Two-step kernel ridge regression for network analysis

Description

This package implements the two-step kernel ridge regression model, a supervised network prediction method that can be used for all kinds of network analyses. Examples are protein-protein interaction, foodwebs, ...

Author(s)

Joris Meys and Michiel Stock

See Also

Send your bug reports to:

https://github.com/CenterForStatistics-UGent/xnet/issues

More background in the paper by Stock et al, 2018:

http://doi.org/10.1093/bib/bby095

Getters for linearFilter objects

Description

These functions allow you to extract slots from objects of the class linearFilter.

Usage

alpha(x)

na_removed(x)

## S3 method for class 'linearFilter'
mean(x, ...)

## S4 method for signature 'linearFilter'
mean(x, ...)

## S4 method for signature 'linearFilter'
colMeans(x)

## S4 method for signature 'linearFilter'
rowMeans(x)

## S4 method for signature 'linearFilter'
alpha(x)

## S4 method for signature 'linearFilter'
na_removed(x)

Arguments

Value

for mean: the mean of the original matrix

for colMeans: a numeric vector with the column means

for rowMeans: a numeric vector with the row means

for alpha: a numeric vector of length 4 with the alpha values.

for na_removed: a logical value indicating whether missing values were removed prior to the fitting of the filter.

Examples

data(drugtarget)
lf <- linear_filter(drugTargetInteraction, alpha = 0.25)
alpha(lf)
mean(lf)
colMeans(lf)
na_removed(lf)

convert tskrr models

Description

These functions allow converting models that inherit from the tskrr and tskrrTune class into each other, keeping track of whether the model is homogeneous or heterogeneous. The dots argument allows specifying values for possible extra slots when converting from tskrr to tskrrTune. More information on these slots can be found on the help page of tskrrTune. These functions are not exported.

Usage

as_tuned(x, ...)

as_tskrr(x, ...)

## S4 method for signature 'tskrrHomogeneous'
as_tuned(x, ...)

## S4 method for signature 'tskrrHeterogeneous'
as_tuned(x, ...)

## S4 method for signature 'tskrrTune'
as_tskrr(x)

## S4 method for signature 'tskrrImpute'
as_tskrr(x)

## S4 method for signature 'tskrr'
as_tskrr(x)

Arguments

Value

For as_tuned: a tskrrTune object of the proper class (homogeneous or heterogeneous)

For as_tskrr: an object of class tskrrHomogeneous or tskrrHeterogeneous depending on whether the original object was homogeneous or heterogeneous.

Warning

This functions do NOT tune a model. they are used internally to make the connection between both types in the methods.

See Also

• tune for actually tuning a model.

• tskrrTune for names and possible values of the slots passed through ...

Create a grid of values for tuning tskrr

Description

This function creates a grid of values for tuning a tskrr model. The grid is equally spaced on a logarithmic scale. Normally it's not needed to call this method directly, it's usually called from tune.

Usage

create_grid(lim = c(1e-04, 10000), ngrid = 10)

Arguments

Details

The lim argument sets the boundaries of the domain in which the lambdas are sought. The lambda values at which the function is evaluated, are calculated as:

exp(seq(log(1e-4), log(1e4), length.out = ngrid))

Value

a numeric vector with values evenly spaced on a logarithmic scale.

See Also

tune for tuning a tskrr model.

Examples

create_grid(lim = c(1e-4, 1), ngrid = 5)

Get the dimensions of a tskrr object

Description

These functions allow you to extract the dimensions of a tskrr object. These dimensions are essentially the dimensions of the label matrix y.

Usage

## S4 method for signature 'tskrr'
dim(x)

Arguments

Value

a vector with two values indicating the number of rows and the number of columns.

Examples

data(drugtarget)
mod <- tskrr(drugTargetInteraction, targetSim, drugSim)
dim(mod)
nrow(mod)
ncol(mod)

drug target interactions for neural receptors

Description

A dataset for examining the interaction between 54 drugs and 26 neural receptors. It consists of three different matrices.

Usage

drugTargetInteraction

Format

• for drugTargetInteraction: a numeric matrix of 26 rows by 54 columns.

• For drugSim: a numeric square matrix with 54 rows/columns.

• For targetSim: a numeric square matrix with 26 rows/columns.

Details

The dataset consists of the following objects :

• drugTargetInteraction: a matrix indicating whether or not a certain drug compound interacts with a certain neural receptor.

• targetSim: a similarity matrix for the neural receptors.

