| Version: | 1.1.0 |
| Date: | 2023-08-12 |
| Title: | Procrustes Cross-Validation |
| Maintainer: | Sergey Kucheryavskiy <svkucheryavski@gmail.com> |
| Description: | Implements Procrustes cross-validation method for Principal Component Analysis, Principal Component Regression and Partial Least Squares regression models. S. Kucheryavskiy (2023) <doi:10.1016/j.aca.2023.341096>. |
| Encoding: | UTF-8 |
| License: | MIT + file LICENSE |
| Imports: | graphics, grDevices, stats |
| RoxygenNote: | 7.2.3 |
| Suggests: | testthat |
| NeedsCompilation: | no |
| Depends: | R (≥ 3.5.0) |
| URL: | https://github.com/svkucheryavski/pcv |
| BugReports: | https://github.com/svkucheryavski/pcv/issues |
| Packaged: | 2023-08-12 18:52:49 UTC; svkucheryavski |
| Author: | Sergey Kucheryavskiy
 [aut, cre] |
| Repository: | CRAN |
| Date/Publication: | 2023-08-12 19:20:02 UTC |
Corn data
Description
NIR spectra and moisture of 80 Corn samples.
Usage
data(corn)Format
A list with two matrices, spectra and moisture.
Details
This is a part of Corn dataset, which was downloaded from Eigenvector Research, Inc. website (https://eigenvector.com/resources/data-sets/), where it is availble publicly. This dataset contains several NIR spectra of corn samples recorded using different instruments. For our examples we took "mp5" spectra and corrected them using Standard Normal Variate transformation.
Source
1. Eigenvector Research, Inc. (https://eigenvector.com/resources/data-sets/)
Returns parameters for cross-validation based on 'cv' value
Description
Returns parameters for cross-validation based on 'cv' value
Usage
getCrossvalParams(cv, nobj)
Arguments
cv |
settings for cross-validation provided by user |
nobj |
number of objects in calibration set |
Creates rotation matrix to map a set vectors base1 to a set of vectors base2.
Description
In both sets vectors should be orthonormal.
Usage
getR(base1, base2)
Arguments
base1 |
Matrix (JxA) with A orthonormal vectors as columns to be rotated (A <= J) |
base2 |
Matrix (JxA) with A orthonormal vectors as columns, |
Value
Rotation matrix (JxJ)
Generates the orthogonal part for Xpv
Description
Generates the orthogonal part for Xpv
Usage
getxpvorth(q.k, X.k, PRM)
Arguments
q.k |
vector with orthogonal distances for cross-validation set for segment k |
X.k |
matrix with local validation set for segment k |
PRM |
projecton matrix for orthogonalization of residuals |
Value
A matrix with orthogonal part for Xpv
Normalization rows or columns of a matrix
Description
Normalization rows or columns of a matrix
Usage
normalize(
X,
dim = 1,
weights = if (dim == 1) 1/sqrt(rowSums(X^2)) else 1/sqrt(colSums(X^2))
)
Arguments
X |
matrix with numeric values |
dim |
which dimension to normalize (1 for rows, 2 for columns) |
weights |
vector with normalization weights, by default 2-norm is used |
Compute matrix with pseudo-validation set
Description
Compute matrix with pseudo-validation set
Usage
pcv(
X,
ncomp = min(round(nrow(X)/nseg) - 1, col(X), 20),
nseg = 4,
scale = FALSE
)
Arguments
X |
matrix with calibration set (IxJ) |
ncomp |
number of components for PCA decomposition |
nseg |
number of segments in cross-validation |
scale |
logical, standardize columns of X prior to decompositon or not |
Details
This is the old (original) version of PCV algorithm for PCA models. Use pcvpca
instead. Ane check project web-site for details: https://github.com/svkucheryavski/pcv
The method computes pseudo-validation matrix Xpv, based on PCA decomposition of calibration set X and systematic (venetian blinds) cross-validation. It is assumed that data rows are ordered correctly, so systematic cross-validation can be applied
Value
Pseudo-validation matrix (IxJ)
Generate sequence of indices for cross-validation
Description
Generates and returns sequence of object indices for each segment in random segmented cross-validation
Usage
pcvcrossval(cv = 1, nobj = NULL, resp = NULL)
Arguments
cv |
cross-validation settings, can be a number, a list or a vector with integers. |
nobj |
number of objects in a dataset |
resp |
vector or matrix with response values to use in case of venetian blinds |
Details
Parameter 'cv' defines how to split the rows of the training set. The split is similar to cross-validation splits, as PCV is based on cross-validation. This parameter can have the following values:
1. A number (e.g. 'cv = 4'). In this case this number specifies number of segments for random splits, except 'cv = 1' which is a special case for leave-one-out (full cross-validation).
