Package 'mixKernel'

Center and scale

Description

Center and scale a dataset.

Usage

center.scale(X)

Arguments

X	a numeric matrix (or data frame) to center and scaled. NAs not allowed.

Value

center.scale returns a centered and scaled matrix.

Author(s)

Celine Brouard <[email protected]> Jerome Mariette <[email protected]> Nathalie Vialaneix <[email protected]>

See Also

compute.kernel, combine.kernels

Examples

data("nutrimouse")
## Not run: 
 nutrimouse.sc <- center.scale(nutrimouse$gene)

## End(Not run)

---

Compute and display similarities between multiple kernels

Description

Compute cosine from Frobenius norm between kernels and display the corresponding correlation plot.

Usage

cim.kernel(
  ...,
  scale = TRUE,
  method = c("circle", "square", "number", "shade", "color", "pie")
)

Arguments

...	list of kernels (called 'blocks') computed on different datasets and measured on the same samples.
scale	boleean. If scale = TRUE, each block is standardized to zero mean and unit variance and cosine normalization is performed on the kernel. Default: TRUE.
method	character. The visualization method to be used. Currently, seven methods are supported (see Details).

Details

The displayed similarities are the kernel generalization of the RV-coefficient described in Lavit et al., 1994.

The plot is displayed using the corrplot package. Seven visualization methods are implemented: "circle" (default), "square", "number", "pie", "shade" and "color". Circle and square areas are proportional to the absolute value of corresponding similarities coefficients.

Value

cim.kernel returns a matrix containing the cosine from Frobenius norm between kernels.

Author(s)

Jerome Mariette <[email protected]> Nathalie Vialaneix <[email protected]>

References

Lavit C., Escoufier Y., Sabatier R. and Traissac P. (1994). The ACT (STATIS method). Computational Statistics and Data Analysis, 18(1), 97-119.

Mariette J. and Villa-Vialaneix N. (2018). Unsupervised multiple kernel learning for heterogeneous data integration. Bioinformatics, 34(6), 1009-1015.

See Also

compute.kernel

Examples

data(TARAoceans)

# compute one kernel per dataset
phychem.kernel <- compute.kernel(TARAoceans$phychem, kernel.func = "linear")
pro.phylo.kernel <- compute.kernel(TARAoceans$pro.phylo, 
                                   kernel.func = "abundance")
pro.NOGs.kernel <- compute.kernel(TARAoceans$pro.NOGs, 
                                  kernel.func = "abundance")

# display similarities between kernels
cim.kernel(phychem = phychem.kernel,
           pro.phylo = pro.phylo.kernel,
           pro.NOGs = pro.NOGs.kernel, 
           method = "square")

---

Combine multiple kernels into a meta-kernel

Description

Compute multiple kernels into a single meta-kernel

Usage

combine.kernels(
  ...,
  scale = TRUE,
  method = c("full-UMKL", "STATIS-UMKL", "sparse-UMKL"),
  knn = 5,
  rho = 20
)

Arguments

...	list of kernels (called 'blocks') computed on different datasets and measured on the same samples.
scale	boleean. If scale = TRUE, each block is standardized to zero mean and unit variance and cosine normalization is performed on the kernel. Default: TRUE.
method	character. Which method should be used to compute the meta-kernel. Default: "full-UMKL".
knn	integer. If method = "sparse-UMKL" or method = "full-UMKL", number of neighbors used to get a proxy of the local topology of the datasets from each kernel. Default: 5.
rho	integer. Parameters for the augmented Lagrangian method. Default: 20.

Details

The arguments method allows to specify the Unsupervised Multiple Kernel Learning (UMKL) method to use:

• "STATIS-UMKL": combines input kernels into the best consensus of all kernels;

• "full-UMKL": computes a kernel that minimizes the distortion between the meta-kernel and the k-NN graphs obtained from all input kernels;

• "sparse-UMKL": a sparse variant of the "full-UMKL" approach.

