This appendix contains the Matlab¹ programs that were used to conduct the classification exercises described in Chapter 5 of this report.

% -------------------------------------------------------------------------

% NRC Committee on Drinking Water Contaminants

% Filename: class_init.m

% Matlab code to initialize the classification

problem.

% Data are loaded and attributes are analyzed.

% After running this, run either lin_class.m or

nn_class.m.

% ------------------------------------------------------------------------

% Load the training data set and set up data

variables

S=load(‘caldata.txt’); % the name of the

calibration data file

id=S(:,1) ;

t=S(:,2) ; % class labels (target)

X=S(:,3:7) ; % attributes

fid=fopen(‘caldata_id.txt’,‘r’); % the file

containing the contaminant names

names=[] ;

for i=1:length(t)

if i==1

else

end

end

fclose(fid) ;

X1=[] ; X0=[] ;

for i=1:length(t)

if t(i)==1

end

if t(i)==0

end

end

aaa=size (X1) ; NT1=aaa(1) ; % The number of

contaminants with T=1

aaa=size(X0); NT0=aaa(1); % The number of

contaminants with T=0

% ----------------------------------------------------------------------

% Plot correlation analysis of attributes

figure(1)

str(1)={‘Severity’} ;

str(2)={‘Potency’} ;

str(3)={‘Prevalence’} ;

str(4)={‘Magnitude’} ;

str(5)={‘Persist/Mob’} ;

fs=12;

for i=1:5

subplot (5,5,i) ,

plot (X1 (: , i), X1 (: , 1), ‘kx’, X0 (:,i), X0 (: , 1), ‘ko’, ‘LineW

idth’, 1)

axis square

set (gca, ‘LineWidth’, 1)

text (0, 12, str(i), ‘FontSize’, fs)

if i==1

end

end

for i=2:5

subplot (5,5,i+5) ,

plot (X1 (: , i), X1 (: , 2), ‘kx’, X0 (: , i), X0 (: , 2), ‘ko’, ‘LineW

idth’, 1)

axis square

set (gca, ‘LineWidth’, 1)

if i==2

end

end

for i=3:5

subplot (5,5,i+10) ,

plot (X1(: , i), X1(: , 3), ‘kx’, X0(: , i), X0(: , 3), ‘ko’, ‘LineW

idth’, 1)

axis square

set (gca, ‘LineWidth’, 1)

if i==3

end

end

for i=4:5

subplot (5,5,i+15) ,

plot (X1(: , i), X1(: , 4), ‘kx’, X0(: , i), X0(: , 4), ‘ko’, ‘LineW

idth’, 1)

axis square

set (gca, ‘LineWidth’, 1)

if i==4

end

end

for i=5:5

subplot (5,5,i+20) ,

plot (X1(: , i), X1(: , 5), ‘kx’, X0(: , i), X0(: , 5), ‘ko’, ‘LineW

idth’, 1)

axis square

set (gca, ‘LineWidth’, 1)

if i==5

end

end

% ---------------------------------------------------

% End of program

% ---------------------------------------------------

% ---------------------------------------------------

% NRC Committee on Drinking Water Contaminants

% Filename: lin_class.m

% Matlab code to build a linear classifier on the

training data set.

% After this, run class_error.m and lin_predict.m.

% ------------------------------------------------------

% Linear Regression y=Xw where w is the weight

vector

Xlin=[X ones (length (t) , 1)]; % Add a column of ones

to fit bias/intercept.

X1lin=[X1 ones (NT1, 1)] ; % Add a column of ones to

fit bias/intercept.

X0lin=[X0 ones (NT0, 1)] ; % Add a column of ones to

fit bias/intercept.

w=pinv (Xlin) *t;

disp (‘The weights (five attributes plus offset)

are: ’) ;

disp (w) ;

y=Xlin*w;

y1=X1lin*w;

y0=X0lin*w;

meanse=sum( (y-t) . ^2)/length (t) ;

disp (‘The mean squared error is:’)

disp (meanse) ;

% -------------------------------------------------------

% End of program

% ---------------------------------------------------------------------

% ---------------------------------------------------------------------

% NRC Committee on Drinking Water Contaminants

% Filename: nn_class.m

% Matlab code to build a neural network classifier on

the training data set.

% After this, run class_error.m and nn_predict.m.

% -------------------------------------------------------------------

% Set up Neural Network with two feed forward layers.

% The first is a hidden layer containing two nodes.

% The second is an output layer with a single node.

% Both layers have biases.

% The hidden layer has a hyperbolic tangent sigmoid

transfer function.

% The output layer has a linear transfer function.

% The training algorithm uses a conjugate gradient

search method.