2. A list with 2 values: 'list("name", nseg)'. In this case '"name"' defines the way to make the split, you can select one of the following: '"loo"' for leave-one-out, '"rand"' for random splits or '"ven"' for Venetian blinds (systematic) splits. The second parameter, 'nseg', is a number of segments for splitting the rows into. For example, 'cv = list("ven", 4)', shown in the code examples above, tells PCV to use Venetian blinds splits with 4 segments.
3. A vector with integer numbers, e.g. 'cv = c(1, 2, 3, 1, 2, 3, 1, 2, 3)'. In this case number of values in this vector must be the same as number of rows in the training set. The values specify which segment a particular row will belong to. In case of the example shown here, it is assumed that you have 9 rows in the calibration set, which will be split into 3 segments. The first segment will consist of measurements from rows 1, 4 and 7.
Value
vector with object indices for each segment
Procrustes cross-validation for PCA models
Description
Procrustes cross-validation for PCA models
Usage
pcvpca(
X,
ncomp = min(nrow(X) - 1, ncol(X), 30),
cv = list("ven", 4),
center = TRUE,
scale = FALSE,
cv.scope = "global"
)
Arguments
X |
matrix with predictors from the training set. |
ncomp |
number of components to use (more than the expected optimal number). |
cv |
which split method to use for cross-validation (see description for details). |
center |
logical, to center or not the data sets |
scale |
logical, to scale or not the data sets |
cv.scope |
scope for center/scale operations inside CV loop: 'global' — using globally computed mean and std or 'local' — recompute new for each local calibration set. |
Details
The method computes Procrustes validation set (PV-set), matrix Xpv, based on PCA decomposition of calibration set 'X' and cross-validation. See description of the method in [1].
Parameter 'cv' defines how to split the rows of the training set. The split is similar to cross-validation splits, as PCV is based on cross-validation. This parameter can have the following values:
1. A number (e.g. 'cv = 4'). In this case this number specifies number of segments for random splits, except 'cv = 1' which is a special case for leave-one-out (full cross-validation).
2. A list with 2 values: 'list("name", nseg)'. In this case '"name"' defines the way to make the split, you can select one of the following: '"loo"' for leave-one-out, '"rand"' for random splits or '"ven"' for Venetian blinds (systematic) splits. The second parameter, 'nseg', is a number of segments for splitting the rows into. For example, 'cv = list("ven", 4)', shown in the code examples above, tells PCV to use Venetian blinds splits with 4 segments.
3. A vector with integer numbers, e.g. 'cv = c(1, 2, 3, 1, 2, 3, 1, 2, 3)'. In this case number of values in this vector must be the same as number of rows in the training set. The values specify which segment a particular row will belong to. In case of the example shown here, it is assumed that you have 9 rows in the calibration set, which will be split into 3 segments. The first segment will consist of measurements from rows 1, 4 and 7.
Parameter 'cv.scope' influences how the Procrustean rule is met. In case of "global" scope, the rule will be met strictly - distances for PV-set and the global model will be identical to the distances from conventional cross-validation. In case of "local" scope, every local model will have its own center and scaling factor and hence the rule will be almost met (the distances will be close but not identical).
Value
Matrix with PV-set (same size as X)
References
1. S. Kucheryavskiy, O. Rodionova, A. Pomerantsev. Procrustes cross-validation of multivariate regression models. Analytica Chimica Acta, 1255 (2022) [https://doi.org/10.1016/j.aca.2023.341096]
Examples
# load NIR spectra of Corn samples
data(corn)
X <- corn$spectra
# generate Xpv set based on PCA decomposition with A = 20 and venetian blinds split with 4 segments
Xpv <- pcvpca(X, ncomp = 20, center = TRUE, scale = FALSE, cv = list("ven", 4))
# show the original spectra and the PV-set (as is and mean centered)
oldpar <- par(mfrow = c(2, 2))
matplot(t(X), type = "l", lty = 1, main = "Original data")
matplot(t(Xpv), type = "l", lty = 1, main = "PV-set")
matplot(t(scale(X, scale = FALSE)), type = "l", lty = 1, main = "Original data (mean centered)")
matplot(t(scale(Xpv, scale = FALSE)), type = "l", lty = 1, main = "PV-set (mean centered)")
par(oldpar)
Procrustes cross-validation for PCR models
Description
Procrustes cross-validation for PCR models
Usage
pcvpcr(
X,
Y,
ncomp = min(nrow(X) - 1, ncol(X), 30),
cv = list("ven", 4),
center = TRUE,
scale = FALSE,
cv.scope = "global"
)
Arguments
X |
matrix with predictors from the training set. |
Y |
vector with response values from the training set. |
ncomp |
number of components to use (more than the expected optimal number). |
cv |
which split method to use for cross-validation (see description of method 'pcvpls()' for details). |
center |
logical, to center or not the data sets |
scale |
logical, to scale or not the data sets |
cv.scope |
scope for center/scale operations inside CV loop: 'global' — using globally computed mean and std or 'local' — recompute new for each local calibration set. |
Details
The method computes pseudo-validation matrix Xpv, based on PCR decomposition of calibration set X, y and cross-validation.
