% bayesleastrisk classifier
clear;
clc;
N=29;w=4;n=3;N1=4;N2=7;N3=8;N4=10;
A=[864.45 877.88 1418.79 1449.58
1647.31 2031.66 1775.89 1641.58
2665.9 3071.18 2772.9 3045.12]; % A belongs to w1
B=[2352.12 2297.28 2092.62 2205.36 2949.16 2802.88 2063.54
2557.04 3340.14 3177.21 3243.74 3244.44 3017.11 3199.76
1411.53 535.62 584.32 1202.69 662.42 1984.98 1257.21]; %B belongs to w2
C=[1739.94 1756.77 1803.58 1571.17 1845.59 1692.62 1680.67 1651.52
1675.15 1652 1583.12 1731.04 1918.81 1867.5 1575.78 1713.28
2395.96 1514.98 2163.05 1735.33 2226.49 2108.97 1725.1 1570.38]; %C belongs to w3
D=[373.3 222.85 401.3 363.34 104.8 499.85 172.78 341.59 291.02 237.63
3087.05 3059.54 3259.94 3477.95 3389.83 3305.75 3084.49 3076.62 3095.68 3077.78
2429.47 2002.33 2150.98 2462.86 2421.83 3196.22 2328.65 2438.63 2088.95 2251.96]; % D belongs to w4
X1=mean(A')';X2=mean(B')';X3=mean(C')';X4=mean(D')'; % mean of training samples for each category
S1=cov(A');S2=cov(B');S3=cov(C');S4=cov(D'); % covariance matrix of training samples for each type
S1_=inv(S1);S2_=inv(S2);S3_=inv(S3);S4_=inv(S4);% inverse matrix of training samples for each type
S11=det(S1);S22=det(S2);S33=det(S3);S44=det(S4); % determinant of convariance matrix
Pw1=N1/N;Pw2=N2/N;Pw3=N3/N;Pw4=N4/N;%Priori probability
sample=[1702.8 1639.79 2068.74
1877.93 1860.96 1975.3
867.81 2334.68 2535.1
1831.49 1713.11 1604.68
460.69 3274.77 2172.99
2374.98 3346.98 975.31
2271.89 3482.97 946.7
1783.64 1597.99 2261.31
198.83 3250.45 2445.08
1494.63 2072.59 2550.51
1597.03 1921.52 2126.76
1598.93 1921.08 1623.33
1243.13 1814.07 3441.07
2336.31 2640.26 1599.63
354 3300.12 2373.61
2144.47 2501.62 591.51
426.31 3105.29 2057.8
1507.13 1556.89 1954.51
343.07 3271.72 2036.94
2201.94 3196.22 935.53
2232.43 3077.87 1298.87
1580.1 1752.07 2463.04
1962.4 1594.97 1835.95
1495.18 1957.44 3498.02
1125.17 1594.39 2937.73
24.22 3447.31 2145.01
1269.07 1910.72 2701.97
1802.07 1725.81 1966.35
1817.36 1927.4 2328.79
1860.45 1782.88 1875.13];
% Posterior probability as the following
loss=ones(4)-diag(diag(ones(4))); % define the riskloss function (4*4)
plot(loss);
grid on;
xlabel('type');ylabel('Loss function value');
for k=1:30
P1=-1/2*(sample(k,:)'-X1)'*S1_*(sample(k,:)'-X1)+log(Pw1)-1/2*log(S11);
P2=-1/2*(sample(k,:)'-X2)'*S2_*(sample(k,:)'-X2)+log(Pw2)-1/2*log(S22);
P3=-1/2*(sample(k,:)'-X3)'*S3_*(sample(k,:)'-X3)+log(Pw3)-1/2*log(S33);
P4=-1/2*(sample(k,:)'-X4)'*S4_*(sample(k,:)'-X4)+log(Pw4)-1/2*log(S44);
risk1=loss(1,1)*P1+loss(1,2)*P2+loss(1,3)*P3+loss(1,4)*P4;
risk2=loss(2,1)*P1+loss(2,2)*P2+loss(2,3)*P3+loss(2,4)*P4;
risk3=loss(3,1)*P1+loss(3,2)*P2+loss(3,3)*P3+loss(3,4)*P4;
risk4=loss(4,1)*P1+loss(4,2)*P2+loss(4,3)*P3+loss(4,4)*P4;
risk=[risk1 risk2 risk3 risk4]
minriskloss=min(risk) % find the least riskloss
% return the category of the least riskloss as following
if risk1==min(risk)
w=1
elseif risk2== min(risk)
w=2
elseif risk3==min(risk)
w=3
elseif risk4==min(risk)
w=4
else
return
end
end