Value

combine.kernels returns an object of classes "kernel" and "metaKernel", a list that contains the following components:

kernel	: the computed meta-kernel matrix;
X	: the dataset from which the kernel has been computed, as given by the function compute.kernel. Can be NULL if a kernel matrix was passed to this function;
weights	: a vector containing the weights used to combine the kernels.

Author(s)

Jerome Mariette <[email protected]> Nathalie Vialaneix <[email protected]>

References

Mariette J. and Villa-Vialaneix N. (2018). Unsupervised multiple kernel learning for heterogeneous data integration . Bioinformatics, 34(6), 1009-1015. DOI: doi:10.1093/bioinformatics/btx682.

See Also

compute.kernel, kernel.pca

Examples

data(TARAoceans)

# compute one kernel per dataset
phychem.kernel <- compute.kernel(TARAoceans$phychem, kernel.func = "linear")
pro.phylo.kernel <- compute.kernel(TARAoceans$pro.phylo, kernel.func = "abundance")
pro.NOGs.kernel <- compute.kernel(TARAoceans$pro.NOGs, kernel.func = "abundance")

# compute the meta kernel
meta.kernel <- combine.kernels(phychem = phychem.kernel,
                               pro.phylo = pro.phylo.kernel,
                               pro.NOGs = pro.NOGs.kernel, 
                               method = "full-UMKL")

---

Compute a kernel

Description

Compute a kernel from a given data matrix.

Usage

compute.kernel(X, kernel.func = "linear", ..., test.pos.semidef = FALSE)

Arguments

X	a numeric matrix (or data frame) used to compute the kernel. NAs not allowed.
kernel.func	the kernel function to use. This parameter can be set to any user defined kernel function. Widely used kernel functions are pre-implemented, that can be used by setting kernel.func to one of the following strings: "kidentity", "abundance", "linear", "gaussian.radial.basis", "poisson" or "phylogenetic". Default: "linear".
...	the kernel function arguments. Valid parameters for pre-implemented kernels are: phylogenetic.tree ("phylogenetic"): an instance of phylo-class that contains a phylogenetic tree (required). scale ("linear" or "gaussian.radial.basis"): logical. Should the variables be scaled to unit variance prior the kernel computation? Default: TRUE. sigma ("gaussian.radial.basis"): double. The inverse kernel width used by "gaussian.radial.basis". method ("phylogenetic" or "abundance"): character. Can be "unifrac" or "wunifrac" for "phylogenetic". Which dissimilarity to use for "abundance": one of "bray", "euclidean", "canberra", "manhattan", "kulczynski", "jaccard", "gower", "altGower", "morisita", "horn", "mountford", "raup", "binomial", "chao" and "cao". normalization ("poisson"): character. Can be "deseq" (more robust), "mle" (less robust) or "quantile".
test.pos.semidef	boleean. If test.pos.semidef = TRUE, the positive semidefiniteness of the resulting matrix is checked.

Value

compute.kernel returns an object of classes "kernel", a list that contains the following components:

kernel	: the computed kernel matrix.
X	: the original dataset. If "kidentity", X is set to NULL.
kernel.func	: the kernel function used.
kernel.args	: the arguments used to compute the kernel.

Author(s)

Jerome Mariette <[email protected]> Nathalie Vialaneix <[email protected]>

References

Lozupone C. and Knight R. (2005). UniFrac: a new phylogenetic method for comparing microbial communities. Applied and Environmental Microbiology, 71(12), 8228-8235.

Lozupone C., Hamady M., Kelley S.T. and Knight R. (2007). Quantitative and qualitative beta diversity measures lead to different insights into factors that structure microbial communities. Applied and Environmental Microbiology, 73(5), 1576-1585.

Witten D. (2011). Classification and clustering of sequencing data using a Poisson model. Annals of Applied Statistics, 5(4), 2493-2518.

See Also

combine.kernels, kernel.pca

Examples

data(TARAoceans)
pro.NOGs.kernel <- compute.kernel(TARAoceans$pro.NOGs, 
                                  kernel.func = "abundance")

---

Kernel Principal Components Analysis

Description

Performs a kernel PCA.