Parameter 'cv' defines how to split the rows of the training set. The split is similar to cross-validation splits, as PCV is based on cross-validation. This parameter can have the following values:
1. A number (e.g. 'cv = 4'). In this case this number specifies number of segments for random splits, except 'cv = 1' which is a special case for leave-one-out (full cross-validation).
2. A list with 2 values: 'list("name", nseg)'. In this case '"name"' defines the way to make the split, you can select one of the following: '"loo"' for leave-one-out, '"rand"' for random splits or '"ven"' for Venetian blinds (systematic) splits. The second parameter, 'nseg', is a number of segments for splitting the rows into. For example, 'cv = list("ven", 4)', shown in the code examples above, tells PCV to use Venetian blinds splits with 4 segments.
3. A vector with integer numbers, e.g. 'cv = c(1, 2, 3, 1, 2, 3, 1, 2, 3)'. In this case number of values in this vector must be the same as number of rows in the training set. The values specify which segment a particular row will belong to. In case of the example shown here, it is assumed that you have 9 rows in the calibration set, which will be split into 3 segments. The first segment will consist of measurements from rows 1, 4 and 7.
Parameter 'cv.scope' influences how the Procrustean rule is met. In case of "global" scope, the rule will be met strictly - error of predictions for PV-set and the global model will be identical to the error from conventional cross-validation. In case of "local" scope, every local model will have its own center and hence the rule will be almost met (the errors will be close but not identical).
Value
Pseudo-validation matrix (same size as X) with an additional attribute, 'D' which contains the scaling coefficients (ck/c)
References
1. S. Kucheryavskiy, O. Rodionova, A. Pomerantsev. Procrustes cross-validation of multivariate regression models. Analytica Chimica Acta, 1255 (2022) [https://doi.org/10.1016/j.aca.2023.341096]
Examples
# load NIR spectra of Corn samples
data(corn)
X <- corn$spectra
Y <- corn$moisture
# generate Xpv set based on PCA decomposition with A = 20 and venetian blinds split with 4 segments
Xpv <- pcvpcr(X, Y, ncomp = 20, center = TRUE, scale = FALSE, cv = list("ven", 4))
# show the original spectra and the PV-set (as is and mean centered)
oldpar <- par(mfrow = c(2, 2))
matplot(t(X), type = "l", lty = 1, main = "Original data")
matplot(t(Xpv), type = "l", lty = 1, main = "PV-set")
matplot(t(scale(X, scale = FALSE)), type = "l", lty = 1, main = "Original data (mean centered)")
matplot(t(scale(Xpv, scale = FALSE)), type = "l", lty = 1, main = "PV-set (mean centered)")
par(oldpar)
Procrustes cross-validation for PLS models
Description
Procrustes cross-validation for PLS models
Usage
pcvpls(
X,
Y,
ncomp = min(nrow(X) - 1, ncol(X), 30),
center = TRUE,
scale = FALSE,
cv = list("ven", 4),
cv.scope = "global"
)
Arguments
X |
matrix with predictors from the training set. |
Y |
vector or matrix with response values from the training set. |
ncomp |
number of components to use (more than the expected optimal number). |
center |
logical, to center or not the data sets |
scale |
logical, to scale or not the data sets |
cv |
which split method to use for cross-validation (see description for details). |
cv.scope |
scope for center/scale operations inside CV loop: 'global' — using globally computed mean and std or 'local' — recompute new for each local calibration set. |
Details
The method computes pseudo-validation matrix Xpv, based on PLS decomposition of calibration set X, y and cross-validation.
Parameter 'cv' defines how to split the rows of the training set. The split is similar to cross-validation splits, as PCV is based on cross-validation. This parameter can have the following values:
1. A number (e.g. 'cv = 4'). In this case this number specifies number of segments for random splits, except 'cv = 1' which is a special case for leave-one-out (full cross-validation).
