| Title: | Extensible Data Structures for Multivariate Analysis |
| Version: | 0.2.0 |
| Description: | Provides a set of basic and extensible data structures and functions for multivariate analysis, including dimensionality reduction techniques, projection methods, and preprocessing functions. The aim of this package is to offer a flexible and user-friendly framework for multivariate analysis that can be easily extended for custom requirements and specific data analysis tasks. |
| License: | MIT + file LICENSE |
| Encoding: | UTF-8 |
| RoxygenNote: | 7.3.1 |
| Imports: | rlang, chk, glmnet, corpcor, Matrix, purrr, rsvd, svd, pls, irlba, RSpectra, proxy, matrixStats, fitdistrplus |
| Suggests: | covr, randomForest, testthat, magrittr, knitr, rmarkdown, MASS |
| URL: | https://bbuchsbaum.github.io/multivarious/ |
| VignetteBuilder: | knitr |
| NeedsCompilation: | no |
| Packaged: | 2024-03-27 13:14:27 UTC; bbuchsbaum |
| Author: | Bradley Buchsbaum 
[aut, cre] |
| Maintainer: | Bradley Buchsbaum <brad.buchsbaum@gmail.com> |
| Repository: | CRAN |
| Date/Publication: | 2024-03-28 16:00:02 UTC |
add a pre-processing stage
Description
add a pre-processing stage
Usage
add_node(x, step, ...)
Arguments
x |
the processing pipeline |
step |
the pre-processing step to add |
... |
extra args |
Value
a new pre-processing pipeline with the added step
Apply rotation
Description
Apply a specified rotation to the fitted model
Usage
apply_rotation(x, rotation_matrix, ...)
Arguments
x |
A model object, possibly created using the |
rotation_matrix |
|
... |
extra args |
Value
A modified object with updated components and scores after applying the specified rotation.
apply a pre-processing transform
Description
apply a pre-processing transform
Usage
apply_transform(x, X, colind, ...)
Arguments
x |
the pre_processor |
X |
the data matrix |
colind |
column indices |
... |
extra args |
Value
the transformed data
Construct a bi_projector instance
Description
A bi_projector offers a two-way mapping from samples (rows) to scores and from variables (columns) to components. Thus, one can project from D-dimensional input space to d-dimensional subspace. And one can project (project_vars) from n-dimensional variable space to the d-dimensional component space. The singular value decomposition is a canonical example of such a two-way mapping.
Usage
bi_projector(v, s, sdev, preproc = prep(pass()), classes = NULL, ...)
Arguments
v |
A matrix of coefficients with dimensions |
s |
The score matrix |
sdev |
The standard deviations of the score matrix |
preproc |
(optional) A pre-processing pipeline, default is prep(pass()) |
classes |
(optional) A character vector specifying the class attributes of the object, default is NULL |
... |
Extra arguments to be stored in the |
Value
A bi_projector object
Examples
X <- matrix(rnorm(200), 10, 20)
svdfit <- svd(X)
p <- bi_projector(svdfit$v, s = svdfit$u %% diag(svdfit$d), sdev=svdfit$d)
A Union of Concatenated bi_projector Fits
Description
This function combines a set of bi_projector fits into a single bi_projector instance.
The new instance's weights and associated scores are obtained by concatenating the weights
and scores of the input fits.
Usage
bi_projector_union(fits, outer_block_indices = NULL)
Arguments
fits |
A list of |
outer_block_indices |
An optional list of indices for the outer blocks. If not provided, the function will compute the indices based on the dimensions of the input fits. |
Value
A new bi_projector instance with concatenated weights, scores, and other
properties from the input bi_projector instances.
Examples
X1 <- matrix(rnorm(5*5), 5, 5)
X2 <- matrix(rnorm(5*5), 5, 5)
bpu <- bi_projector_union(list(pca(X1), pca(X2)))
get block_indices
Description
extract the list of indices associated with each block in a multiblock object
Usage
block_indices(x, ...)
Arguments
x |
the object |
... |
extra args |
Value
a list of block indices
get block_lengths
Description
extract the lengths of each block in a multiblock object
Usage
block_lengths(x)
Arguments
x |
the object |
Value
the block lengths
Bootstrap Resampling for Multivariate Models
Description
Perform bootstrap resampling on a multivariate model to estimate the variability of components and scores.
Usage
bootstrap(x, nboot, ...)
Arguments
x |
A fitted model object, such as a |
nboot |
An integer specifying the number of bootstrap resamples to perform. |
... |
Additional arguments to be passed to the specific model implementation of |
Value
A list containing the bootstrap resampled components and scores for the model.
PCA Bootstrap Resampling
Description
Perform bootstrap resampling for Principal Component Analysis (PCA) to estimate component and score variability.
Usage
## S3 method for class 'pca'
bootstrap(x, nboot = 100, k = ncomp(x), ...)
Arguments
x |
A fitted PCA model object. |
nboot |
The number of bootstrap resamples (default: 100). |
k |
The number of components to bootstrap (default: all components in the fitted PCA model). |
... |
Additional arguments to be passed to the specific model implementation of |
Value
A list containing bootstrap z-scores for the loadings (zboot_loadings) and scores (zboot_scores).
References
Fisher, Aaron, Brian Caffo, Brian Schwartz, and Vadim Zipunnikov. 2016. "Fast, Exact Bootstrap Principal Component Analysis for P > 1 Million." Journal of the American Statistical Association 111 (514): 846-60.
