25. m k sigmoid : : )k(p)= yk(p)[1-yk(p)] ek(p : ,3,2,1=ek(p) = Ydk(p) Yk(p) where p : )Wjk (p+1)= wjk(p) +Wjk (p )Wjk (p)= yj(p) k(p : )Wjk (p+1)= wjk(p) + yj(p) k(p : I ) j ( p ) y j ( p) [1 y j ( p)] k ( p ) w jk ( p 1k )Wij (p+1)= Wij (p) + Wij (p ) Wij (p) = Xi(p) j(p : p . 100.0 . 52

26. Code : % ================== % Filename: XOR_bp.m % ================== echo on; % Hit any key to define four 2-element input vectors denoted by "p". pause p=[1 0 1 0;1 1 0 0] % Hit any key to define ten 1-element target vectors denoted by "t". pause t=[0 1 1 0] % Hit any key to define the network architecture. pause s1=3; %Three neurons in the hidden layer s2=1; %One neuron in the output layer % Hit any key to create the network and initialise its weights and biases. pause net=newff([0 1;0 1],[s1,s2],{'tansig','purelin'},'traingd'); % Hit any key to set up the frequency of the training progress to be displayed, % maximum number of epochs, acceptable error, and learning rate. pause net.trainParam.show=1; progress net.trainParam.epochs=1000; net.trainParam.goal=0.001; net.trainParam.lr=0.1; % Number of epochs between showing the % Maximum number of epochs % Performance goal % Learning rate % Hit any key to train the back-propagation network. pause net=train(net,p,t); % Hit any key to see whether the network has learned the XOR operation. pause p=[1;1] a=sim(net,p) 26

27. % Hit any key to continue. pause p=[0;1] a=sim(net,p) % Hit any key to continue. pause p=[1;0] a=sim(net,p) % Hit any key to continue. pause p=[0;0] a=sim(net,p) echo off disp('end of XOR_bp') Output : 27

28. 28

29. 29

30. : GUI 03

31. . . - sm . . . . recurrent . neural network the hopfiled network . Output Signals 2y 2 2x yi i xi yn n xn Input Signals 1y 1 1x . 13

32. : n M Y1,Y2,,YM i j : M m1 y mi y mj , i j 0 ,i j w ij ymi ymj i,j : M T m m w y y MI 1m : . ym . : xm , j y m , j , i 1,2,...n; m 1,2,.., M n ) y mi sign ( wij xmj i 1j ..... .......... .......... .......... .......... .......... xm y m , m 1,2,..., M y m sign ( wx m ), m 1,2,..., M ymi i ym xmj j xm . 23

33. . : n ) x (prob : xym m=1,2,,M )( : j=1,2,,n xj(0) = xj n yi (0) sign( wij x j (0) i ).., i 1,2,..., n 1j )0( xj j x 0= yi(0) p i p 0= p : ) y (0) sign( wx(0) )( )y(p : n ) yi ( p 1) sign( wij x j ( p ) i 1j . : n yi ( p 1) sign( wij y j ( p ) i), i 1,2,..., n 1j : ) y ( p 1) sign( wy ( p ) 33

34. . . 43

35. Code (1): % ==================== % The Hopfield network % ==================== % =========================================================================== % Reference: Negnevitsky, M., "Artificial Intelligence: A Guide to Intelligent % Systems", Addison Wesley, Harlow, England, 2002. % Sec. 6.6 The Hopeld network % =========================================================================== % Hit any key to define two target fundamental memories to be stored % in the network as the two columns of the matrix T. pause T=[1 1 1;-1 -1 -1]' T= 1 -1 1 -1 1 -1 % Hit any key to plot the Hopfield state space with the two fundamental memories % identified by red markers. pause plot3(T(1,:),T(2,:),T(3,:),'r.','markersize',20) axis([-1 1 -1 1 -1 1]); axis manual; hold on; title('Representation of the possible states for the three-neuron Hopfield network') set(gca,'box','on'); view([37.5 30]); % Hit any key to obtain weights and biases of the Hopfield network. pause 35

