Computational Intelligence - August 2015 - 57
August 2015 | IEEE ComputAtIonAl IntEllIgEnCE mAgAzInE
57
Y4
Y3
X4
Z
(A)
Y2
X2
X1 X3
Y1
Class 2: T2 = 0.583
NN1,2,3 (Y1) = [X1, Y2, X3]
NN1,2,3 (Y2) = [Y1, Y3, X1]
NN1,2,3 (Y3) = [Y2, Y4, Y1]
NN1,2,3 (Y4) = [X4, Y3, X2]
f1
Y4
Y3
(B)
X4
Z
Y2
X2
f1
X1 X3
Y1
Y4
Y3
(C)
X4
Z
Y2
Y1
(n1 + 1)k
j=1
Dn11 + k1 - kT1
j=1
n2k
Dn21
=- 0.03,
j=2
T11 + T21 = 1.300, T12 + T22 = 1.483
f2
f1
(n2 + 1)k
Class 1
Assume
Class 2
j=2
-
n1k
Dn12
= 0.15
Class 2: Dn22 = 3, k2 = 1
Class 1: Dn12 = 0, k1 = 2
Class 2: T22 = 0.733
Class 1: T12 = 0.750
[X1, Y2, Z]
[Y1, Y3, Z]
[Z, X4, Y3]
[X2, X1, Z]
[Y2, Z, Y4]
to Z
Class 2
Assign
NN1,2,3 (Y1) = [X1, Y2, X3]
NN1,2,3 (Y2) = [Y1, Y3, X1]
NN1,2,3 (Y4) = [X4, Y3, X2]
Z
Class 2: Dn21 = 1, k2 = 1
Class 1: Dn11 = 1, k1 = 2
Class 2: T21 = 0.500
Class 1: T11 = 0.800
Dn22 + k2 - kT2
X2
X1 X3
ENN: Assume Test Sample Z to Be Class 2
f2
Assume
NN1,2,3 (X4) = [X2, X1, Y4]
NN1,2,3 (Y3) = [Y2, Y4, Y1]
Z
Figure 2 (A), (B) and (C) demonstrate the detailed procedure of two versions of ENN classifier. In (A), training samples are stored and their k nearest neighbors and distances are calculated to
compute the generalized class-wise statistic T1 and T2 . (B) and (C) illustrate the changes of the generalized class-wise statistic for each class, when we iteratively assume Z to be class 1 and
j
class 2. Both of them provide the same classification result, but the recalculation of generalized class-wise statistic T i is avoided in ENN.V1.
According to Eq: (9): fENN.V1 = arg max
j e 1, 2
According to Eq: (8): fENN = arg max
j e 1, 2
Class 1: T1 = 0.750
NN1,2,3 (X1) = [X2, X3, Y1]
NN1,2,3 (X2) = [X1, X4, X3]
NN1,2,3 (X3) = [X1, X2, Y1]
NN1,2,3 (X4) = [X2, X1, Y4]
3-Nearest Neighbors Without Z:
f2
: Test Sample
: Class 2
: Class 1
ENN: Consider 3-Nearest Neighbors (k = 3)
ENN: Assume Test Sample Z to Be Class 1
Table of Contents for the Digital Edition of Computational Intelligence - August 2015
Computational Intelligence - August 2015 - Cover1
Computational Intelligence - August 2015 - Cover2
Computational Intelligence - August 2015 - 1
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Computational Intelligence - August 2015 - Cover3
Computational Intelligence - August 2015 - Cover4
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