• drugSim: a similarity matrix for the drugs

The data originates from Yamanishi et al (2008) but was partly reworked to be suitable for two-step kernel ridge regression. This is explained in detail in the Preparation of the example data vignette.

Source

https://doi.org/10.1093/bioinformatics/btn162

References

Yamanishi et al, 2008 : Prediction of drug-target interaction networks from the integration of chemical and genomic spaces.

Calculate the hat matrix from an eigen decomposition

Description

These functions calculate either the hat matrix, the mapping matrix or the original (kernel) matrix for a two-step kernel ridge regression, based on the eigendecomposition of the kernel matrix.

Usage

eigen2hat(eigen, val, lambda)

eigen2map(eigen, val, lambda)

eigen2matrix(eigen, val)

Arguments

Details

For the hat matrix, this boils down to:

U\Sigma(\Sigma + \lambda I)^{-1} U^{T}

For the map matrix, this is :

U(\Sigma + \lambda I)^{-1} U^{T}

with U the matrix with eigenvectors, \Sigma a diagonal matrix with the eigenvalues on the diagonal, I the identity matrix and \lambda the hyperparameter linked to this kernel. The internal calculation is optimized to avoid having to invert a matrix. This is done using the fact that \Sigma is a diagonal matrix.

Value

a numeric matrix representing either the hat matrix (eigen2hat), the map matrix (eigen2map) or the original matrix (eigen2matrix)

extract the predictions

Description

This functions extracts the fitted predictions from a tskrr object or an object inheriting from that class. The xnet package provides an S4 generic for the function fitted from the package stats, and a method for tskrr objects.

Usage

## S3 method for class 'tskrr'
fitted(object, labels = TRUE, ...)

## S3 method for class 'linearFilter'
fitted(object, ...)

## S4 method for signature 'tskrr'
fitted(object, labels = TRUE, ...)

## S4 method for signature 'linearFilter'
fitted(object, ...)

Arguments

Value

a numeric matrix with the predictions

Examples

data(drugtarget)

mod <- tskrr(drugTargetInteraction, targetSim, drugSim)
pred <- fitted(mod)

Retrieve a loo function

Description

This function returns the correct function needed to perform one of the leave-one-out cross-validations. It's primarily meant for internal use but can be useful when doing simulations.

Usage

get_loo_fun(x, ...)

## S4 method for signature 'tskrrHeterogeneous'
get_loo_fun(
  x,
  exclusion = c("interaction", "row", "column", "both"),
  replaceby0 = FALSE
)

## S4 method for signature 'tskrrHomogeneous'
get_loo_fun(
  x,
  exclusion = c("edges", "vertices", "interaction", "both"),
  replaceby0 = FALSE
)

## S4 method for signature 'linearFilter'
get_loo_fun(x, replaceby0 = FALSE)

## S4 method for signature 'character'
get_loo_fun(
  x = c("tskrrHeterogeneous", "tskrrHomogeneous", "linearFilter"),
  ...
)

## S4 method for signature 'tskrrTune'
get_loo_fun(x, ...)

Arguments

Details

This function can be used to select the correct loo function in a simulation or tuning algorithm, based on the model object you created. Depending on its class, the returned functions will have different arguments, so you should only use this if you know what you're doing and after you checked the actual returned functions in loo_internal.

Using replaceby0 only makes sense if you only remove the interaction. In all other cases, this argument is ignored.

For the class tskrrHomogeneous, it doesn't make sense to remove rows or columns. If you chose this option, the function will throw an error. Removing edges corresponds to the setting "edges" or "interaction". Removing vertices corresponds to the setting "vertices" or "both". These terms can be used interchangeably.

For the class linearFilter it only makes sense to exclude the interaction (i.e., a single cell). Therefore you do not have an argument exclusion for that method.

For the classes tskrrTune and tskrrImpute, not specifying exclusion or replaceby0 returns the used loo function. If you specify either of them, it will use the method for the appropriate model and return a new loo function.

Value

a function taking the arguments y, and possibly pred for calculating the leave-one-out cross-validation. For class tskrrHeterogeneous, the returned function also has an argument Hk and Hg, representing the hat matrix for the rows and the columns respectively. For class tskrrHomogeneous, only the extra argument Hk is available. For class linearFilter, the extra argument is called alpha and takes the alpha vector of that model.

See Also

loo for carrying out a leave on out crossvalidation, and loo_internal for more information on the internal functions one retrieves with this one.

