PLSR |
Partial least squares regression |
GPR |
Gaussian process regression |
R2
|
Coefficient of determination |
RMSE |
Root mean square error |
ARI |
Anthocyanin reflectance index |
mARI |
Modified anthocyanin reflectance index |
VARI |
Visible atmospherically resistant vegetation index |
ACI |
Anthocyanin content index |
PROSPECT |
Leaf optical properties spectra |
ANN |
Artificial neural network |
PRESS |
Predictive residual sum of squares |
SS |
Sum of squares |
GP |
Gaussian process |
ARD |
Automatic relevance determination |
r
|
Pearson correlation coefficient |
P |
Significance level for correlation |
SBBR |
Sequential backward band removal |
σm
|
Characteristic length scale for a variable in GPR |
|β| |
Absolute value of the regression coefficient β in PLSR |
R
|
Reflectance |
log(1/R) |
Logarithmic transformation to R
|
NDVI |
Normalized difference vegetation index |
Mathematical symbols and notation in Section 2.3
|
Matrixes are capitalized and vectors are in the lowercase bold type. The subscript asterisk (e.g., X*) indicates the test set quantity. |
′ |
The transpose of a matrix or vector |
𝒟 |
Data set: 𝒟 = {(xi, yi,)|i = 1, 2, …, n} |
ℝb
|
b-dimensional real numbers |
∼ |
Distributed according to (e.g., Gaussian distribution) |
𝒢𝒫 |
Gaussian process |
𝒩 |
Gaussian (normal) distribution |
|
Noise variance |
0
|
Vector of all 0′s |
k(x,y) |
Covariance (or kernel) function evaluated at x and y
|
K(X,Y) |
Covariance (or Gram) matrix evaluated with X and Y
|
y|x and p(y|x) |
Conditional random variable y given x and the corresponding probability |
θ
|
Vector of hyperparameters |
f
|
Gaussian process latent function values |