Examples
X <- matrix(rnorm(10*100), 10, 100)
x <- pca(X, ncomp=9)
bootstrap_results <- bootstrap(x)
center a data matrix
Description
remove mean of all columns in matrix
Usage
center(preproc = prepper(), cmeans = NULL)
Arguments
preproc |
the pre-processing pipeline |
cmeans |
optional vector of precomputed column means |
Value
a prepper list
Construct a Classifier
Description
Create a classifier from a given model object (e.g., projector). This classifier can generate predictions for new data points.
Usage
classifier(x, colind, ...)
Arguments
x |
A model object, such as a |
colind |
Optional vector of column indices used for prediction. If not provided, all columns will be used. |
... |
Additional arguments to be passed to the specific model implementation of |
Value
A classifier function that can be used to make predictions on new data points.
Create a k-NN classifier for a discriminant projector
Description
Constructs a k-NN classifier for a discriminant projector, with an option to use a subset of the components.
Usage
## S3 method for class 'discriminant_projector'
classifier(x, colind = NULL, knn = 1, ...)
Arguments
x |
the discriminant projector object |
colind |
an optional vector specifying the column indices of the components to use for prediction (NULL by default) |
knn |
the number of nearest neighbors to consider in the k-NN classifier (default is 1) |
... |
extra arguments |
Value
a classifier object
Multiblock Bi-Projector Classifier
Description
Constructs a classifier for a multiblock bi-projector model that can generate predictions for new data points.
Usage
## S3 method for class 'multiblock_biprojector'
classifier(
x,
colind = NULL,
labels,
new_data = NULL,
block = NULL,
knn = 1,
...
)
Arguments
x |
A fitted multiblock bi-projector model object. |
colind |
An optional vector of column indices used for prediction (default: NULL). |
labels |
A factor or vector of class labels for the training data. |
new_data |
An optional data matrix for which to generate predictions (default: NULL). |
block |
An optional block index for prediction (default: NULL). |
knn |
The number of nearest neighbors to consider in the classifier (default: 1). |
... |
Additional arguments to be passed to the specific model implementation of |
Value
A multiblock classifier object.
See Also
Other classifier:
classifier.projector()
create classifier from a projector
Description
create classifier from a projector
Usage
## S3 method for class 'projector'
classifier(x, colind = NULL, labels, new_data, knn = 1, ...)
Arguments
x |
A model object, such as a |
colind |
Optional vector of column indices used for prediction. If not provided, all columns will be used. |
labels |
the labels associated with the rows of the projected data (see |
new_data |
reference data associated with |
knn |
the number of nearest neighbors to use when classifying a new point. |
... |
Additional arguments to be passed to the specific model implementation of |
Value
a classifier object
See Also
Other classifier:
classifier.multiblock_biprojector()
Examples
data(iris)
X <- iris[,1:4]
pcres <- pca(as.matrix(X),2)
cfier <- classifier(pcres, labels=iris[,5], new_data=as.matrix(iris[,1:4]))
p <- predict(cfier, as.matrix(iris[,1:4]))
Extract coefficients from a cross_projector object
Description
Extract coefficients from a cross_projector object
Usage
## S3 method for class 'cross_projector'
coef(object, source = c("X", "Y"), ...)
Arguments
object |
the model fit |
source |
the source of the data (X or Y block), either "X" or "Y" |
... |
extra args |
Value
the coefficients
scale a data matrix
Description
normalize each column by a scale factor.
Usage
colscale(preproc = prepper(), type = c("unit", "z", "weights"), weights = NULL)
Arguments
preproc |
the pre-processing pipeline |
type |
the kind of scaling, |
weights |
optional precomputed weights |
Value
a prepper list
get the components
Description
Extract the component matrix of a fit.
Usage
components(x, ...)
Arguments
x |
the model fit |
... |
extra args |
Value
the component matrix
Compose Two Projectors
Description
Combine two projector models into a single projector by sequentially applying the first projector and then the second projector.
Usage
compose_projector(x, y, ...)
Arguments
x |
A fitted model object (e.g., |
y |
A second fitted model object (e.g., |
... |
Additional arguments to be passed to the specific model implementation of |
Value
A new projector object representing the composed projector, which can be used to project data onto the combined subspace.
Projector Composition
Description
Compose a sequence of projector objects in forward order.
This function allows the composition of multiple projectors, applying them sequentially to the input data.
Usage
compose_projectors(...)
Arguments
... |
The sequence of |
Value
A composed_projector object that extends the function class, allowing the composed projectors to be
applied to input data.
See Also
Examples
# Create two PCA projectors and compose them
X <- matrix(rnorm(20*20), 20, 20)
pca1 <- pca(X, ncomp=10)
X2 <- scores(pca1)
pca2 <- pca(X2, ncomp=4)
# Compose the PCA projectors
cproj <- compose_projectors(pca1, pca2)
# Ensure the output of the composed projectors has the expected dimensions
stopifnot(ncol(cproj(X)) == 4)
# Check that the composed projectors work as expected
all.equal(project(cproj, X), cproj(X))
bind together blockwise pre-processors
Description
concatenate a sequence of pre-processors, each previously applied to a block of data.
