Pattern Recognition Assignments I

Pattern Recognition - Oruntu Tanima alaninda calismaniz icin Mean Vector, Covariance Matrix, Med - minimum euclid distance, ozdeger, oz vektor ve standart sapma konulari ornek niteliginde isinize yarayabilecek soru ve cevaplari bu makale iceriginde bulabilirsiniz.

Assignment I

QA1 ) (2,1), (3,2), (2,3), (1,2) degerleri verilmistir. Mean Vector M ve Covariance Matrix S 'i hesaplayalim. Matlab Kodu; clear all; close all; clc; X = <2,1; 3,2; 2,3; 1,2>

meanVectorM = mean(X,1)   % 1 dimension meanVectorM2 = mean(X,2)  % 2 dimension covarianceMatrixS = cov(X) nokta = <2,3,2,1; 1,2,3,2>

; figure; plot(nokta(1,:),nokta(2,:),'*r'); axis(<0 10 0 10>

); grid on; Cozum; X =     <2     1 3     2 2     3 1     2>

meanVectorM =   [ 2     2 ] meanVectorM2 =  <   1.5000 2.5000 2.5000 1.5000  >

covarianceMatrixS =  [ 0.6667         0 0    0.6667]

Assignment II

QA2 ) iki adet training set olusturup bunlari MED yani minimum euclid distance uzerinde hesaplanmasi; Matlab Kodu; clear all; close all; clc; X = <80,70,50,90,85;>

' Y = <85,60,70,70,75;>

' MEDistance  = sqrt(sum((X - Y) .^ 2)) nokta1 = <80,70,50,90,85; >

; nokta2 = <85,60,70,70,75;>

; figure; plot(nokta1(1,:),'*r'); hold on; plot(nokta2(1,:),'*b'); axis(<40 100 40 100>

); axis equal; grid on; Cozum; X =            80 70 50 90 85 Y =          85 60 70 70 75 MEDistance =   32.0156

Assignment III

QA3 ) (2,1) (1,2) degerleri verilmistir. Ozdeger ve oz vektorleri bulunacaktir. Standart sapmasi nedir? Matlab Kodu; clear all; close all; clc; % oz cozumleri bulmak icin % A*v = Lambda*V => A*v - Lambda*V = 0 => (A - Lambda)*V = 0 A = <2,1;1,2;>

v = <0,0>

' lamba1 = 1/2 * (

+ sqrt(

^2 + 4 * (A(1,2)^2) )   ) lamba2 = 1/2 * (

- sqrt(

^2 + 4 * (A(1,2)^2) )   ) I = eye(2) % oz deger hesaplanmasi icin birim matris olusturulur. eigenValue1 = A - lamba1 * I eigenValue2 = A - lamba2 * I v1 = eigenValue1(1,1) + eigenValue1(2,2) % eigenValue1(1,1) + eigenValue1(2,2) = trace(eigenValue1) v2 = eigenValue2(1,1) + eigenValue2(2,2) % eigenValue2(1,1) + eigenValue2(2,2) = trace(eigenValue2) eigenVector =

'   % oz vektor hesaplanir standardDeviation = std(eigenVector) % standart sapma hesaplanir Cozum; A =     2     1 1     2 v =      0 0 lamba1 =     3 lamba2 =     1 I =     1     0 0     1 eigenValue1 =   -1     1 1    -1 eigenValue2 =    1     1 1     1 v1 =    -2 v2 =     2 eigenVector =    -2 2 standardDeviation =    2.8284

Assignment IV

QA4 ) Standart sapmanin bulundugu alan hesaplanir. Matlab Kodu; clear all; close all; clc; X = <3/5,-4/5; 4/5,3/5>

meanVectorM = mean(X,1)   % 1 dimension meanVectorM2 = mean(X,2)  % 2 dimension medyan = median(X) covarianceMatrixS = cov(X) standartSapma = std(X) nokta = <3/5,4/5; -4/5,3/5>