Getters for tskrrImpute objects

Description

The functions described here are convenience functions to get information out of a tskrrImpute object.

Usage

has_imputed_values(x)

which_imputed(x)

is_imputed(x)

Arguments

Value

For has_imputed_values: a logical value indicating whether the model has imputed values. If x is not some form of a tskrr model, the function will return an error.

For which_imputed: a integer vector with the positions for which the values are imputed.

for is_imputed: a matrix of the same dimensions as the label matrix. It contains the value FALSE at positions that were not imputed, and TRUE at positions that were.

Examples

data(drugtarget)

mod <- tskrr(drugTargetInteraction, targetSim, drugSim)

naid <- sample(length(drugTargetInteraction), 30)
drugTargetInteraction[naid] <- NA

impmod <- impute_tskrr(drugTargetInteraction, targetSim, drugSim)

has_imputed_values(mod)
has_imputed_values(impmod)

# For illustration: extract imputed values
id <- is_imputed(impmod)
fitted(impmod)[id]

Return the hat matrix of a tskrr model

Description

This function returns the hat matrix or hat matrices of a tskrr model. xnet creates an S4 generic for hat and links the default method to the hat function of stats

Usage

hat(x, ...)

## S4 method for signature 'tskrrHeterogeneous'
hat(x, which = c("row", "column"))

## S4 method for signature 'tskrrHomogeneous'
hat(x, ...)

Arguments

Value

the requested hat matrix of the model.

Impute missing values in a label matrix

Description

This function implements an optimization algorithm that allows imputing missing values in the label matrix while fitting a tskrr model.

Usage

impute_tskrr(
  y,
  k,
  g = NULL,
  lambda = 0.01,
  testdim = TRUE,
  testlabels = TRUE,
  symmetry = c("auto", "symmetric", "skewed"),
  keep = FALSE,
  niter = 10000,
  tol = sqrt(.Machine$double.eps),
  start = mean(y, na.rm = TRUE),
  verbose = FALSE
)

Arguments

Value

A tskrr model of the class tskrrImputeHeterogeneous or tskrrImputeHomogeneous depending on whether or not g has a value.

Examples

data(drugtarget)

naid <- sample(length(drugTargetInteraction), 30)
drugTargetInteraction[naid] <- NA

impute_tskrr(drugTargetInteraction, targetSim, drugSim)

Impute values based on a two-step kernel ridge regression

Description

This function provides an interface for the imputation of values based on a tskrr model and is the internal function used by impute_tskrr.

Usage

impute_tskrr.fit(y, Hk, Hg, naid = NULL, niter, tol, start, verbose)

Arguments

Details

This function is mostly available for internal use. In most cases, it makes much more sense to use impute_tskrr, as that function returns an object one can work with. The function impute_tskrr.fit could be useful when doing simulations or creating fitting algorithms.

Value

a list with two elements:

• a matrix y with the imputed values filled in.

• a numeric value niter with the amount of iterations

See Also

• impute_tskrr for the user-level function, and

• eigen2hat for conversion of a eigen decomposition to a hat matrix.

Examples

data(drugtarget)

K <- eigen(targetSim)
G <- eigen(drugSim)

Hk <- eigen2hat(K$vectors, K$values, lambda = 0.01)
Hg <- eigen2hat(G$vectors, G$values, lambda = 0.05)

drugTargetInteraction[c(3,17,123)] <- NA

res <- impute_tskrr.fit(drugTargetInteraction, Hk, Hg,
                        niter = 1000, tol = 10e-10,
                        start = 0, verbose = FALSE)

Test symmetry of a matrix

Description

The function isSymmetric tests for symmetry of a matrix but also takes row and column names into account. This function is a toned-down (and slightly faster) version that ignores row and column names. Currently, the function only works for real matrices, not complex ones.

Usage

is_symmetric(x, tol = 100 * .Machine$double.eps)

Arguments

Value

a logical value indicating whether or not the matrix is symmetric

Examples

x <- matrix(1:16,ncol = 4)
is_symmetric(x)

x <- x %*% t(x)
is_symmetric(x)

Getters for tskrrTune objects

Description

The functions described here are convenience functions to get information out of a tskrrTune object.

Usage

is_tuned(x)

get_grid(x)

get_loss_values(x)

has_onedim(x)

Arguments

Value

For is_tuned: a logical value indicating whether the model is tuned.