Usage
concat_pre_processors(preprocs, block_indices)
Arguments
preprocs |
a list of initialized |
block_indices |
a list of block indices where each vector in the list contains the global indices of the variables. |
Value
a new prepper object
Examples
p1 <- center() |> prep()
p2 <- center() |> prep()
x1 <- rbind(1:10, 2:11)
x2 <- rbind(1:10, 2:11)
p1a <- init_transform(p1,x1)
p2a <- init_transform(p2,x2)
clist <- concat_pre_processors(list(p1,p2), list(1:10, 11:20))
t1 <- apply_transform(clist, cbind(x1,x2))
t2 <- apply_transform(clist, cbind(x1,x2[,1:5]), colind=1:15)
Transfer data from one input domain to another via common latent space
Description
Convert between data representations in a multiblock decomposition/alignment by projecting the input data onto a common latent space and then reconstructing it in the target domain.
Usage
convert_domain(x, new_data, i, j, comp, rowind, colind, ...)
Arguments
x |
The model fit, typically an object of a class that implements a |
new_data |
The data to transfer, with the same number of rows as the source data block |
i |
The index of the source data block |
j |
The index of the destination data block |
comp |
A vector of component indices to use in the reconstruction |
rowind |
Optional set of row indices to transfer (default: all rows) |
colind |
Optional set of column indices to transfer (default: all columns) |
... |
Additional arguments passed to the underlying |
Value
A matrix or data frame representing the transferred data in the target domain
See Also
project_block for projecting a single block of data onto the subspace
Two-way (cross) projection to latent components
Description
A projector that reduces two blocks of data, X and Y, yielding a pair of weights for each component. This structure can be used, for example, to store weights derived from canonical correlation analysis.
Usage
cross_projector(
vx,
vy,
preproc_x = prep(pass()),
preproc_y = prep(pass()),
...,
classes = NULL
)
Arguments
vx |
the X coefficients |
vy |
the Y coefficients |
preproc_x |
the X pre-processor |
preproc_y |
the Y pre-processor |
... |
extra parameters or results to store |
classes |
additional class names |
Details
This class extends projector and therefore basic operations such as project, shape, reprocess,
and coef work, but by default, it is assumed that the X block is primary. To access Y block operations, an
additional argument source must be supplied to the relevant functions, e.g., coef(fit, source = "Y")
Value
a cross_projector object
Examples
# Create two scaled matrices X and Y
X <- scale(matrix(rnorm(10 * 5), 10, 5))
Y <- scale(matrix(rnorm(10 * 5), 10, 5))
# Perform canonical correlation analysis on X and Y
cres <- cancor(X, Y)
sx <- X %*% cres$xcoef
sy <- Y %*% cres$ycoef
# Create a cross_projector object using the canonical correlation analysis results
canfit <- cross_projector(cres$xcoef, cres$ycoef, cor = cres$cor,
sx = sx, sy = sy, classes = "cancor")
Construct a Discriminant Projector
Description
A discriminant_projector is an instance that extends bi_projector with a projection that maximizes class separation.
This can be useful for dimensionality reduction techniques that take class labels into account, such as Linear Discriminant Analysis (LDA).
Usage
discriminant_projector(
v,
s,
sdev,
preproc = prep(pass()),
labels,
classes = NULL,
...
)
Arguments
v |
A matrix of coefficients with dimensions |
s |
The score matrix |
sdev |
The standard deviations of the score matrix |
preproc |
(optional) A pre-processing pipeline, default is prep(pass()) |
labels |
A factor or character vector of class labels corresponding to the rows of the score matrix |
classes |
(optional) A character vector specifying the class attributes of the object, default is NULL |
... |
Extra arguments to be stored in the |
Value
A discriminant_projector object.
See Also
bi_projector
Examples
# Simulate data and labels
set.seed(123)
X <- matrix(rnorm(100 * 10), 100, 10)
labels <- factor(rep(1:2, each = 50))
# Perform LDA and create a discriminant projector
lda_fit <- MASS::lda(X, labels)
dp <- discriminant_projector(lda_fit$scaling, X %*% lda_fit$scaling, sdev = lda_fit$svd,
labels = labels)
Get a fresh pre-processing node cleared of any cached data
Description
Get a fresh pre-processing node cleared of any cached data
Usage
fresh(x, ...)
Arguments
x |
the processing pipeline |
... |
extra args |
Value
a fresh pre-processing pipeline
Compute column-wise mean in X for each factor level of Y
Description
This function computes group means for each factor level of Y in the provided data matrix X.
Usage
group_means(Y, X)
Arguments
Y |
a vector of labels to compute means over disjoint sets |
X |
a data matrix from which to compute means |
Value
a matrix with row names corresponding to factor levels of Y and column-wise means for each factor level
Examples
# Example data
X <- matrix(rnorm(50), 10, 5)
Y <- factor(rep(1:2, each = 5))
# Compute group means
gm <- group_means(Y, X)
initialize a transform
Description
initialize a transform
Usage
init_transform(x, X, ...)
Arguments
x |
the pre_processor |
X |
the data matrix |
Value
an initialized pre-processor
Inverse of the Component Matrix
Description
Return the inverse projection matrix, which can be used to map back to data space. If the component matrix is orthogonal, then the inverse projection is the transpose of the component matrix.
Usage
inverse_projection(x, ...)