Usage

kernel.pca(K, ncomp = nrow(K$kernel))

Arguments

K	a kernel object obtained using either compute.kernel or combine.kernels.
ncomp	integer. Indicates the number of components to return..

Value

kernel.pca returns an object of classes "kernel.pca" and "pca", which is a list containing the following entries:

ncomp	: the number of principal components;
X	: the input kernel matrix;
kernel	: the input kernel object provided by the user;
sdev	: the singular values (square root of the eigenvalues);
rotation	: the matrix of variable loadings (i.e., a matrix whose columns contain the eigenvectors);
loadings	: same as 'rotation' to keep the mixOmics spirit;
x	: same as 'rotation' to keep the mixOmics spirit;

Author(s)

Jerome Mariette <[email protected]> Nathalie Vialaneix <[email protected]>

References

Scholkopf B., Smola A. and Muller K.R. (1998) Nonlinear component analysis as a kernel eigenvalue problem. Neural Computation, 10, 1299-1319.

See Also

compute.kernel, combine.kernels

Examples

data(TARAoceans)
phychem.kernel <- compute.kernel(TARAoceans$phychem, kernel.func = "linear")
kernel.pca.result <- kernel.pca(phychem.kernel, ncomp = 3)

---

Assess variable importance

Description

Assess importance of variables on a given PC component by computing the Crone-Crosby distance between original sample positions and sample positions obtained by a random permutation of the variables.

Usage

kernel.pca.permute(kpca.result, ncomp = 1, ..., directory = NULL)

Arguments

kpca.result	a kernel.pca object returned by the kernel.pca function.
ncomp	integer. Number of KPCA components used to compute the importance. Default: 1.
...	list of character vectors. The parameter name must be the kernel name to be considered for permutation of variables. Provided vectors length has to be equal to the number of variables of the input dataset. A kernel is performed on each unique variables values. Crone-Crosby distances are computed on each KPCA performed on resulted kernels or meta-kernels and can be displayed using the plotVar.kernel.pca.
directory	character. To limit computational burden, this argument allows to store / read temporary computed kernels.

Details

plotVar.kernel.pca produces a barplot for each block. The variables for which the importance has been computed with kernel.pca.permute are displayed. The representation is limited to the ndisplay most important variables.

Value

kernel.pca.permute returns a copy of the input kpca.result results and add values in the three entries: cc.distances, cc.variables and cc.blocks.

Author(s)

Jerome Mariette <[email protected]> Nathalie Vialaneix <[email protected]>

References

Mariette J. and Villa-Vialaneix N. (2018). Unsupervised multiple kernel learning for heterogeneous data integration. Bioinformatics, 34(6), 1009-1015. DOI: doi:10.1093/bioinformatics/btx682

Crone L. and Crosby D. (1995). Statistical applications of a metric on subspaces to satellite meteorology. Technometrics, 37(3), 324-328.

See Also

compute.kernel, kernel.pca

Examples

data(TARAoceans)

# compute one kernel for the psychem dataset
phychem.kernel <- compute.kernel(TARAoceans$phychem, kernel.func = "linear")
# perform a KPCA
kernel.pca.result <- kernel.pca(phychem.kernel)

# compute importance for all variables in this kernel
kernel.pca.result <- kernel.pca.permute(kernel.pca.result, 
                                        phychem = colnames(TARAoceans$phychem))

---

View mixKernel User's Guide

Description

Find the location of the mixKernel User's Guide and optionnaly opens it

Usage

mixKernel.users.guide(html = TRUE, view = html)

Arguments

html	logical. Should the document returned by the function be the compiled PDF or the Rmd source. Default to TRUE
view	logical. Should the document be opened using the default HTML viewer? Default to html. It has no effect if html = FALSE

Details

If the operating system is not Windows, then the HTML viewer used is that given by Sys.getenv("R_BROWSER"). The HTML viewer can be changed using Sys.setenv(R_BROWSER = ).

