the weighting schemes all had negative differences, since they
all worsened the accuracy in all three study areas.
Which Transformed Scheme Is Better?
Performance evaluation based on
MAE
indicated that only
NSMA
could perform better than the untransformed scheme
in all three study areas. Other schemes illustrated unstable
performance or weakened the accuracy.
DA
can get rid of unnecessary signal components and
highlight minor absorption features by using spectral smooth-
ing and the feature-reduction method. However, it can also
raise the possibility of ignoring essential spectral features
(Youngentob
et al.
2011). Different locations may have differ-
ent essential spectral features.
DA
may miss different features
in different study areas. Thus, the performance of
DA
var-
ies from place to place. The results of this study illustrate
unstable performance, since
DA
performed better only in
some regions, while it was weaker in others. Additionally,
DA1
and
DA2
showed worse performances than in the results
of Zhang
et al.
(2004). This may be attributed to different data
sources, since that study applied hyperspectral data, which
are different from the multispectral images we used in this
study. Hyperspectral data, with more spectral information
compared to multispectral imagery, may be effective for
SMA
.
However, Zhang
et al.
did not provide a comparison with
untransformed and transformed data, which makes it difficult
to evaluate the improvement of derivative spectral unmixing.
We did not observe satisfactory performance for
PCA
,
MNF
,
TC
, or
BN
in this study.
PCA
evaluates the components based on
eigenvalues, while
MNF
uses the signal-to-noise ratio to rank
the importance of each component. The limitations of
PCA
and
MNF
may be attributed to many subtle material substances in
Landsat images not being identified by second-order statistics
(Wang and Chang 2006), which may provide confusion be-
tween classes. The last three bands of
PCA
,
TC
, and
MNF
contain
little variance. This may reduce between-classes variance and
increase within-class variance, adding more confusion during
the fraction calculation.
BN
does not seem t
SMA
, because of its poor performance in all
ICA
showed an opposite result from the
Chang (2006): It did not perform better tha
statistics-based methods like
PCA
and
MNF
. That may be due to
the theory of
ICA
that it conserves only crucial and critical in-
formation such as anomalies, end members, and small targets,
instead of the variance preserved by
PCA
and
MNF
. However,
there is not a clear pattern for
ICA
,
PCA
, and
MNF
, as the results
indicate that their performance varied from place to place.
DWT
performance conflicted with the results of Li (2004).
The differences between this study and that one are due to
the land cover types, data sources, wavelet types, and end-
member model. Li used higher-level wavelet types (e.g., Db3,
Sym3), while our study used on only lower-level wavelet
transformation (e.g., db1, Sym2). Further, Li’s land cover
types were agricultural lands that contained soybean, large
crabgrass, and soil, which was different from our study areas
containing commercial areas, residential areas, vegetation,
and so on. Moreover, Li's study used two- and three-end-
member models, while we used a four-end-member model.
Another limitation of Li’s study is that the untransformed
scheme was not tested, which limits knowledge of how
DWT
improved the
SMA
result. Paired-sample
t
tests in the current
study demonstrated that lower-level
DWT
might not be effec-
tive for
SMA
, as it could not improve the accuracy.
CR
’s performance varied dramatically. Results for Colum-
bus are similar to the results of Youngentob
et al.
(2011).
However, results for Janesville and Asheville demonstrated
opposite outcomes. Though
CR
produced a promising result
in estimating chemical concentrations in leaves by removing
irrelevant background reflectance and emphasizing absorp-
tion features of interest, it did not show stable performance
in this study. This may be due to the difference of spectral
characteristics between leaves and impervious surfaces and
the complexity of spectral reflectance in urban and residen-
tial areas.
CR
can enlarge band-depth differences, reducing
the error in spectroscopic estimation of vegetation quality
(Mutanga, Skidmore, Kumar and Ferwerda 2005). However,
the variability in impervious surface area, of both high and
low albedo, is larger than for vegetation, implying that
CR
may
enlarge within-class variance as well. Some scholars state that
CR
might introduce more signal-to-noise interference, increas-
ing the within-class variability of the same class (Carvalho
and Guimaraes 2001), explaining why
CR
weakened the
SMA
results for Janesville and Ashville.
Spatial filters, especially
HP
and
GHP
, are not suitable for
SMA
, as they all reduced accuracy dramatically in all three
study areas.
GLP
and
LP
still provided limited improvement
in some areas; however, statistical tests could not achieve
significance. Therefore, spatial filters may serve best as edge
detection or image smoothing instead of
SMA
.
NSMA
addressed the confusion between impervious surface
areas and soil effectively. Between-classes variance between
soil and impervious surface increased after application of
NSMA
. Moreover, the effect of shade can be removed by bright-
ness normalization. Both aspects improve the accuracy of
SMA
.
NSMA
had similar performance in all three study areas,
proving its stability in urban and suburban environments.
Conclusions
This study examined the performance of 26 transforma-
tions in the Janesville, Asheville, and Columbus areas. Each
scheme was tested 100 times with different spectra using
the V-ISAh-ISAl-S end-member model. Differences between
untransformed and transformed schemes were analyzed using
paired-sample
t
tests. Several conclusions can be drawn. First,
st reliable transformed scheme, since it showed
ovement in all three study areas. Second, some
emes, such as
DA1–3
,
ICA
, and
MNF
, may need
ration, since they showed unstable perfor-
mance in different study areas. Finally, the remaining trans-
formed schemes cannot contribute to the accuracy improve-
ment, since they worsen
SMA
results in all three study areas.
Acknowledgments
The authors would like to thank the anonymous
reviewers for their constructive comments. This work was
supported in part by the GDAS Project of Science and
Technology Development, China (2019GDASYL-0103004,
2016GDASRC-0211, 2018GDASCX-0403), Guangdong
Innovative and Entrepreneurial Research Team Program
(2016ZT06D336), the Research Growth Initiative of the
Graduate School of the University of Wisconsin-Milwaukee,
and the Natural Science Foundation of Hunan Province,
China (2016WK2017).
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