Arguments
x |
The model fit. |
... |
Extra arguments. |
Value
The inverse projection matrix.
See Also
project for projecting data onto the subspace.
is it orthogonal
Description
test whether components are orthogonal
Usage
is_orthogonal(x)
Arguments
x |
the object |
Value
a logical value indicating whether the transformation is orthogonal
Create a Multiblock Bi-Projector
Description
Constructs a multiblock bi-projector using the given component matrix (v), score matrix (s), singular values (sdev),
a preprocessing function, and a list of block indices. This allows for the projection of multiblock data, where each block
represents a different set of variables or features, with two-way mapping from samples to scores and from variables to components.
Usage
multiblock_biprojector(
v,
s,
sdev,
preproc = prep(pass()),
...,
block_indices,
classes = NULL
)
Arguments
v |
A matrix of components with dimensions |
s |
A matrix of scores. |
sdev |
A numeric vector of singular values. |
preproc |
A pre-processing function for the data (default is a pass-through with |
... |
Extra arguments. |
block_indices |
A list of numeric vectors specifying the indices of each data block. |
classes |
(optional) A character vector specifying the class attributes of the object, default is NULL. |
Value
A multiblock_biprojector object.
See Also
bi_projector, multiblock_projector
Create a Multiblock Projector
Description
Constructs a multiblock projector using the given component matrix (v), a preprocessing function, and a list of block indices.
This allows for the projection of multiblock data, where each block represents a different set of variables or features.
Usage
multiblock_projector(
v,
preproc = prep(pass()),
...,
block_indices,
classes = NULL
)
Arguments
v |
A matrix of components with dimensions |
preproc |
A pre-processing function for the data (default is a pass-through with |
... |
Extra arguments. |
block_indices |
A list of numeric vectors specifying the indices of each data block. |
classes |
(optional) A character vector specifying the class attributes of the object, default is NULL. |
Value
A multiblock_projector object.
See Also
projector
Examples
# Generate some example data
X1 <- matrix(rnorm(10 * 5), 10, 5)
X2 <- matrix(rnorm(10 * 5), 10, 5)
X <- cbind(X1, X2)
# Compute PCA on the combined data
pc <- pca(X, ncomp = 8)
# Create a multiblock projector using PCA components and block indices
mb_proj <- multiblock_projector(pc$v, block_indices = list(1:5, 6:10))
# Project the multiblock data using the multiblock projector
mb_scores <- project(mb_proj, X)
get the number of blocks
Description
The number of data blocks in a multiblock element
Usage
nblocks(x)
Arguments
x |
the object |
Value
the number of blocks
Get the number of components
Description
This function returns the total number of components in the fitted model.
Usage
ncomp(x)
Arguments
x |
A fitted model object. |
Value
The number of components in the fitted model.
Examples
# Example using the svd_wrapper function
data(iris)
X <- iris[, 1:4]
fit <- svd_wrapper(X, ncomp = 3, preproc = center(), method = "base")
ncomp(fit) # Should return 3
Nystrom method for out-of-sample embedding
Description
Approximate the embedding of a new data point using the Nystrom method, which is particularly useful for large datasets and data-dependent embedding spaces, such as multidimensional scaling (MDS).
Usage
nystrom_embedding(
new_data,
landmark_data,
kernel_function,
eigenvectors,
eigenvalues,
...
)
Arguments
new_data |
A matrix or data frame containing the new data points to be projected. |
landmark_data |
A matrix or data frame containing the landmark data points used for approximation. |
kernel_function |
A function used to compute the kernel matrix (e.g., a distance function for MDS). |
eigenvectors |
A matrix containing the eigenvectors obtained from the eigendecomposition of the kernel matrix between the landmark points. |
eigenvalues |
A vector containing the eigenvalues obtained from the eigendecomposition of the kernel matrix between the landmark points. |
... |
Additional arguments passed to the kernel_function. |
Value
A matrix containing the approximate embedding of the new_data in the data-dependent space.
Partial Inverse Projection of a Columnwise Subset of Component Matrix
Description
Compute the inverse projection of a columnwise subset of the component matrix (e.g., a sub-block). Even when the full component matrix is orthogonal, there is no guarantee that the partial component matrix is orthogonal.
Usage
partial_inverse_projection(x, colind, ...)
Arguments
x |
A fitted model object, such as a |
colind |
A numeric vector specifying the column indices of the component matrix to consider for the partial inverse projection. |
... |
Additional arguments to be passed to the specific model implementation of |
Value
A matrix representing the partial inverse projection.
Partially project a new sample onto subspace
Description
Project a selected subset of column indices onto the subspace. This function allows for the projection of new data onto a lower-dimensional space using only a subset of the variables, as specified by the column indices.
Usage
partial_project(x, new_data, colind)
Arguments
x |
The model fit, typically an object of class |
new_data |
A matrix or vector of new observations with a subset of columns equal to length of |
colind |
A numeric vector of column indices to select in the projection matrix. These indices correspond to the variables used for the partial projection |
Value
A matrix or vector of the partially projected observations, where rows represent observations and columns represent the lower-dimensional space
See Also
bi_projector for an example of a class that implements a partial_project method
Examples
# Example with the bi_projector class
X <- matrix(rnorm(10*20), 10, 20)
svdfit <- svd(X)
p <- bi_projector(svdfit$v, s = svdfit$u %*% diag(svdfit$d), sdev=svdfit$d)
# Partially project new_data onto the same subspace as the original data
# using only the first 10 variables
new_data <- matrix(rnorm(5*20), 5, 20)
colind <- 1:10
partially_projected_data <- partial_project(p, new_data[,colind], colind)
Construct a partial projector
Description
Create a new projector instance restricted to a subset of input columns. This function allows for the generation of a new projection object that focuses only on the specified columns, enabling the projection of data using a limited set of variables.