Value

Character string giving the file location. If html = TRUE and view = TRUE, the HTML document reader is started and the User's Guide is opened in it.

Author(s)

Jerome Mariette <[email protected]> Nathalie Vialaneix <[email protected]>

Examples

mixKernel.users.guide(view = FALSE)
mixKernel.users.guide(html = FALSE)
## Not run: mixKernel.users.guide()

---

Plot importance of variables in kernel PCA

Description

Provides a representation of variable importance in kernel PCA.

Usage

plotVar.kernel.pca(
  object,
  blocks = unique(object$cc.blocks),
  ndisplay = 5,
  ncol = 2,
  ...
)

Arguments

object	: a kernel.pca object returned by kernel.pca.
blocks	a numerical vector indicating the block variables to display.
ndisplay	integer. The number of important variables per blocks shown in the representation. Default: 5.
ncol	integer. Each block of variables is displayed in a separate subfigure. ncol sets the number of columns for the global figure. Default: 2.
...	external arguments.

Details

plotVar.kernel.pca produces a barplot for each block. The variables for which the importance has been computed with kernel.pca.permute are displayed. The representation is limited to the ndisplay most important variables.

Author(s)

Jerome Mariette <[email protected]> Nathalie Vialaneix <[email protected]>

References

Crone L. and Crosby D. (1995). Statistical applications of a metric on subspaces to satellite meteorology. Technometrics, 37(3), 324-328.

See Also

kernel.pca, kernel.pca.permute

Examples

data(TARAoceans)

# compute one kernel for the psychem dataset
phychem.kernel <- compute.kernel(TARAoceans$phychem, kernel.func = "linear")
# perform a KPCA
kernel.pca.result <- kernel.pca(phychem.kernel)
# compute importance for all variables in this kernel
kernel.pca.result <- kernel.pca.permute(kernel.pca.result, phychem = colnames(TARAoceans$phychem))

## Not run: plotVar.kernel.pca(kernel.pca.result, ndisplay = 10)

---

Select important features

Description

Select features using supervised or unsupervised kernel method. A supervised feature selection method is performed if Y is provided.

Usage

## S3 method for class 'features'
select(
  X,
  Y = NULL,
  kx.func = c("linear", "gaussian.radial.basis", "bray"),
  ky.func = c("linear", "gaussian.radial.basis"),
  keepX = NULL,
  method = c("kernel", "kpca", "graph"),
  lambda = NULL,
  n_components = 2,
  Lg = NULL,
  mu = 1,
  max_iter = 100,
  nstep = 50,
  ...
)

Arguments

X	a numeric matrix (or data frame) used to select variables. NAs not allowed.
Y	a numeric matrix (or data frame) used to select variables. NAs not allowed.
kx.func	the kernel function name to use on X. Widely used kernel functions are pre-implemented, and can be directly used by setting kx.func to one of the following values: "linear", "gaussian.radial.basis" or "bray". Default: "linear". If Y is provided, the kernel "bray" is not allowed.
ky.func	the kernel function name to use on Y. Available kernels are: "linear", and "gaussian.radial.basis". Default: "linear". This value is ignored when Y is not provided.
keepX	the number of variables to select.
method	the method to use. Either an unsupervised variable selection method ("kernel"), a kernel PCA oriented variable selection method ("kpca") or a structure driven variable selection selection ("graph"). Default: "kernel".
lambda	the penalization parameter that controls the trade-off between the minimization of the distorsion and the sparsity of the solution parameter.
n_components	how many principal components should be used with method "kpca". Required with method "kpca". Default: 2.
Lg	the Laplacian matrix of the graph representing relations between the input dataset variables. Required with method "graph".
mu	the penalization parameter that controls the trade-off between the the distorsion and the influence of the graph. Default: 1.
max_iter	the maximum number of iterations. Default: 100.
nstep	the number of values used for the regularization path. Default: 50.
...	the kernel function arguments. In particular, sigma("gaussian.radial.basis"): double. The inverse kernel width used by "gaussian.radial.basis".