36. net=newhop(T); % Hit any key to test the network with six unstable states represented as the % six-column matrix P. Unstable states are identified by blue markers. pause P=[-1 1 1;1 -1 1;1 1 -1;-1 -1 1;-1 1 -1;1 -1 -1]' P= -1 1 1 -1 1 1 -1 -1 1 -1 1 -1 1 1 -1 1 -1 -1 for i=1:6 a = {P(:,i)}; [y,Pf,Af]=sim(net,{1 10},{},a); record=[cell2mat(a) cell2mat(y)]; start=cell2mat(a); plot3(start(1,1),start(2,1),start(3,1),'b*',record(1,:),record(2,:),record(3,:)) drawnow; % Hit any key to continue. pause a = {P(:,i)}; [y,Pf,Af]=sim(net,{1 10},{},a); record=[cell2mat(a) cell2mat(y)]; start=cell2mat(a); plot3(start(1,1),start(2,1),start(3,1),'b*',record(1,:),record(2,:),record(3,:)) drawnow; % Hit any key to continue. 36

37. pause a = {P(:,i)}; [y,Pf,Af]=sim(net,{1 10},{},a); record=[cell2mat(a) cell2mat(y)]; start=cell2mat(a); plot3(start(1,1),start(2,1),start(3,1),'b*',record(1,:),record(2,:),record(3,:)) drawnow; % Hit any key to continue. pause a = {P(:,i)}; [y,Pf,Af]=sim(net,{1 10},{},a); record=[cell2mat(a) cell2mat(y)]; start=cell2mat(a); plot3(start(1,1),start(2,1),start(3,1),'b*',record(1,:),record(2,:),record(3,:)) drawnow; % Hit any key to continue. pause a = {P(:,i)}; [y,Pf,Af]=sim(net,{1 10},{},a); record=[cell2mat(a) cell2mat(y)]; start=cell2mat(a); plot3(start(1,1),start(2,1),start(3,1),'b*',record(1,:),record(2,:),record(3,:)) drawnow; % Hit any key to continue. pause 37

38. a = {P(:,i)}; [y,Pf,Af]=sim(net,{1 10},{},a); record=[cell2mat(a) cell2mat(y)]; start=cell2mat(a); plot3(start(1,1),start(2,1),start(3,1),'b*',record(1,:),record(2,:),record(3,:)) drawnow; % Hit any key to continue. pause Output(1) : 38

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42. Code(2) : function varargout = hopfieldNetwork(varargin) gui_Singleton = 1; gui_State = struct('gui_Name', mfilename, ... 'gui_Singleton', gui_Singleton, ... 'gui_OpeningFcn', @hopfieldNetwork_OpeningFcn, ... 'gui_OutputFcn', @hopfieldNetwork_OutputFcn, ... 'gui_LayoutFcn', [] , ... 'gui_Callback', []); if nargin && ischar(varargin{1}) gui_State.gui_Callback = str2func(varargin{1}); end if nargout [varargout{1:nargout}] = gui_mainfcn(gui_State, varargin{:}); else gui_mainfcn(gui_State, varargin{:}); end % End initialization code - DO NOT EDIT % --- Executes just before hopfieldNetwork is made visible. function hopfieldNetwork_OpeningFcn(hObject, eventdata, handles, varargin) % Choose default command line output for hopfieldNetwork handles.output = hObject; N = str2num(get(handles.imageSize,'string')); handles.W = []; handles.hPatternsDisplay = []; % Update handles structure guidata(hObject, handles); % --- Outputs from this function are returned to the command line. function varargout = hopfieldNetwork_OutputFcn(hObject, eventdata, handles) % varargout cell array for returning output args (see VARARGOUT); % hObject handle to figure % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) % Get default command line output from handles structure varargout{1} = handles.output; % --- Executes on button press in reset. function reset_Callback(hObject, eventdata, handles) % cleans all data and enables the change of the number of neurons used for n=1 : length(handles.hPatternsDisplay) delete(handles.hPatternsDisplay(n)); 42

