Environmental Engineering Reference
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3
X
346
T
1
T
2
t
1
p
t
2
p
×
×
3
3
516
1×3
1×3
Reorganization
PCA
+
=
+
X
E
(516
×
346)
×
1
516×346
(516×346)×1
516×346
T
⊗
p
T
⊗
p
1
1
2
2
3×1
3×1
=
+
516×346
516×346
E
346
+
3
516
Figure 3.5
Application of multi-way PCA (MPCA) to decompose the spectral information con-
tained within a multivariate image. Adapted from Bharati and MacGregor [25]
Multivariate
image
X
Score image,
T
1
Loading vector,
p
1
B
0
G
-0.1
R
-0.2
=
-0.3
-0.4
-0.5
-0.6
-0.7
R
GB
1
2
3
+
Score image,
T
2
Loading vector,
p
2
0.8
0.6
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
R
GB
1
2
3
Score density histogram
t
1
-
t
2
Residual image
E
B
G
R
t
2
+
t
1
Figure 3.6
Visual interpretation of score and loading vectors obtained from MPCA when applied
for image analysis. Adapted from Liu
et al.
[37]
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