Usage
partial_projector(x, colind, ...)
Arguments
x |
The original |
colind |
A numeric vector of column indices to select in the projection matrix. These indices correspond to the variables used for the partial projector |
... |
Additional arguments passed to the underlying |
Value
A new projector instance, with the same class as the original object, that is restricted to the specified subset of input columns
See Also
bi_projector for an example of a class that implements a partial_projector method
Examples
# Example with the bi_projector class
X <- matrix(rnorm(10*20), 10, 20)
svdfit <- svd(X)
p <- bi_projector(svdfit$v, s = svdfit$u %*% diag(svdfit$d), sdev=svdfit$d)
# Create a partial projector using only the first 10 variables
colind <- 1:10
partial_p <- partial_projector(p, colind)
construct a partial_projector from a projector instance
Description
construct a partial_projector from a projector instance
Usage
## S3 method for class 'projector'
partial_projector(x, colind, ...)
Arguments
x |
The original |
colind |
A numeric vector of column indices to select in the projection matrix. These indices correspond to the variables used for the partial projector |
... |
Additional arguments passed to the underlying |
Value
A partial_projector instance
Examples
X <- matrix(rnorm(10*10), 10, 10)
pfit <- pca(X, ncomp=9)
proj <- project(pfit, X)
pp <- partial_projector(pfit, 1:5)
a no-op pre-processing step
Description
pass simply passes its data through the chain
Usage
pass(preproc = prepper())
Arguments
preproc |
the pre-processing pipeline |
Value
a prepper list
Principal Components Analysis (PCA)
Description
Compute the directions of maximal variance in a data matrix using the Singular Value Decomposition (SVD).
Usage
pca(
X,
ncomp = min(dim(X)),
preproc = center(),
method = c("fast", "base", "irlba", "propack", "rsvd", "svds"),
...
)
Arguments
X |
The data matrix. |
ncomp |
The number of requested components to estimate (default is the minimum dimension of the data matrix). |
preproc |
The pre-processing function to apply to the data matrix (default is centering). |
method |
The SVD method to use, passed to |
... |
Extra arguments to send to |
Value
A bi_projector object containing the PCA results.
See Also
svd_wrapper for details on SVD methods.
Examples
data(iris)
X <- as.matrix(iris[, 1:4])
res <- pca(X, ncomp = 4)
tres <- truncate(res, 3)
Permutation Confidence Intervals
Description
Estimate confidence intervals for model parameters using permutation testing.
Usage
perm_ci(x, X, nperm, ...)
Arguments
x |
A model fit object. |
X |
The original data matrix used to fit the model. |
nperm |
The number of permutations to perform for the confidence interval estimation. |
... |
Additional arguments to be passed to the specific model implementation of |
Value
A list containing the estimated lower and upper bounds of the confidence intervals for model parameters.
predict with a classifier object
Description
predict with a classifier object
Usage
## S3 method for class 'classifier'
predict(
object,
new_data,
ncomp = NULL,
colind = NULL,
metric = c("cosine", "euclidean"),
...
)
Arguments
object |
the model fit |
new_data |
new data to predict on |
ncomp |
the number of components to use |
colind |
the column indices to select in the projection matrix |
metric |
the similarity metric ("euclidean" or "cosine") |
... |
additional arguments to projection function |
Value
a list with the predicted class and probabilities
prepare a dataset by applying a pre-processing pipeline
Description
prepare a dataset by applying a pre-processing pipeline
Usage
prep(x, ...)
Arguments
x |
the pipeline |
... |
extra args |
Value
the pre-processed data
Compute principal angles for a set of subspaces
Description
This function calculates the principal angles between subspaces derived from a list of bi_projector instances.
Usage
prinang(fits)
Arguments
fits |
a list of |
Value
a numeric vector of principal angles with length equal to the minimum dimension of input subspaces
Examples
data(iris)
X <- as.matrix(iris[, 1:4])
res <- pca(X, ncomp = 4)
fits_list <- list(res,res,res)
principal_angles <- prinang(fits_list)
Pretty Print S3 Method for bi_projector Class
Description
Pretty Print S3 Method for bi_projector Class
Usage
## S3 method for class 'bi_projector'
print(x, ...)
Arguments
x |
A |
... |
Additional arguments passed to the print function |
Value
Invisible bi_projector object
Pretty Print S3 Method for bi_projector_union Class
Description
Pretty Print S3 Method for bi_projector_union Class
Usage
## S3 method for class 'bi_projector_union'
print(x, ...)
Arguments
x |
A |
... |
Additional arguments passed to the print function |
Value
Invisible bi_projector_union object
Pretty Print Method for classifier Objects
Description
Display a human-readable summary of a classifier object, including information about the k-NN classifier, the model fit, and the dimensions of the scores matrix.
Usage
## S3 method for class 'classifier'
print(x, ...)
Arguments
x |
A |
... |
Additional arguments passed to |
Value
classifier object.