43. end handles.hPatternsDisplay = []; set(handles.imageSize,'enable','on'); handles.W = []; guidata(hObject, handles); function imageSize_Callback(hObject, eventdata, handles) % hObject handle to imageSize (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) num = get(hObject,'string'); n = str2num(num); if isempty(n) num = '32'; set(hObject,'string',num); end if n > 32 warndlg('It is strongly recomended NOT to work with networks with more then 32^2 neurons!','!! Warning !!') end % --- Executes during object creation, after setting all properties. function imageSize_CreateFcn(hObject, eventdata, handles) . if ispc set(hObject,'BackgroundColor','white'); else set(hObject,'BackgroundColor',get(0,'defaultUicontrolBackgroundColor') ); end % --- Executes on button press in loadIm. function loadIm_Callback(hObject, eventdata, handles) [fName dirName] = uigetfile('*.bmp;*.tif;*.jpg;*.tiff'); if fName set(handles.imageSize,'enable','off'); cd(dirName); im = imread(fName); N = str2num(get(handles.imageSize,'string')); im = fixImage(im,N); imagesc(im,'Parent',handles.neurons); colormap('gray'); end % --- Executes on button press in train. function train_Callback(hObject, eventdata, handles) 43

44. Npattern = length(handles.hPatternsDisplay); if Npattern > 9 msgbox('more then 10 paterns isn''t supported!','error'); return end im = getimage(handles.neurons); N = get(handles.imageSize,'string'); N = str2num(N); W = handles.W; %weights vector avg = mean(im(:)); %removing the cross talk part if ~isempty(W) %W = W +( kron(im,im))/(N^2); W = W + ( kron(im-avg,im-avg))/(N^2)/avg/(1-avg); else % W = kron(im,im)/(N^2); W = ( kron(im-avg,im-avg))/(N^2)/avg/(1-avg); end % Erasing self weight ind = 1:N^2; f = find(mod(ind,N+1)==1); W(ind(f),ind(f)) = 0; handles.W = W; % Placing the new pattern in the figure... xStart = 0.01; xEnd = 0.99; height = 0.65; width = 0.09; xLength = xEnd-xStart; xStep = xLength/10; offset = 4-ceil(Npattern/2); offset = max(offset,0); y = 0.1; if Npattern > 0 for n=1 : Npattern x = xStart+(n+offset-1)*xStep; h = handles.hPatternsDisplay(n); set(h,'units','normalized'); set(h,'position',[x y width height]); end x = xStart+(n+offset)*xStep; h = axes('units','normalized','position',[x y width height]); handles.hPatternsDisplay(n+1) = h; imagesc(im,'Parent',h); else x = xStart+(offset)*xStep; h = axes('units','normalized','position',[x y width height]); handles.hPatternsDisplay = h; end 44

45. imagesc(im,'Parent',h); set(h, 'YTick',[],'XTick',[],'XTickMode','manual','Parent',handles.learnedPat erns); guidata(hObject, handles); % --- Executes on button press in addNoise. function addNoise_Callback(hObject, eventdata, handles) im = getimage(handles.neurons); % N = get(handles.imageSize,'string'); % N = floor(str2num(N)/2)+1; noisePercent = get( handles.noiseAmount, 'value' ); N = round( length(im(:))* noisePercent ); N = max(N,1); %minimum change one neuron ind = ceil(rand(N,1)*length(im(:))); % im(ind) = -1*im(ind); %!!!! im(ind) = ~im(ind); imagesc(im,'Parent',handles.neurons); colormap('gray'); % --- Executes on button press in run. function run_Callback(hObject, eventdata, handles) im = getimage(handles.neurons); [rows cols] = size(im); if rows ~= cols msgbox('I don''t support non square images','error'); return; end N = rows; W = handles.W; if isempty(W) msgbox('No train data - doing nothing!','error'); return; end %figure; imagesc(W) mat = repmat(im,N,N); mat = mat.*W; mat = im2col(mat,[N,N],'distinct'); networkResult = sum(mat); networkResult = reshape(networkResult,N,N); im = fixImage(networkResult,N); imagesc(im,'Parent',handles.neurons); function im = fixImage(im,N) % if isrgb(im) if length( size(im) ) == 3 im = rgb2gray(im); 45

46. end im = double(im); m = min(im(:)); M = max(im(:)); im = (im-m)/(M-m); %normelizing the image im = imresize(im,[N N],'bilinear'); %im = (im > 0.5)*2-1; %changing image values to -1 & 1 im = (im > 0.5); %changing image values to 0 & 1 % --- Executes on slider movement. function noiseAmount_Callback(hObject, eventdata, handles) % hObject handle to noiseAmount (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) percent = get(hObject,'value'); percent = round(percent*100); set(handles.noisePercent,'string',num2str(percent)); % --- Executes during object creation, after setting all properties. function noiseAmount_CreateFcn(hObject, eventdata, handles) set(hObject,'BackgroundColor',[.9 .9 .9]); else set(hObject,'BackgroundColor',get(0,'defaultUicontrolBackgroundColor') ); end Output(2) : 46