% Network performance is measured according to the

mean of squared errors.

figure(2)

Xminmax=[1 10; 1 10; 1 10; 1 10; 1 10] ;

tranfuns={‘tansig’ ‘purelin’};

net=newff (Xminmax, [2 1] , tranfuns, ‘traincgb’,

‘learngdm’, ’mse‘) ;

net.trainParam.min_grad=1e-10;

net.trainParam.epochs=1000000;

net.trainParam.minstep=1.0e-10;

net=train(net,X’, t’);

disp (‘Input weight matrix, bias, and transfer

function in first layer’);

net.IW{1, 1}

net.b{1}

net.layers{1}.transferFcn

if net.numLayers>1

for i=2:net.numLayers

function for next layer’);

end

end

y=sim(net,X’) ; y=y’ ;

y1=sim (net, X1’); y1=y1’ ;

y0=sim(net, X0’) ; y0=y0’ ;

% ----------------------------------------------------------------

% End of program

% ----------------------------------------------------------------

% ----------------------------------------------------------------

% NRC Committee on Drinking Water Contaminants

% Filename: class_error.m

% Matlab code to determine classification error and

optimize the threshold.

% After this, run either lin_predict.m or

nn_predict.m.

% -------------------------------------------------------------------

% Classification error in training data set

minthresh=min(0, min(min(y1), min(y0)));

int=.05;

Threshrange=minthresh:int:max(max(y1) , max(y0));

idxZero=(t==0) ;

idxOne=(t>0) ;

E0=[] ; E1=[] ;

N0misclass=[] ; N1misclass=[] ; Nmisclass=[] ;

for thresh=Threshrange

classOne=(y>thresh) ;

classZero=(y<=thresh);

N0mc=sum(idxZero & classOne) ;

N1mc=sum(idxOne & classZero) ;

Nmc=N0mc+N1mc;

N0misclass=[N0misclass N0mc]; %The number of

T=0 misclassified

N1misclass=[N1misclass N1mc]; %The number of

T=1 misclassified

Nmisclass=[Nmisclass Nmc]; %The total number misclassified

e00=N0mc/sum(idxZero) ;

e11=N1mc/sum(idxOne) ;

E0=[E0 e00] ; % The fraction of T=0 contaminants that are misclassified as 1

E1=[E1 e11] ; % The fraction of T=1 contaminants that are misclassified as 0

end

figure(3)

plot (Threshrange, 100*E0, ‘ko--

’, Threshrange, 100*E1, ‘kx:’, ‘Markersize’, 8, ‘LineWidth’

, 1.5)

set (gca, ‘LineWidth’, 2, ‘fontsize’, fs);

xlabel (‘Threshold’, ‘FontSize’, fs)

ylabel (‘Classification Error (%)’, ‘FontSize’, fs)

legend (‘error for T=0 contaminants’, ‘error for T=1

contaminants’, 0)

figure(4)

plot (Threshrange, N0misclass, ‘ko--

’, Threshrange, N1misclass, ‘kx:’, Threshrange, Nmisclass,

‘k + −’, ‘Markersize’, 8, ‘LineWidth’, 1.5)

set (gca, ‘LineWidth’, 2, ‘fontsize’, fs);

xlabel (‘Threshold’, ‘FontSize’, fs)

ylabel (‘Classification Error (number that are

misclassified)’, ‘FontSize’, fs)

legend (‘number of misclassified T=0

contaminants’, ‘number of misclassified T=1

contaminants’, ‘total number of misclassified

contaminants’, 0)

% ----------------------------------------------------------------------

% Find the threshold that minimizes the total number

of misclassified contaminants

inda=find(Nmisclass==min(Nmisclass)) ;

threshes=Threshrange(inda) ;

sthreshes=size(threshes) ;

if sthreshes(2)>1 % If there are more than one

threshold values…

indb=

find(E0(inda)+E1(inda)==min(E0(inda)+E1(inda))) ;

thresh=threshes(indb); %…fine the one the minimizes the total percent error

else

thresh=threshes;

end

sthresh=size(thresh);

if sthresh(2)>1 % If there are still more than

one threshold values…

thresh=min(thresh); %…choose the smallest one.

end

disp (‘The optimal threshold is:’) ;

disp (thresh) ;

indc=find(Threshrange==thresh) ;

disp (‘The percent error in misclassifying T=1

contaminants is:’) ;

disp (100*E1(indc)) ;

disp (‘The percent error in misclassifying T=0

contaminants is:’) ;

disp (100*E0(indc)) ;

disp (‘The total number of misclassified contaminants

is:’) ;

disp (Nmisclass(indc)) ;

mis_y1=find(y1<thresh) ;

mis_y0=find(y0>thresh) ;

disp (‘Misclassified T=1 contaminants are:’) ;

for i=1:N1misclass(indc)

disp (names(mis_y1(i),:)) ;

disp ([mis_y1(i), y1(mis_y1(i))]) ;

end

disp (‘Misclassified T=0 contaminants are:’) ;

for i=1:N0misclass(indc)

disp (names(NT1+mis_y0(i),:)) ;

disp ([mis_y0 (i), y0 (mis_y0 (i))]) ;

end

% --------------------------------------------------------------

% Plot classification results as a histogram

figure(5)

fs=12;