Pretty Print Method for composed_projector Objects
Description
Display a human-readable summary of a composed_projector object, including information about the number and order of projectors.
Usage
## S3 method for class 'composed_projector'
print(x, ...)
Arguments
x |
A |
... |
Additional arguments passed to |
Value
The composed_projector object.
Examples
# Create two PCA projectors and compose them
X <- matrix(rnorm(20*20), 20, 20)
pca1 <- pca(X, ncomp=10)
X2 <- scores(pca1)
pca2 <- pca(X2, ncomp=4)
cproj <- compose_projectors(pca1, pca2)
Pretty Print Method for multiblock_biprojector Objects
Description
Display a human-readable summary of a multiblock_biprojector object, including information about the dimensions of the projection matrix, the pre-processing pipeline, and block indices.
Usage
## S3 method for class 'multiblock_biprojector'
print(x, ...)
Arguments
x |
A |
... |
Additional arguments passed to |
Value
Invisible multiblock_biprojector object.
Examples
# Generate some example data
X1 <- matrix(rnorm(10 * 5), 10, 5)
X2 <- matrix(rnorm(10 * 5), 10, 5)
X <- cbind(X1, X2)
# Compute PCA on the combined data
pc <- pca(X, ncomp = 8)
# Create a multiblock bi-projector using PCA components and block indices
mb_biproj <- multiblock_biprojector(pc$v, s = pc$u %*% diag(sdev(pc)), sdev = sdev(pc),
block_indices = list(1:5, 6:10))
# Pretty print the multiblock bi-projector object
print(mb_biproj)
Pretty Print Method for projector Objects
Description
Display a human-readable summary of a projector object, including information about the dimensions of the projection matrix and the pre-processing pipeline.
Usage
## S3 method for class 'projector'
print(x, ...)
## S3 method for class 'projector'
print(x, ...)
Arguments
x |
A |
... |
Additional arguments passed to |
Value
the projector object
Examples
X <- matrix(rnorm(10*10), 10, 10)
svdfit <- svd(X)
p <- projector(svdfit$v)
print(p)
New sample projection
Description
Project one or more samples onto a subspace. This function takes a model fit and new observations, and projects them onto the subspace defined by the model. This allows for the transformation of new data into the same lower-dimensional space as the original data.
Usage
project(x, new_data, ...)
Arguments
x |
The model fit, typically an object of class bi_projector or any other class that implements a project method |
new_data |
A matrix or vector of new observations with the same number of columns as the original data. Rows represent observations and columns represent variables |
... |
Extra arguments to be passed to the specific project method for the object's class |
Value
A matrix or vector of the projected observations, where rows represent observations and columns represent the lower-dimensional space
See Also
bi_projector for an example of a class that implements a project method
Other project:
project.cross_projector(),
project_block(),
project_vars()
Examples
# Example with the bi_projector class
X <- matrix(rnorm(10*20), 10, 20)
svdfit <- svd(X)
p <- bi_projector(svdfit$v, s = svdfit$u %% diag(svdfit$d), sdev=svdfit$d)
# Project new_data onto the same subspace as the original data
new_data <- matrix(rnorm(5*20), 5, 20)
projected_data <- project(p, new_data)
project a cross_projector instance
Description
project a cross_projector instance
Usage
## S3 method for class 'cross_projector'
project(x, new_data, source = c("X", "Y"), ...)
Arguments
x |
The model fit, typically an object of class bi_projector or any other class that implements a project method |
new_data |
A matrix or vector of new observations with the same number of columns as the original data. Rows represent observations and columns represent variables |
source |
the source of the data (X or Y block) |
... |
Extra arguments to be passed to the specific project method for the object's class |
Value
the projected data
See Also
Other project:
project(),
project_block(),
project_vars()
Project a single "block" of data onto the subspace
Description
When observations are concatenated into "blocks", it may be useful to project one block from the set. This function facilitates the projection of a specific block of data onto a subspace. It is a convenience method for multi-block fits and is equivalent to a "partial projection" where the column indices are associated with a given block.
Usage
project_block(x, new_data, block, ...)
Arguments
x |
The model fit, typically an object of a class that implements a |
new_data |
A matrix or vector of new observation(s) with the same number of columns as the original data |
block |
An integer representing the block ID to select in the block projection matrix. This ID corresponds to the specific block of data to be projected |
... |
Additional arguments passed to the underlying |
Value
A matrix or vector of the projected data for the specified block
See Also
project for the generic projection function
Other project:
project(),
project.cross_projector(),
project_vars()
Project one or more variables onto a subspace
Description
This function projects one or more variables onto a subspace. It is often called supplementary variable projection and can be computed for a biorthogonal decomposition, such as Singular Value Decomposition (SVD).
Usage
project_vars(x, new_data, ...)
Arguments
x |
The model fit, typically an object of a class that implements a |
new_data |
A matrix or vector of new observation(s) with the same number of rows as the original data |
... |
Additional arguments passed to the underlying |
Value
A matrix or vector of the projected variables in the subspace
See Also
project for the generic projection function for samples
Other project:
project(),
project.cross_projector(),
project_block()
Construct a projector instance
Description
A projector maps a matrix from an N-dimensional space to d-dimensional space, where d may be less than N.
The projection matrix, v, is not necessarily orthogonal. This function constructs a projector instance which can be
used for various dimensionality reduction techniques like PCA, LDA, etc.