For get_grid a list with the elements k and possibly g, each containing the different lambdas tried in the tuning for the row and column kernel matrices respectively.

For get_loss_values a matrix with the calculated loss values. Note that each row represents the result for one lambda value related to the row kernel matrix K. For heterogeneous models, every column represents the result for one lambda related to the column kernel matrix G.

for is_onedim a single logical value telling whether the grid search in the object was onedimensional.

Examples

data(drugtarget)

mod <- tskrr(drugTargetInteraction, targetSim, drugSim)
tuned <- tune(mod, ngrid = 10)

is_tuned(mod)
is_tuned(tuned)

# Basic visualization of the grid.

gridvals <- get_grid(tuned)
z <- get_loss_values(tuned)

## Not run: 
image(gridvals$k,gridvals$g,log(z), log = 'xy',
xlab = "lambda k", ylab = "lambda g")

## End(Not run)

Extract labels from a tskrr object

Description

These functions allow you to extract the labels from a tskrr object. The function labels and the function dimnames are aliases and do the exact same thing. The functions rownames and colnames work like you would expect. Note that contrary to the latter two, labels will never return NULL. If no labels are found, it will construct labels using the prefixes defined in the argument prefix.

Usage

## S3 method for class 'tskrr'
labels(
  object,
  prefix = if (is_homogeneous(object)) "row" else c("row", "col"),
  ...
)

## S4 method for signature 'tskrr'
labels(
  object,
  prefix = if (is_homogeneous(object)) "row" else c("row", "col"),
  ...
)

## S4 method for signature 'tskrr'
dimnames(x)

## S4 method for signature 'tskrr'
rownames(x, do.NULL = TRUE, prefix = "row")

## S4 method for signature 'tskrr'
colnames(x, do.NULL = TRUE, prefix = "col")

Arguments

Value

for labels and dimnames: a list with two elements k and g

Warning

If the original data didn't contain row- or column names for the label matrix, rownames and colnames will return NULL. Other functions will extract the automatically generated labels, so don't count on rownames and colnames if you want to predict output from other functions!

Class linearFilter

Description

The class represents the outcome of a linear filter, and is normally generated by the function linear_filter

Slots

y

the original label matrix with responses.

alpha

a numeric vector with the 4 alpha values of the model.

pred

a matrix with the predictions

mean

a numeric vector containing the global mean of y

colmeans

a numeric vector containing the column means of y

rowmeans

a numeric vector containing the row means of y.

na.rm

a logical value indicating whether missing values were removed prior to the calculation of the means.

See Also

linear_filter for creating a linear filter model, and getter fuctions for linearFilter.

Fit a linear filter over a label matrix

Description

This function fits a linear filter over a label matrix. It calculates the row, column and total means, and uses those to construct the linear filter.

Usage

linear_filter(y, alpha = 0.25, na.rm = FALSE)

Arguments

Details

If there are missing values and they are removed before calculating the means, a warning is issued. If na.rm = FALSE and there are missing values present, the outcome is, by definition, a matrix filled with NA values.

Value

an object of class linearFilter

Examples

data(drugtarget)
linear_filter(drugTargetInteraction, alpha = 0.25)
linear_filter(drugTargetInteraction, alpha = c(0.1,0.1,0.4,0.4))

Leave-one-out cross-validation for tskrr

Description

Perform a leave-one-out cross-validation for two-step kernel ridge regression based on the shortcuts described in Stock et al, 2018. (http://doi.org/10.1093/bib/bby095).

Usage

loo(x, ...)

## S4 method for signature 'tskrrHeterogeneous'
loo(
  x,
  exclusion = c("interaction", "row", "column", "both"),
  replaceby0 = FALSE
)

## S4 method for signature 'tskrrHomogeneous'
loo(
  x,
  exclusion = c("edges", "vertices", "interaction", "both"),
  replaceby0 = FALSE
)

## S4 method for signature 'linearFilter'
loo(x, replaceby0 = FALSE)

Arguments

Details

The parameter exclusion defines what is left out. The value "interaction" means that a single interaction is removed. In the case of a homogeneous model, this can be interpreted as the removal of the interaction between two edges. The values "row" and "column" mean that all interactions for a row edge resp. a column edge are removed. The value "both" removes all interactions for a row and a column edge.

In the case of a homogeneous model, "row" and "column" don't make sense and will be replaced by "both" with a warning. This can be interpreted as removing vertices, i.e. all interactions between one edge and all other edges. Alternatively one can use "edges" to remove edges and "vertices" to remove vertices. In the case of a homogeneous model, the setting "edges" translates to "interaction", and "vertices" translates to "both". For more information, see Stock et al. (2018).

