Description Usage Arguments Details Value Author(s) References See Also Examples
This function computes the spectral information divergence/dissimilarity between spectra based on the kullbackleibler divergence algorithm (see details).
1 2 3 4 5 6 7 8 
Xr 
a matrix containing the spectral (reference) data. 
Xu 
an optional matrix containing the spectral data of a second set of observations. 
mode 
the method to be used for computing the spectral information
divergence. Options are 
center 
a logical indicating if the computations must be carried out on
the centred 
scale 
a logical indicating if the computations must be carried out on
the variance scaled 
kernel 
if 
n 
if 
bw 
if 
reg 
a numerical value larger than 0 which indicates a regularization parameter. Values (probabilities) below this threshold are replaced by this value for numerical stability. Default is 1e4. 
... 
additional arguments to be passed to the

This function computes the spectral information divergence (distance)
between spectra.
When mode = "density"
, the function first computes the probability
distribution of each spectrum which result in a matrix of density
distribution estimates. The density distributions of all the observations in
the data sets are compared based on the kullbackleibler divergence algorithm.
When mode = "feature"
, the kullbackleibler divergence between all
the observations is computed directly on the spectral variables.
The spectral information divergence (SID) algorithm (Chang, 2000) uses the
KullbackLeibler divergence (\mjeqnKLKL) or relative entropy
(Kullback and Leibler, 1951) to account for the visNIR information provided
by each spectrum. The SID between two spectra (\mjeqnx_ix_i and
\mjeqnx_jx_j) is computed as follows:
sid(x_i,x_j) = KL(x_i \left \right  x_j) + KL(x_j \left \right  x_i)sid(x_i,x_j) = KL(x_i \  x_j) + KL(x_j \  x_i)
\mjdeqnsid(x_i,x_j) = \sum_l=1^k p_l \ log(\fracp_lq_l) + \sum_l=1^k q_l \ log(\fracq_lp_l)sid(x_i,x_j) = \sum_l=1^k p_l \ log(p_l/q_l) + \sum_l=1^k q_l \ log(q_l/p_l)
where \mjeqnkk represents the number of variables or spectral features, \mjeqnpp and \mjeqnqq are the probability vectors of \mjeqnx_ix_i and \mjeqnx_ix_j respectively which are calculated as:
\mjdeqnp = \fracx_i\sum_l=1^k x_i,lp = x_i/\sum_l=1^k x_i,l
\mjdeqnq = \fracx_j\sum_l=1^k x_j,lq = x_j1/\sum_l=1^k x_j,l
From the above equations it can be seen that the original SID algorithm
assumes that all the components in the data matrices are nonnegative.
Therefore centering cannot be applied when mode = "feature"
. If a
data matrix with negative values is provided and mode = "feature"
,
the sid
function automatically scales the matrix as follows:
X_s = \fracXmin(X)max(X)min(X)X_s = Xmin(X)/max(X)min(X)
or
\mjdeqnX_s = \fracXmin(X, Xu)max(X, Xu)min(X, Xu)X_s = Xmin(X, Xu)/max(X, Xu)min(X, Xu)
\mjdeqnXu_s = \fracXumin(X, Xu)max(X, Xu)min(X, Xu)Xu_s = Xumin(X, Xu)/max(X, Xu)min(X, Xu)
if Xu
is specified. The 0 values are replaced by a regularization
parameter (reg
argument) for numerical stability.
The default of the sid
function is to compute the SID based on the
density distributions of the spectra (mode = "density"
). For each
spectrum in X
the density distribution is computed using the
density
function of the stats
package.
The 0 values of the estimated density distributions of the spectra are
replaced by a regularization parameter ("reg"
argument) for numerical
stability. Finally the divergence between the computed spectral histogramas
is computed using the SID algorithm. Note that if mode = "density"
,
the sid
function will accept negative values and matrix centering
will be possible.
a list
with the following components:
sid
if only "X"
is specified (i.e. Xu = NULL
),
a square symmetric matrix of SID distances between all the components in
"X"
. If both "X"
and "Xu"
are specified, a matrix
of SID distances between the components in "X"
and the components
in "Xu"
) where the rows represent the objects in "X"
and the
columns represent the objects in "Xu"
Xr
the (centered and/or scaled if specified) spectral
X
matrix
Xu
the (centered and/or scaled if specified) spectral
Xu
matrix
densityDisXr
if mode = "density"
, the computed
density distributions of Xr
densityDisXu
if mode = "density"
, the computed
density distributions of Xu
Leonardo RamirezLopez
Chang, C.I. 2000. An information theoreticbased approach to spectral variability, similarity and discriminability for hyperspectral image analysis. IEEE Transactions on Information Theory 46, 19271932.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22  library(prospectr)
data(NIRsoil)
Xu < NIRsoil$spc[!as.logical(NIRsoil$train), ]
Yu < NIRsoil$CEC[!as.logical(NIRsoil$train)]
Yr < NIRsoil$CEC[as.logical(NIRsoil$train)]
Xr < NIRsoil$spc[as.logical(NIRsoil$train), ]
Xu < Xu[!is.na(Yu), ]
Xr < Xr[!is.na(Yr), ]
# Example 1
# Compute the SID distance between all the observations in Xr
xr_sid < sid(Xr)
xr_sid
# Example 2
# Compute the SID distance between the observations in Xr and the observations
# in Xu
xr_xu_sid < sid(Xr, Xu)
xr_xu_sid

Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.