This function computes dissimilarities (in an orthogonal space) between either observations in a given set or between observations in two different sets.The dissimilarities are computed based on either principal component projection or partial least squares projection of the data. After projecting the data, the Mahalanobis distance is applied.
ortho_diss(Xr, Xu = NULL,
Yr = NULL,
pc_selection = list(method = "var", value = 0.01),
diss_method = "pca",
.local = FALSE,
pre_k,
center = TRUE,
scale = FALSE,
compute_all = FALSE,
return_projection = FALSE,
allow_parallel = TRUE, ...)a list of class ortho_diss with the following elements:
n_components: the number of components (either principal
components or partial least squares components) used for computing the
global dissimilarities.
global_variance_info: the information about the expalined
variance(s) of the projection. When .local = TRUE, the information
corresponds to the global projection done prior computing the local
projections.
local_n_components: if .local = TRUE, a data.table
which specifies the number of local components (either principal components
or partial least squares components) used for computing the dissimilarity
between each target observation and its neighbor observations.
dissimilarity: the computed dissimilarity matrix. If
.local = FALSE a distance matrix. If .local = TRUE a matrix of
class local_ortho_diss. In this case, each column represent the dissimilarity
between a target observation and its neighbor observations.
projection: if return_projection = TRUE,
an ortho_projection object.
a matrix containing n reference observations rows and
p variablescolumns.
an optional matrix containing data of a second set of observations
with p variables/columns.
a matrix of n rows and one or more columns (variables) with
side information corresponding to the observations in Xr (e.g. response
variables). It can be numeric with multiple variables/columns, or character
with one single column. This argument is
required if:
diss_method == 'pls': Yr is required to project the variables
to orthogonal directions such that the covariance between the extracted pls
components and Yr is maximized.
pc_selection$method == 'opc': Yr is required to optimize
the number of components. The optimal number of projected components is the one
for which its distance matrix minimizes the differences between the Yr
value of each observation and the Yr value of its closest observation.
See sim_eval.
a list of length 2 which specifies the method to be used
for optimizing the number of components (principal components or pls factors)
to be retained. This list must contain two elements (in the following order):
method (a character indicating the method for selecting the number of
components) and value (a numerical value that complements the selected
method). The methods available are:
"opc": optimized principal component selection based on
Ramirez-Lopez et al. (2013a, 2013b). The optimal number of components
(of a given set of observations) is the one for which its distance
matrix minimizes the differences between the Yr value of each
observation and the Yr value of its closest observation. In this
case, value must be a value (larger than 0 and
below min(nrow(Xr) + nrow(Xu), ncol(Xr)) indicating the maximum
number of principal components to be tested. See the
ortho_projection function for more details.
"cumvar": selection of the principal components based
on a given cumulative amount of explained variance. In this case,
value must be a value (larger than 0 and below or equal to 1)
indicating the minimum amount of cumulative variance that the
combination of retained components should explain.
"var": selection of the principal components based
on a given amount of explained variance. In this case,
value must be a value (larger than 0 and below or equal to 1)
indicating the minimum amount of variance that a single component
should explain in order to be retained.
"manual": for manually specifying a fix number of
principal components. In this case, value must be a value
(larger than 0 and
below the minimum dimension of Xr or Xr and Xu
combined).
indicating the minimum amount of variance that a component should
explain in order to be retained.
Default is list(method = "var", value = 0.01).
Optionally, the pc_selection argument admits "opc" or
"cumvar" or "var" or "manual" as a single character
string. In such case, the default "value" when either "opc" or
"manual" are used is 40. When "cumvar" is used the default
"value" is set to 0.99 and when "var" is used, the default
"value" is set to 0.01.
a character value indicating the type of projection on which
the dissimilarities must be computed. This argument is equivalent to
method argument in the ortho_projection function.
Options are:
"pca": principal component analysis using the singular value
decomposition algorithm)
"pca.nipals": principal component analysis using
the non-linear iterative partial least squares algorithm.
"pls": partial least squares.
"mpls": modified partial least squares (Shenk and Westerhaus,
1991 and Westerhaus, 2014).