Replacing by 0 only makes sense when exclusion = "interaction" and the label matrix contains only 0 and 1 values. The function checks whether the conditions are fulfilled and if not, returns an error.

Value

a numeric matrix with the leave-one-out predictions for the model.

Examples

data(drugtarget)

mod <- tskrr(drugTargetInteraction, targetSim, drugSim,
             lambda = c(0.01,0.01))

delta <- loo(mod, exclusion = 'both') - response(mod)
delta0 <- loo(mod, replaceby0 = TRUE) - response(mod)

Leave-one-out cross-validation for two-step kernel ridge regression

Description

These functions implement different cross-validation scenarios for two-step kernel ridge regression. It uses the shortcuts for leave-one-out cross-validation.

Usage

loo.i(Y, Hk, Hg, pred)

loo.i0(Y, Hk, Hg, pred)

loo.r(Y, Hk, Hg, ...)

loo.c(Y, Hk, Hg, ...)

loo.b(Y, Hk, Hg, ...)

loo.e.sym(Y, Hk, pred)

loo.e.skew(Y, Hk, pred)

loo.e0.sym(Y, Hk, pred)

loo.e0.skew(Y, Hk, pred)

loo.v(Y, Hk, ...)

loo.i.lf(Y, alpha, pred)

loo.i0.lf(Y, alpha, pred)

Arguments

Details

These functions are primarily for internal use and hence not exported. Be careful when using them, as they do not perform any sanity check on the input. It is up to the user to make sure the input makes sense.

Value

a matrix with the leave-one-out predictions

See Also

loo for the user-level function.

Calculate or extract the loss of a tskrr model

Description

This function allows calculating the loss of a tskrr model using either one of the functions defined in loss_functions or a custom user function. If the model inherits from class tskrrTune and no additional arguments are given, the loss is returned for the settings used when tuning. The function can also be used to extract the original loss from a permtest object.

Usage

loss(x, ...)

## S4 method for signature 'tskrr'
loss(
  x,
  fun = loss_mse,
  exclusion = c("interaction", "row", "column", "both"),
  replaceby0 = FALSE,
  predictions = FALSE,
  ...
)

## S4 method for signature 'tskrrTune'
loss(
  x,
  fun = loss_mse,
  exclusion = c("interaction", "row", "column", "both"),
  replaceby0 = FALSE,
  predictions = FALSE,
  ...
)

## S4 method for signature 'permtest'
loss(x, ...)

Arguments

Value

a numeric value with the calculated loss

See Also

• loss_functions for possible loss functions

• tune for tuning a model based on loss functions

Examples

data(drugtarget)

mod <- tskrr(drugTargetInteraction, targetSim, drugSim)

loss(mod, fun = loss_auc)

tuned <- tune(mod, fun = loss_auc)

loss(tuned)
loss(tuned, fun = loss_mse)

loss functions

Description

These functions can be used as loss functions in tune. Currently, two functions are provided: a function calculating the classic mean squared error (loss_mse) and a function calculating 1 - AUC (loss_auc).

Usage

loss_mse(Y, LOO, na.rm = FALSE)

loss_auc(Y, LOO)

Arguments

Details

The AUC is calculated by sorting the Y matrix based on the order of the values in the LOO matrix. The false and true positive rates are calculated solely based on that ordering, which allows for values in LOO outside the range [0,1]. It's a naive implementation which is good enough for tuning, but shouldn't be used as a correct value for 1 - auc in case the values in LOO are outside the range [0,1].

Note

The function loss_auc should only be used for a Y matrix that contains solely the values 0 and 1.

See Also

tune for application of the loss function

Examples

x <- c(1,0,0,1,0,0,1,0,1)
y <- c(0.8,-0.1,0.2,0.2,0.4,0.01,1.12,0.9,0.9)
loss_mse(x,y)
loss_auc(x,y)

Reorder the label matrix

Description

Reorders the label matrix based on the labels of the kernel matrices. In case there are no labels, the original label matrix is returned, but with the labels in rows and cols as rownames and column names respectively.

Usage

match_labels(y, rows, cols = NULL)

Arguments

Value

a matrix with the rows and columns reordered.