Usage
projector(v, preproc = prep(pass()), ..., classes = NULL)
Arguments
v |
A matrix of coefficients with dimensions |
preproc |
A prepped pre-processing object. Default is the no-processing |
... |
Extra arguments to be stored in the |
classes |
Additional class information used for creating subtypes of |
Value
An instance of type projector.
Examples
X <- matrix(rnorm(10*10), 10, 10)
svdfit <- svd(X)
p <- projector(svdfit$v)
proj <- project(p, X)
Reconstruct the data
Description
Reconstruct a data set from its (possibly) low-rank representation. This can be useful when analyzing the impact of dimensionality reduction or when visualizing approximations of the original data.
Usage
reconstruct(x, comp, rowind, colind, ...)
Arguments
x |
The model fit, typically an object of a class that implements a |
comp |
A vector of component indices to use in the reconstruction |
rowind |
The row indices to reconstruct (optional). If not provided, all rows are used. |
colind |
The column indices to reconstruct (optional). If not provided, all columns are used. |
... |
Additional arguments passed to the underlying |
Value
A reconstructed data set based on the selected components, rows, and columns
See Also
bi_projector for an example of a two-way mapping model that can be reconstructed
refit a model
Description
refit a model given new data or new parameter(s)
Usage
refit(x, new_data, ...)
Arguments
x |
the original model fit object |
new_data |
the new data to process |
... |
extra args |
Value
a refit model object
Multi-output linear regression
Description
Fit a multivariate regression model for a matrix of basis functions, X, and a response matrix Y.
The goal is to find a projection matrix that can be used for mapping and reconstruction.
Usage
regress(
X,
Y,
preproc = NULL,
method = c("lm", "enet", "mridge", "pls"),
intercept = FALSE,
lambda = 0.001,
alpha = 0,
ncomp = ceiling(ncol(X)/2),
...
)
Arguments
X |
the set of independent (basis) variables |
Y |
the response matrix |
preproc |
the pre-processor (currently unused) |
method |
the regression method: |
intercept |
whether to include an intercept term |
lambda |
ridge shrinkage parameter (for methods |
alpha |
the elastic net mixing parameter if method is |
ncomp |
number of PLS components if method is |
... |
extra arguments sent to the underlying fitting function |
Value
a bi-projector of type regress
Examples
# Generate synthetic data
Y <- matrix(rnorm(100 * 10), 10, 100)
X <- matrix(rnorm(10 * 9), 10, 9)
# Fit regression models and reconstruct the response matrix
r_lm <- regress(X, Y, intercept = FALSE, method = "lm")
recon_lm <- reconstruct(r_lm)
r_mridge <- regress(X, Y, intercept = TRUE, method = "mridge", lambda = 0.001)
recon_mridge <- reconstruct(r_mridge)
r_enet <- regress(X, Y, intercept = TRUE, method = "enet", lambda = 0.001, alpha = 0.5)
recon_enet <- reconstruct(r_enet)
r_pls <- regress(X, Y, intercept = TRUE, method = "pls", ncomp = 5)
recon_pls <- reconstruct(r_pls)
apply pre-processing parameters to a new data matrix
Description
Given a new dataset, process it in the same way the original data was processed (e.g. centering, scaling, etc.)
Usage
reprocess(x, new_data, colind, ...)
Arguments
x |
the model fit object |
new_data |
the new data to process |
colind |
the column indices of the new data |
... |
extra args |
Value
the reprocessed data
reprocess a cross_projector instance
Description
reprocess a cross_projector instance
Usage
## S3 method for class 'cross_projector'
reprocess(x, new_data, colind = NULL, source = c("X", "Y"), ...)
Arguments
x |
the model fit object |
new_data |
the new data to process |
colind |
the column indices of the new data |
source |
the source of the data (X or Y block) |
... |
extra args |
Value
the re(pre-)processed data
Compute a regression model for each column in a matrix and return residual matrix
Description
Compute a regression model for each column in a matrix and return residual matrix
Usage
residualize(form, X, design, intercept = FALSE)
Arguments
form |
the formula defining the model to fit for residuals |
X |
the response matrix |
design |
the |
intercept |
add an intercept term (default is FALSE) |
Value
a matrix of residuals
Examples
X <- matrix(rnorm(20*10), 20, 10)
des <- data.frame(a=rep(letters[1:4], 5), b=factor(rep(1:5, each=4)))
xresid <- residualize(~ a+b, X, design=des)
## design is saturated, residuals should be zero
xresid2 <- residualize(~ a*b, X, design=des)
sum(xresid2) == 0
Obtain residuals of a component model fit
Description
Calculate the residuals of a model after removing the effect of the first ncomp components.
This function is useful to assess the quality of the fit or to identify patterns that are not
captured by the model.
Usage
residuals(x, ncomp, xorig, ...)
Arguments
x |
The model fit object. |
ncomp |
The number of components to factor out before calculating residuals. |
xorig |
The original data matrix (X) used to fit the model. |
... |
Additional arguments passed to the method. |
Value
A matrix of residuals, with the same dimensions as the original data matrix.
reverse a pre-processing transform
Description
reverse a pre-processing transform
Usage
reverse_transform(x, X, colind, ...)