; figure; plot(nokta(1,:),nokta(2,:),'*r'); axis(<-1 1 -1 1>

); axis equal; grid on; Cozum; X =    0.6000   -0.8000 0.8000    0.6000 meanVectorM =    0.7000   -0.1000 meanVectorM2 =    -0.1000 0.7000 medyan =    0.7000   -0.1000 covarianceMatrixS =     0.0200    0.1400 0.1400    0.9800 standartSapma =    0.1414    0.9899

Assignment V

QA5 ) Ci: (2,2) (4,0) (10,2) (8,4) (8,0) (4,4) ve Cj: (4,10) (8,18) (8,10) (6,6) (4,18) (6,22) training set verilmistir. grafik uzerinde noktalar gosterilip, med ve nn classification uygulanip, gelen yeni noktanin nereye ait oldugu belirlenmistir. Matlab Kodu; clear all; close all; clc; X1 = <2,2; 4,0; 10,2; 8,4; 8,0; 4,4>

X2 = <4,10; 8,18; 8,10; 6,6; 4,18; 6,22>

noktaX1 = <2,4,10,8,8,4; 2,0,2,4,0,4,>

; noktaX2 = <4,8,8,6,4,6; 10,18,10,6,18,22>

; figure; plot(noktaX1(1,:),noktaX1(2,:),'*r'); hold on; plot(noktaX2(1,:),noktaX2(2,:),'*b'); axis(<-5 10 -7 30>

); axis equal; grid on; %%%%%%%% A sikki %%%%%%%%% meanVectorM1 = mean(X1,1)   % 1 dimension meanVectorM12 = mean(X1,2)  % 2 dimension covarianceMatrixS1 = cov(X1) meanVectorM2 = mean(X2,1)   % 1 dimension meanVectorM22 = mean(X2,2)  % 2 dimension covarianceMatrixS2 = cov(X2) %%%%%%%% B sikki %%%%%%%%% %% iki vektorun MED yani oklit uzakliklarini hesaplariz MED = distance(X1,X2) %%%%%%%% C sikki %%%%%%%%% % gelen yeni degeri her iki matristede yerini belirleriz. prototype = <7,6>

for i=1:length(X1) sonuc(i,:) = <(prototype(1,1) - x1(i,1))^2  + (prototype(1,2) - x1(i,2))^2>

; end NNMatrixX1 = sonuc(:,:) vektorAraligi1 = min(NNMatrixX1) for i=1:length(X2) sonuc(i,:) = <(prototype(1,1) - x2(i,1))^2  + (prototype(1,2) - x2(i,2))^2>

; end NNMatrixX2 = sonuc(:,:) vektorAraligi2 = min(NNMatrixX2) %%%%%%%% D sikki %%%%%%%%% hold on; prototypeNokta = <7; 6>

; plot(prototypeNokta(1,:),prototypeNokta(2,:),'Or'); Cozum; X1 =       2     2 4     0 10     2 8     4 8     0 4     4 X2 =       4    10 8    18 8    10 6     6 4    18 6    22 meanVectorM1 =     6     2 meanVectorM12 =          2 2 6 6 4 4 covarianceMatrixS1 = 9.6000         0 0        3.2000 meanVectorM2 =     6    14 meanVectorM22 =           7 13 9 6 11 14 covarianceMatrixS2 =       3.2000         0 0        38.4000 MED =      8.2352 18.3384 8.1501 2.8178 18.3384 18.0412 prototype =     7     6 NNMatrixX1 =        41 45 25 5 37 13 vektorAraligi1 =     5         (4. satir) NNMatrixX2 =       25 145 17 1 153 257 vektorAraligi2 =     1           (4. satir) Yeni gelen (7,6) noktasi her ikisinde 4.satir'a ait yerlerde bulunmaktadir. Ayni zamanda sekilde de O sekli ile hangi alana ait oldugu gosterilmektedir. Keyifli Calismalar Dilerim.