2. A list with 2 values: 'list("name", nseg)'. In this case '"name"' defines the way to make the split, you can select one of the following: '"loo"' for leave-one-out, '"rand"' for random splits or '"ven"' for Venetian blinds (systematic) splits. The second parameter, 'nseg', is a number of segments for splitting the rows into. For example, 'cv = list("ven", 4)', shown in the code examples above, tells PCV to use Venetian blinds splits with 4 segments.
3. A vector with integer numbers, e.g. 'cv = c(1, 2, 3, 1, 2, 3, 1, 2, 3)'. In this case number of values in this vector must be the same as number of rows in the training set. The values specify which segment a particular row will belong to. In case of the example shown here, it is assumed that you have 9 rows in the calibration set, which will be split into 3 segments. The first segment will consist of measurements from rows 1, 4 and 7.
Parameter 'cv.scope' influences how the Procrustean rule is met. In case of "global" scope, the rule will be met strictly - error of predictions for PV-set and the global model will be identical to the error from conventional cross-validation. In case of "local" scope, every local model will have its own center and hence the rule will be almost met (the errors will be close but not identical).
Value
Pseudo-validation matrix (same size as X) with an additional attribute, 'D' which contains the scaling coefficients (ck/c)
References
1. S. Kucheryavskiy, O. Rodionova, A. Pomerantsev. Procrustes cross-validation of multivariate regression models. Analytica Chimica Acta, 1255 (2022) [https://doi.org/10.1016/j.aca.2023.341096]
Examples
# load NIR spectra of Corn samples
data(corn)
X <- corn$spectra
Y <- corn$moisture
# generate Xpv set based on PCA decomposition with A = 20 and venetian blinds split with 4 segments
Xpv <- pcvpls(X, Y, ncomp = 20, center = TRUE, scale = FALSE, cv = list("ven", 4))
# show the original spectra and the PV-set (as is and mean centered)
oldpar <- par(mfrow = c(2, 2))
matplot(t(X), type = "l", lty = 1, main = "Original data")
matplot(t(Xpv), type = "l", lty = 1, main = "PV-set")
matplot(t(scale(X, scale = FALSE)), type = "l", lty = 1, main = "Original data (mean centered)")
matplot(t(scale(Xpv, scale = FALSE)), type = "l", lty = 1, main = "PV-set (mean centered)")
par(oldpar)
# show the heatmap with the scaling coefficients
plotD(Xpv)
Procrustes cross-validation for multivariate regression models
Description
This is a generic method, use 'pcvpls()' or 'pcvpcr()' instead.
Usage
pcvreg(
X,
Y,
ncomp = min(nrow(X) - 1, ncol(X), 30),
cv = list("ven", 4),
center = TRUE,
scale = FALSE,
funlist = list(),
cv.scope = "global"
)
Arguments
X |
matrix with predictors from the training set. |
Y |
vector with response values from the training set. |
ncomp |
number of components to use (more than the expected optimal number). |
cv |
which split method to use for cross-validation (see description of method 'pcvpls()' for details). |
center |
logical, to center or not the data sets |
scale |
logical, to scale or not the data sets |
funlist |
list with functions for particular implementation |
cv.scope |
scope for center/scale operations inside CV loop: 'global' — using globally computed mean and std or 'local' — recompute new for each local calibration set. |
Plots heatmap for scaling coefficients obtained when generating PV-set for PCR or PLS
Description
Plots heatmap for scaling coefficients obtained when generating PV-set for PCR or PLS
Usage
plotD(
Xpv,
colmap = colorRampPalette(c("blue", "white", "red"))(256),
lim = c(-2, 4),
xlab = "Components",
ylab = "Segments",
...
)
Arguments
Xpv |
PV-set generated by 'pcvpcr()' or 'pcvpls()'. |
colmap |
colormap - any with 256 colors. |
lim |
limits for color map (smallest/largest expected value), centered around 1. |
xlab |
label for x-axis |
ylab |
label for y-axis |
... |
any other parameters for method 'image' |
Value
No return value, just creates a plot.
Creates a rotation matrix to map a vector x to [1 0 0 ... 0]
Description
Creates a rotation matrix to map a vector x to [1 0 0 ... 0]
Usage
rotationMatrixToX1(x)
Arguments
x |
Vector (sequence with J coordinates) |
Value
Rotation matrix (JxJ)
SIMPLS algorithm
Description
SIMPLS algorithm for calibration of PLS model
Usage
simpls(X, Y, ncomp)
Arguments
X |
a matrix with x values (predictors) |
Y |
a matrix with y values (responses) |
ncomp |
number of components to calculate |
Value
a list with computed weights, x- and y-loadings for PLS regression model.
References
[1]. S. de Jong. SIMPLS: An Alternative approach to partial least squares regression. Chemometrics and Intelligent Laboratory Systems, 18, 1993 (251-263).