Arguments
x |
the pre_processor |
X |
the data matrix |
colind |
column indices |
... |
extra args |
Value
the reverse-transformed data
construct a random forest wrapper classifier
Description
Given a model object (e.g. projector construct a random forest classifier that can generate predictions for new data points.
Usage
rf_classifier(x, colind, ...)
Arguments
x |
the model object |
colind |
the (optional) column indices used for prediction |
... |
extra arguments to |
Value
a random forest classifier
create a random forest classifier
Description
create a random forest classifier
Usage
## S3 method for class 'projector'
rf_classifier(x, colind = NULL, labels, scores, ...)
Arguments
x |
the model object |
colind |
the (optional) column indices used for prediction |
labels |
A factor or vector of class labels for the training data. |
scores |
a matrix of references scores used for classification |
... |
extra arguments to |
Value
a rf_classifier object
Examples
data(iris)
X <- iris[,1:4]
pcres <- pca(as.matrix(X),2)
cfier <- rf_classifier(pcres, labels=iris[,5], scores=scores(pcres))
p <- predict(cfier, new_data=as.matrix(iris[,1:4]))
Rotate a Component Solution
Description
Perform a rotation of the component loadings to improve interpretability.
Usage
rotate(x, ncomp, type)
Arguments
x |
The model fit, typically a result from a dimensionality reduction method like PCA. |
ncomp |
The number of components to rotate. |
type |
The type of rotation to apply (e.g., "varimax", "quartimax", "promax"). |
Value
A modified model fit with the rotated components.
Retrieve the component scores
Description
Extract the factor score matrix from a fitted model. The factor scores represent the projections of the data onto the components, which can be used for further analysis or visualization.
Usage
scores(x, ...)
Arguments
x |
The model fit object. |
... |
Additional arguments passed to the method. |
Value
A matrix of factor scores, with rows corresponding to samples and columns to components.
See Also
project for projecting new data onto the components.
standard deviations
Description
The standard deviations of the projected data matrix
Usage
sdev(x)
Arguments
x |
the model fit |
Value
the standard deviations
Shape of the Projector
Description
Get the input/output shape of the projector.
Usage
shape(x, ...)
Arguments
x |
The model fit. |
... |
Extra arguments. |
Details
This function retrieves the dimensions of the sample loadings matrix v in the form of a vector with two elements.
The first element is the number of rows in the v matrix, and the second element is the number of columns.
Value
A vector containing the dimensions of the sample loadings matrix v (number of rows and columns).
shape of a cross_projector instance
Description
shape of a cross_projector instance
Usage
## S3 method for class 'cross_projector'
shape(x, source = c("X", "Y"), ...)
Arguments
x |
The model fit. |
source |
the source of the data (X or Y block) |
... |
Extra arguments. |
Value
the shape of the data
center and scale each vector of a matrix
Description
center and scale each vector of a matrix
Usage
standardize(preproc = prepper(), cmeans = NULL, sds = NULL)
Arguments
preproc |
the pre-processing pipeline |
cmeans |
an optional vector of column means |
sds |
an optional vector of sds |
Value
a prepper list
Compute standardized component scores
Description
Calculate standardized factor scores from a fitted model. Standardized scores are useful for comparing the contributions of different components on the same scale, which can help in interpreting the results.
Usage
std_scores(x, ...)
Arguments
x |
The model fit object. |
... |
Additional arguments passed to the method. |
Value
A matrix of standardized factor scores, with rows corresponding to samples and columns to components.
See Also
scores for retrieving the original component scores.
Singular Value Decomposition (SVD) Wrapper
Description
Computes the singular value decomposition of a matrix using one of the specified methods. It is designed to be an easy-to-use wrapper for various SVD methods available in R.
Usage
svd_wrapper(
X,
ncomp = min(dim(X)),
preproc = pass(),
method = c("fast", "base", "irlba", "propack", "rsvd", "svds"),
q = 2,
p = 10,
tol = .Machine$double.eps,
...
)
Arguments
X |
the input matrix |
ncomp |
the number of components to estimate (default: min(dim(X))) |
preproc |
the pre-processor to apply on the input matrix (e.g., |
method |
the SVD method to use: 'base', 'fast', 'irlba', 'propack', 'rsvd', or 'svds' |
q |
parameter passed to method |
p |
parameter passed to method |
tol |
minimum eigenvalue magnitude, otherwise component is dropped (default: .Machine$double.eps) |
... |
extra arguments passed to the selected SVD function |
Value
an SVD object that extends projector
Examples
# Load iris dataset and select the first four columns
data(iris)
X <- iris[, 1:4]
# Compute SVD using the base method and 3 components
fit <- svd_wrapper(X, ncomp = 3, preproc = center(), method = "base")
Transpose a model
Description
This function transposes a model by switching coefficients and scores. It is useful when you want to reverse the roles of samples and variables in a model, especially in the context of dimensionality reduction methods.
Usage
transpose(x, ...)
Arguments
x |
The model fit, typically an object of a class that implements a |
... |
Additional arguments passed to the underlying |
Value
A transposed model with coefficients and scores switched
See Also
bi_projector for an example of a two-way mapping model that can be transposed
truncate a component fit
Description
take the first n components of a decomposition
Usage
truncate(x, ncomp)
Arguments
x |
the object to truncate |
ncomp |
number of components to retain |
Value
a truncated object (e.g. PCA with 'ncomp' components)