sid {resemble} | R Documentation |
This function computes the spectral information divergence (distance) between spectra based on the kullback-leibler divergence algorithm (see details).
sid(Xr, X2 = NULL, mode = "density", center = FALSE, scaled = TRUE, kernel = "gaussian", n = if(mode == "density") round(0.5 * ncol(Xr)), bw = "nrd0", reg = 1e-04, ...)
Xr |
a |
X2 |
an optional |
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 centered |
scaled |
a logical indicating if the computations must be carried out on the variance scaled |
kernel |
if |
n |
if |
bw |
if |
reg |
a numerical value higher than 0 which indicates a regularization parameter. Values (probabilities) below this threshold are replaced by this value for numerical stability. Default is 1e-4. |
... |
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 samples in the datasets are compared based on the kullback-leibler divergence algorithm.
When mode = "feature"
, the kullback-leibler divergence between all the samples is computed directly on the spectral variables.
The spectral information divergence (SID) algorithm (Chang, 2000) uses the Kullback-Leibler divergence (KL) or relative entropy (Kullback and Leibler, 1951) to account for the vis-NIR information provided by each spectrum. The SID between two spectra (x_{i} and x_{j}) is computed as follows:
SID(x_{i},x_{j}) = KL(x_{i} ≤ft |\right | x_{j}) + KL(x_{j} ≤ft |\right | x_{i})
SID(x_{i},x_{j}) = ∑_{l=1}^{k} p_l \ log(\frac{p_l}{q_l}) + ∑_{l=1}^{k} q_l \ log(\frac{q_l}{p_l})
where k represents the number of variables or spectral features, p and q are the probability vectors of x_{i} and x_{j} respectively which are calculated as:
p = \frac{x_i}{∑_{l=1}^{k} x_{i,l}}
q = \frac{x_j}{∑_{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 = \frac{X-min(X)}{max(X)-min(X)}
or
X_{s} = \frac{X-min(X, X2)}{max(X, X2)-min(X, X2)}
X2_{s} = \frac{X2-min(X, X2)}{max(X, X2)-min(X, X2)}
if X2
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. X2 = NULL
), a square symmetric matrix of SID distances between all the components in "X"
. If both "X"
and "X2"
are specified, a matrix of SID distances between the components in "X"
and the components in "X2"
) where the rows represent the objects in "X"
and the columns represent the objects in "X2"
Xr
the (centered and/or scaled if specified) spectral X
matrix
X2
the (centered and/or scaled if specified) spectral X2
matrix
densityDisXr
if mode = "density"
, the computed density distributions of Xr
densityDisX2
if mode = "density"
, the computed density distributions of X2
Leonardo Ramirez-Lopez
Chang, C.I. 2000. An information theoretic-based approach to spectral variability, similarity and discriminability for hyperspectral image analysis. IEEE Transactions on Information Theory 46, 1927-1932.
## Not run: require(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 samples in Xr xr.sid <- sid(Xr = Xr) xr.sid # Example 2 # Compute the SID distance between the samples in Xr and the samples # in Xu xru.sid <- sid(Xr = Xr, X2 = Xu) xru.sid # Example 3 # Compute the SID distance between the samples in Xr and the samples # in Xu using the histograms xru.sid.hist <- sid(Xr = Xr, X2 = Xu, mode = "feature") xru.sid.hist ## End(Not run)