See the ortho_projection function for further details on the
projection methods.
a logical indicating whether or not to compute the dissimilarities
locally (i.e. projecting locally the data) by using the pre_k nearest
neighbor observations of each target observation. Default is FALSE. See details.
if .local = TRUE a numeric integer value which indicates the
number of nearest neighbors to (pre-)retain for each observation to
compute the (local) orthogonal dissimilarities to each observation in its
neighborhhod.
a logical indicating if the Xr and Xu must be
centered. If Xu is provided the data is centered around the mean of
the pooled Xr and Xu matrices (Xr XuXr U Xu). For
dissimilarity computations based on pls, the data is always centered for
the projections.
a logical indicating if the Xr and Xu must be
scaled. If Xu is provided the data is scaled based on the standard
deviation of the the pooled Xr and Xu matrices (Xr XuXr U Xu).
if center = TRUE, scaling is applied after centering.
a logical. In case Xu is specified it indicates
whether or not the distances between all the elements resulting from the
pooled Xr and Xu matrices (Xr XuXr U Xu must be computed).
a logical. If TRUE the ortho_projection object
on which the dissimilarities are computed will be returned. Default is FALSE. Note that
for .local = TRUE only the initial projection is returned (i.e. local
projections are not).
a logical (default TRUE). It allows parallel computing
of the local distance matrices (i.e. when .local = TRUE). This is done
via foreach function of the 'foreach' package.
additional arguments to be passed to the
ortho_projection function.
When .local = TRUE, first a global dissimilarity matrix is computed based on
the parameters specified. Then, by using this matrix for each target
observation, a given set of nearest neighbors (pre_k) are identified.
These neighbors (together with the target observation) are projected
(from the original data space) onto a (local) orthogonal space (using the
same parameters specified in the function). In this projected space the
Mahalanobis distance between the target observation and its neighbors is
recomputed. A missing value is assigned to the observations that do not belong to
this set of neighbors (non-neighbor observations).
In this case the dissimilarity matrix cannot be considered as a distance
metric since it does not necessarily satisfies the symmetry condition for
distance matrices (i.e. given two observations x_ix_i and x_jx_j, the local
dissimilarity (dd) between them is relative since generally
d(x_i, x_j) d(x_j, x_i)d(x_i, x_j) ne d(x_j, x_i)). On the other hand, when
.local = FALSE, the dissimilarity matrix obtained can be considered as
a distance matrix.
In the cases where "Yr" is required to compute the dissimilarities and
if .local = TRUE, care must be taken as some neighborhoods might
not have enough observations with non-missing "Yr" values, which might retrieve
unreliable dissimilarity computations.
If "opc" or "manual" are used in pc_selection$method
and .local = TRUE, the minimum number of observations with non-missing
"Yr" values at each neighborhood is determined by
pc_selection$value (i.e. the maximum number of components to compute).
Ramirez-Lopez, L., Behrens, T., Schmidt, K., Stevens, A., Dematte, J.A.M., Scholten, T. 2013a. The spectrum-based learner: A new local approach for modeling soil vis-NIR spectra of complex data sets. Geoderma 195-196, 268-279.
Ramirez-Lopez, L., Behrens, T., Schmidt, K., Viscarra Rossel, R., Dematte, J. A. M., Scholten, T. 2013b. Distance and similarity-search metrics for use with soil vis-NIR spectra. Geoderma 199, 43-53.
ortho_projection, sim_eval
library(prospectr)
data(NIRsoil)
Xu <- NIRsoil$spc[!as.logical(NIRsoil$train), ]
Yu <- NIRsoil[!as.logical(NIRsoil$train), "CEC", drop = FALSE]
Yr <- NIRsoil[as.logical(NIRsoil$train), "CEC", drop = FALSE]
Xr <- NIRsoil$spc[as.logical(NIRsoil$train), ]
Xu <- Xu[!is.na(Yu), ]
Yu <- Yu[!is.na(Yu), , drop = FALSE]
Xr <- Xr[!is.na(Yr), ]
Yr <- Yr[!is.na(Yr), , drop = FALSE]
# Computation of the orthogonal dissimilarity matrix using the
# default parameters
pca_diss <- ortho_diss(Xr, Xu)
# Computation of a principal component dissimilarity matrix using
# the "opc" method for the selection of the principal components
pca_diss_optim <- ortho_diss(
Xr, Xu, Yr,
pc_selection = list("opc", 40),
compute_all = TRUE
)
# Computation of a partial least squares (PLS) dissimilarity
# matrix using the "opc" method for the selection of the PLS
# components
pls_diss_optim <- ortho_diss(
Xr = Xr, Xu = Xu,
Yr = Yr,
pc_selection = list("opc", 40),
diss_method = "pls"
)
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