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50. : 05

51. self-organizing neural network . habbian learning i j j i : - . - . . . 15

52. : ]1,0[ . . : p n y j ( p ) xi ( p) wij ( p ) j 1i n j j : : )1+Wij(p)+= Wij(p) Wij(p ) Wij(p p : ])Wij(p)= yj(p)[xj(p) - Wij(p =/ : p 25

53. x1 x2 x3 x4 1 0 0 0 1 y1 x 2 0 y2 x 3 3 0 y3 x 4 4 0 y4 x 1 1 2 1 5 x5 Input layer 53 1 y5 Output layer 5 1 0 0 0 0 y1 2 1 y2 3 3 0 y3 4 4 0 y4 1 1 2 1 5 x Input layer 1 y5 Output layer 5

54. Code : function digit_recognition disp(' =====================================') disp(' Character recognition neural networks') disp(' =====================================') disp(' ====================================================================== ======') disp(' Reference: Negnevitsky, M., "Artificial Intelligence: A Guide to Intelligent') disp(' Systems", Addison Wesley, Harlow, England, 2002. ') disp(' Sec. 9.4 Will a neural network work for my problem? ') disp(' ====================================================================== ======') disp(' ====================================================================== =========') disp(' Problem: A multilayer feedforward network is used for the recognition of digits') disp(' from 0 to 9. Each digit is represented by a 5 x 9 bit map. ') disp(' ====================================================================== =========') disp(' Hit any key to visualise bit maps of the digits.') disp(' ') pause [digit1,digit2,digit3,digit4,digit5,digit6,digit7,digit8,digit9,digit0 ] = bit_maps; disp(' Hit any key to obtain ten 45-element input vectors denoted by "p".') pause p=[digit1(:),digit2(:),digit3(:),digit4(:),digit5(:),digit6(:),digit7( :),digit8(:),digit9(:),digit0(:)] disp(' Hit any key to define ten 10-element target vectors denoted by "t". ') pause t = eye(10) 54

55. disp(' Hit any key to define the network architecture.') pause s1=12; % Number of neurons in the hidden layer s2=10; % Number of neurons in the output layer disp(' ') fprintf(1,' s1=%.0f; fprintf(1,' s2=%.0f; disp(' ') Number of neurons in the hidden layern',s1); Number of neurons in the output layern',s2); disp(' Hit any key to create the network, initialise its weights and biases, ') disp(' and set up training parameters.') pause net = newff(minmax(p),[s1 s2],{'logsig' 'purelin'},'traingdx'); net.trainParam.show = 20; progress net.trainParam.epochs = 1000; net.trainParam.goal = 0.001; net.trainParam.lr=0.1; % Number of epochs between showing the % Maximum number of epochs % Performance goal % Learning rate disp(' ') fprintf(1,' net.trainParam.show=%.0f; Number of epochs between showing the progressn',net.trainParam.show); fprintf(1,' net.trainParam.epochs=%.0f; Maximum number of epochsn',net.trainParam.epochs); fprintf(1,' net.trainParam.goal=%.3f; Performance goaln',net.trainParam.goal); fprintf(1,' net.trainParam.lr=%.2f; Learning raten',net.trainParam.lr); disp(' ') disp(' Hit any key to train the back-propagation network.') pause disp(' ') disp(' net = train(net,p,t)') disp(' ') net = train(net,p,t); disp(' Hit any key to see how the network recognises a digit, for example digit 3.') pause digit3 probe=digit3(:); a=sim(net,probe); disp(' a=sim(net,probe)') 55

56. a=round(a) disp(' Hit any key to see how "noise" distorts the bit map of a digit, for example digit 5.') disp(' ') pause probe=digit5; figure('name','"Noisy" bit maps') subplot(1,2,1) probe_plot(probe) title('Noise level: 0%') disp(' Hit any key to continue.') disp(' ') pause probe=digit5+randn(size(probe))*0.1; subplot(1,2,2) probe_plot(probe) title('Noise level: 10%') disp(' Hit any key to continue.') disp(' ') pause probe=digit5+randn(size(probe))*0.2; figure('name','"Noisy" bit maps') subplot(1,2,1) probe_plot(probe) title('Noise level: 20%') disp(' Hit any key to continue.') disp(' ') pause probe=digit5+randn(size(probe))*0.5; subplot(1,2,2) probe_plot(probe) title('Noise level: 50%') disp(' Hit any key to evaluate the digit recognition neural network.') disp(' ') pause % Set parameters for the test. noise_range = 0:.05:.50; % Range of noise max_test = 100; % Number of test examples for each digit to be recognised average_error = []; % Average recognition error for a particular noise level 56

