Variable Importance in the Projection (
VIP
) Method
The
VIP
selection method (Equation 1) was first published by
Wold and coauthors.
VIP
scores summarize the influence of
individual variables on the
PLS
model (Maimaitiyiming M et al.,
2017).
VIP
scores provide a useful measure to select the
x
vari-
ables that contribute the most to the
y
variance explanation. For
a given model and data set, there is always only one
VIP
scores-
vector summarizing all components and
y
variables (Wold S et
al. 2001). The
VIP
score for the
j
variable is given as follows:
VIP
W SSY J
SSY F
j
f
F
jf
f
total
=
=
∑
1
2
·
·
·
(1)
where W
jf
is the weight value for the
j
th
variable and
f
th
component, and
SSY
f
is the sum of squares of the explained
variance for the
f
th
component and all
J
variables.
SSY
total
is
the total sum of squares explained of the dependent variable,
and
F
is the total number of components. The indicates the
importance of the
j
th
variable in each
f
th
component; and VIP
j
is a measure of the global contribution of the
j
th
variable in
the complete
PLS
model. In case of a one-dimensional space
y
,
then
SSY
f
=
b
f
2
t
f
t
f
,
SSY
total
=
b
2
TT
, where T is the variable scores
matrix and
b
is the
PLS
inner relation vector of coefficients.
Model Validation
Validation of the models is an important step to ensure model
quality (Karunaratne
et al
., 2014; Fidahussein
et al
., 2004).
Once all the developed models were tested, we selected
models with (a) a high coefficient of determination of calibra-
tion
R
2
Cal
and a high coefficient of determination of predic-
tion
R
2
Pre
, indicating a strong linear relationship; and (b) low
root mean square errors of calibration (
RMSE
Cal
), and low root
mean square errors of prediction (
RMSE
Pre
). The
R
2
Cal
and
R
2
Pre
were used to stabilize the determination of the model; values
close to 1 indicate that the model exhibits better stability. As
a result, the best implemented
PLSR
model that met all the
model selection and validation criteria was selected and used
to predict relative chlorophyll content in spring wheat.
Results
Relationships Between the Relative chlorophyll Content and Hyperspec-
tral Reflectance Indices
Figure 2 summarizes the correlation (
r
) of the previously pub-
lished indices of relative chlorophyll content. Relative chloro-
phyll content exhibited moderate to strong correlations with
mostly leaf pigment and greenness indices. The correlations
(|
r
|) were obtained with the carotenoid reflectance index-1
(CRI1), optimized soil-adjusted vegetation index (
OSAVI
), G-M
and carotenoid reflectance index-2 (CRI2). Among them, CRI1
was the only index that exhibited a high correlation with rela-
tive chlorophyll content (|
r
|
≤
0.46). Note that several green-
ness-based indices (e.g., TVI, SR, REIP, GNDVI, EVI, NDVI
et
al
.) exhibited very low correlations with relative chlorophyll
content (|
r
|
≤
0.30). To summarize these analyses, all the
published indices designed for relative chlorophyll content
estimation exhibited a very weak correlation with the relative
chlorophyll content in spring wheat.
Using Hyperspectral Reflectance Data Analysis on Optimized Spectral
Indices
In this paper, two-dimensional maps of correlation (
r
) were
calculated using a spectral range (400~1300 nm) and relative
chlorophyll content in spring wheat (Figure 3). The
NDSIs
,
RSIs
, and
CIs
with the highest correlation (|
r
|
≤
0.7) were iden-
tified in the
VNIR
spectral range. In most cases, the spectral
range 500~600 nm correlated relatively well with the rela-
tive chlorophyll content when only combined with the
VNIR
region (0.4
≤
|
r
|
≤
0.6). Compared with the short-wavelength
infrared (
SWIR
) (1300-2500 nm) band, the
VNIR
band increased
the signal-to-noise ratio. In addition, compared with the
VNIR
band, the
SWIR
band of imaging spectroscopies had lower spa-
tial resolution due to physical limitations (Hunt
et al
., 2016).
Longer wavelengths tend to be affected by strong atmospheric
H
2
O and CO
2
absorption, and it is difficult to completely
remove the effects, even with a perfect atmospheric correc-
tion (Abduwasit
et al
., 2007). Therefore, we focused on the
400~1300 nm spectral region, corresponding to
VNIR
band, for
the remainder of this study.
Table 3 presents the strengths of the correlations between
relative chlorophyll content and the selected indices (
NDSIs
,
RSIs
, and
CIs
). Figure 3 presents the
NDSI
,
RSI
, and
CI
analyses
Figure 2. Pearson correlation (
r
) between previously published indices and measured relative chlorophyll content.
PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING
December 2018
805