Value

ukfs returns a vector of sorted selected features indexes.

Author(s)

Celine Brouard <[email protected]> Jerome Mariette <[email protected]> Nathalie Vialaneix <[email protected]>

References

Brouard C., Mariette J., Flamary R. and Vialaneix N. (2022). Feature selection for kernel methods in systems biology. NAR Genomics and Bioinformatics, 4(1), lqac014. DOI: doi:10.1093/nargab/lqac014.

See Also

compute.kernel

Examples

## These examples require the installation of python modules
## See installation instruction at: http://mixkernel.clementine.wf

data("Koren.16S")
## Not run: 
 sf.res <- select.features(Koren.16S$data.raw, kx.func = "bray", lambda = 1,
                           keepX = 40, nstep = 1)
 colnames(Koren.16S$data.raw)[sf.res]

## End(Not run)

data("nutrimouse")
## Not run: 
 grb.func <- "gaussian.radial.basis"
 genes <- center.scale(nutrimouse$gene)
 lipids <- center.scale(nutrimouse$lipid)
 sf.res <- select.features(genes, lipids, kx.func = grb.func, 
                           ky.func = grb.func, keepX = 40)
 colnames(nutrimouse$gene)[sf.res]

## End(Not run)

---

TARA ocean microbiome data

Description

The TARA Oceans expedition facilitated the study of plankton communities by providing oceans metagenomic data combined with environmental measures to the scientific community. This dataset focuses on 139 prokaryotic-enriched samples collected from 68 stations and spread across three depth layers: the surface (SRF), the deep chlorophyll maximum (DCM) layer and the mesopelagic (MES) zones. Samples were located in height different oceans or seas: Indian Ocean (IO), Mediterranean Sea (MS), North Atlantic Ocean (NAO), North Pacific Ocean (NPO), Red Sea (RS), South Atlantic Ocean (SAO), South Pacific Ocean (SPO) and South Ocean (SO). Here, only a subset of the original data is provided (1% of the 35,650 prokaryotic operational taxonomic units (OTUs) and of the 39,246 bacterial genes (NOGs) (selected at random).

Usage

data(TARAoceans)

Format

A list containing the following components:

phychem

data matrix with 139 rows and 22 columns. Each row represents a sample and each column an environmental variable.

pro.phylo

data matrix with 139 rows (samples) and 356 columns (prokaryotic OTUs).

taxonomy

data matrix with 356 rows (prokaryotic OTUs) and 6 columns indicating the taxonomy of each OTU.

phylogenetic.tree

a phylo object (see package 'ape') representing the prokaryotic OTUs phylogenetic tree.

pro.NOGs

data matrix with 139 rows (samples) and 638 columns (NOGs).

sample

a list containing three following entries (all three are character vectors): name (sample name), ocean (oceanic region of the sample) and depth (sample depth).

Source

The raw data were downloaded from http://ocean-microbiome.embl.de/companion.html.

References

Sunagawa S., Coelho L.P., Chaffron S., Kultima J.R., Labadie K., Salazar F., Djahanschiri B., Zeller G., Mende D.R., Alberti A., Cornejo-Castillo F., Costea P.I., Cruaud C., d'Oviedo F., Engelen S., Ferrera I., Gasol J., Guidi L., Hildebrand F., Kokoszka F., Lepoivre C., Lima-Mendez G., Poulain J., Poulos B., Royo-Llonch M., Sarmento H., Vieira-Silva S., Dimier C., Picheral M., Searson S., Kandels-Lewis S., Tara Oceans coordinators, Bowler C., de Vargas C., Gorsky G., Grimsley N., Hingamp P., Iudicone D., Jaillon O., Not F., Ogata H., Pesant S., Speich S., Stemmann L., Sullivan M., Weissenbach J., Wincker P., Karsenti E., Raes J., Acinas S. and Bork P. (2015). Structure and function of the global ocean microbiome. Science, 348, 6237.

---