57. % Evaluate the digit recognition network. for noise_level=noise_range error=0; for i=1:max_test probe=p+randn(size(p))*noise_level; a=compet(sim(net,probe)); error=error+sum(sum(abs(a-t)))/2; end average_error = [average_error error/10/max_test]; fprintf('Noise level: %.0f percent; Average error: %.0f percentn',noise_level*100,error/10/max_test*100); end disp(' ') disp(' Hit any key to plot the test results.') disp(' ') pause h = figure; plot(noise_range*100,average_error*100,'b-'); title('Performance of the digit recognition network') xlabel('Noise level, %'); ylabel('Recognition error, %'); disp(' ') disp(' Hit any key to train the digit recognition network with "noisy" examples.') disp(' ') pause figure net.trainParam.epochs = 1000; % Maximum number of epochs to train. t_noise = [t t t t]; for pass = 1:10 fprintf('Pass = %.0fn',pass); p_noise=[p p (p+randn(size(p))*0.1) (p+randn(size(p))*0.2)]; net= train(net,p_noise,t_noise); end disp(' Hit any key to evaluate the digit recognition network trained with "noisy" examples.') disp(' ') pause average_error = []; for noise_level = noise_range error = 0; 57

58. for i=1:max_test probe=p+randn(size(p))*noise_level; a=compet(sim(net,probe)); error=error+sum(sum(abs(a-t)))/2; end average_error = [average_error error/10/max_test]; fprintf('Noise level: %.0f percent; Average error: %.0f percentn',noise_level*100,error/10/max_test*100); end disp(' ') disp(' Hit any key to plot the test results.') disp(' ') pause figure(h) hold on plot(noise_range*100,average_error*100,'r-'); legend('Network trained with "perfect" examples','Network trained with "noisy" examples',2); hold off disp('end of digit_recognition') function probe_plot(probe); [m n]=size(probe); probe_plot=[probe probe(:,[n])]'; probe_plot=[probe_plot probe_plot(:,[m])]'; pcolor(probe_plot) colormap(gray) axis('ij') axis image Output : 58

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70. competitive learning . . )(winner-takes-all KOHNEN learning )self-organizing map (SOM ) (forward connection ) (lateral connection . ) -winner (taked-all-neuron . . . 07

71. . ) ( ) (an inhibitory ) ( . . . . yj j ) ( . standard competitive learning rule : ( xi wij ), if neuron j wins the competition wij ,0 if neuron j loses the competition xi wj j . x Euclidean distance . 17

72. x 1) wi (n 1 n 2 d x wj ( xi wij ) 2 1 i xi wij x wj wj x d x wj wj x jx x j x min x wj , j 1,2,..., m m . 27

73. Code : echo on; pause rand('seed',1234); p=rands(2,1000); plot(p(1,:),p(2,:),'r.') title('Input vectors'); xlabel('p(1)'); ylabel('p(2)'); pause s1=6; s2=6; net=newsom([-1 1; -1 1],[s1 s2]); plotsom(net.iw{1,1},net.layers{1}.distances) pause net.trainParam.show=100; progress % Number of epochs between showing the for i=1:10 hold on; net.trainParam.epochs=i*net.trainParam.show; net=train(net,p); delete(findobj(gcf,'color',[0 0 1])); delete(findobj(gcf,'color',[1 0 0])); plotsom(net.IW{1,1},net.layers{1}.distances); hold off; pause(0.001) end echo off; for i=1:(s1*s2); text(net.iw{1,1}(i,1)+0.02,net.iw{1,1}(i,2),sprintf('%g',i)); end echo on; pause for i=1:3 probe=rands(2,1); hold on; plot(probe(1,1),probe(2,1),'.g','markersize',25); a=sim(net,probe); a=find(a) text(probe(1,1)+0.03,probe(2,1),sprintf('%g',(a))); hold off 73

74. % Hit any key to continue. if i