T1col=‘w’; T0col=‘k’;

histax=Threshrange+int;

[n,xout]=hist(y1,histax) ;

bar (xout,n,.4, T1col) ;

h=findobj (gca, ‘Type’, ‘patch’) ;

set (h, ‘LineWidth’, 2)

if max(n)>30

set (gca, ‘ylim’, [0 30])

upval=num2str(max(n)) ;

text (1.025, 29, ‘\uparrow’) ;

text (1.025, 27.5, upval) ;

else

yset=max(n)+1;

set (gca, ‘Ylim’, [0 yset]) ;

end

hold on

[n,xout]=hist(y0,histax-int/2) ;

bar (xout, n,.4, T0col)

xlabel (‘ {\itY}_{\iti} ’, ‘FontSize’, fs)

ylabel (‘Number of contaminants’, ‘FontSize’, fs)

set (gca, ‘LineWidth’, 2, ‘fontsize’, fs) ;

xx=get (gca, ‘xlim’) ;

yy=get (gca, ‘ylim’) ;

line([thresh, thresh], [0,

. 9*yy (2)], ‘color’, ‘k’, ‘LineStyle’, ‘:’, ‘LineWidth’, 2) ;

ymul=.9; ymo=.1;

labxpos=xx(1)+.04*(xx(2)–xx(1)) ;

labypos=.9*yy(2) ;

boxx=[labxpos labxpos; labxpos+int/2 labxpos+int/2;

labxpos+int/2 labxpos+int/2; labxpos labxpos] ;

boxy=[ymul*labypos (ymul+ymo)*labypos; ymul*labypos

(ymul+ymo)*labypos; ymul*labypos+.05*labypos

(ymul+ymo)*labypos+.05*labypos;

ymul*labypos+.05*labypos

(ymul+ymo)*labypos+.05*labypos] ;

patch(boxx(: , 1), boxy(: , 1), T0col)

patch (boxx(: , 2), boxy(: , 2), T1col, ‘linewidth’, 2)

text (labxpos+int, (ymul+ymo)*labypos,

‘T=1’, ‘Verticalalignment’, ‘bottom’, ‘fontsize’, fs)

text (labxpos+int, ymul*labypos,

‘T=0’, ‘Verticalalignment’, ‘bottom’, ‘fontsize’, fs)

strg(1)={‘Classifier \rightarrow’} ;

strg(2)={‘Threshold ’} ;

text (thresh,. 6*yy(2), strg(1), ‘horizontalalignment’, ‘r

ight’, ‘Fontsize’, fs)

text (thresh,. 53*yy(2), strg(2), ‘horizontalalignment’, ‘

right’, ‘Fontsize’, fs)

hold off

% ------------------------------------------------------------------

% End of program

% ------------------------------------------------------------------

% ------------------------------------------------------------------

% NRC Committee on Drinking Water Contaminants

% Filename: lin_predict.m

% Matlab code to predict classification for test

cases using linear classifier.

% Run this after running lin_class.m and

class_error.m.

% ------------------------------------------------------------------

% Prediction for test cases

SP=load (‘testdata.txt’) ; % the name of the data

file containing test cases

idP=SP(: , 1) ;

XP=SP(: , 2:6) ;

XP=[XP ones(length(idP), 1)] ;

YP=XP*w;

disp (‘The predicted values for the test cases are:’) ;

for i=1:length(idP)

disp ([idP(i), YP(i)]) ;

end

% -------------------------------------------------------------------

% End of program

% -------------------------------------------------------------------

% -------------------------------------------------------------------

% NRC Committee on Drinking Water Contaminants

% Filename: nn_predict.m

% Matlab code to predict classification for test

cases using neural network classifier.

% Run this after running nn_class.m and

class_error.m.

% -------------------------------------------------------------------

% Prediction for test cases

SP=load (‘testdata.txt’) ; % the name of the data

file containing test cases

idP=SP(: , 1) ;

XP=SP(: , 2:6) ;

YP=sim (net, XP’) ;

disp (‘The predicted values for the test cases are:’) ;

for i=1:length(idP)

disp ([idP(i) , YP(i)]) ;

end

% ------------------------------------------------------------------

% End of program

% ------------------------------------------------------------------