Examples

mat <- matrix(1:6, ncol = 2,
              dimnames = list(c("b", "a", "d"),
                              c("ca", "cb"))
             )

match_labels(mat, c("a","b", "d"), c("ca","cb"))

#Using matrices
data(drugtarget)
out <- match_labels(drugTargetInteraction, targetSim, drugSim)

Calculate the relative importance of the edges

Description

This function does a permutation-based evaluation of the impact of different edges on the final result. It does so by permuting the kernel matrices, refitting the model and calculating a loss function.

Usage

permtest(x, ...)

## S3 method for class 'permtest'
print(x, digits = max(3L, getOption("digits") - 3), ...)

## S4 method for signature 'tskrrHeterogeneous'
permtest(
  x,
  n = 100,
  permutation = c("both", "row", "column"),
  exclusion = c("interaction", "row", "column", "both"),
  replaceby0 = FALSE,
  fun = loss_mse,
  exact = FALSE
)

## S4 method for signature 'tskrrHomogeneous'
permtest(
  x,
  n = 100,
  permutation = c("both"),
  exclusion = c("interaction", "both"),
  replaceby0 = FALSE,
  fun = loss_mse,
  exact = FALSE
)

## S4 method for signature 'tskrrTune'
permtest(x, permutation = c("both", "row", "column"), n = 100)

Arguments

Details

The test involved uses a normal approximation. It assumes that under the null hypothesis, the loss values are approximately normally distributed. The cumulative probability of a loss as small or smaller than the one found in the original model, is calculated based on a normal distribution from which the mean and sd are calculated from the permutations.

Value

An object of the class permtest.

Warning

It should be noted that this normal approximation is an ad-hoc approach. There's no guarantee that the actual distribution of the loss under the null hypothesis is normal. Depending on the loss function, a significant deviation from the theoretic distribution can exist. Hence this functions should only be used as a rough guidance in model evaluation.

Examples

# Heterogeneous network

data(drugtarget)

mod <- tskrr(drugTargetInteraction, targetSim, drugSim)
permtest(mod, fun = loss_auc)

Class permtest

Description

This class represents the permutation test outcomes. See also the function permtest.

Slots

orig_loss

a numeric value with the original loss of the model.

perm_losses

a numeric vector with the losses of the different permutations.

n

the number of permutations

loss_function

the function used to calculate the losses.

exclusion

a character value indicating the exclusion setting used for the test

replaceby0

a locigal value that indicates whether the exclusion was done by replacing with zero. See also loo.

permutation

a character value that indicats in which kernel matrices were permuted.

pval

a p value indicating how likely it is to find a smaller loss than the one of the model based on a normal approximation.

exact

a logical value indicating whether the P value was calculated exactly or approximated by the normal distribution.

See Also

• the function permtest for the actual test.

• the function loo for the leave one out procedures

• the function t.test for the actual test

Getters for permtest objects

Description

The functions described here are convenience functions to get information out of a permtest object.

Usage

permutations(x)

## S4 method for signature 'permtest'
x[i]

Arguments

Value

the requested values

See Also

loss to extract the original loss value.

Examples

data(drugtarget)

mod <- tskrr(drugTargetInteraction, targetSim, drugSim)
ptest <- permtest(mod, fun = loss_auc)

loss(ptest)
ptest[c(2,3)]
permutations(ptest)

plot a heatmap of the predictions from a tskrr model

Description

This function plots a heatmap of the fitted values in a tskrr model. The function is loosely based on heatmap, but uses a different mechanism and adds a legend by default.

Usage

## S3 method for class 'tskrr'
plot(
  x,
  dendro = c("both", "row", "col", "none"),
  which = c("fitted", "loo", "response", "residuals"),
  exclusion = c("interaction", "row", "column", "both"),
  replaceby0 = FALSE,
  nbest = 0,
  rows,
  cols,
  col = rev(heat.colors(20)),
  breaks = NULL,
  legend = TRUE,
  main = NULL,
  xlab = NULL,
  ylab = NULL,
  labRow = NULL,
  labCol = NULL,
  margins = c(5, 5),
  ...
)

Arguments

Details

The function can select a part of the model for plotting. Either you specify rows and cols, or you specify nbest. If nbest is specified, rows and cols are ignored. The n highest values are looked up in the plotted values, and only the rows and columns related to these values are shown then. This allows for a quick selection of the highest predictions.

Dendrograms are created by converting the kernel matrices to a distance, using

d(x,y) = K(x,x)^2 + K(y,y)^2 - 2*K(x,y)

with K being the kernel function. The resulting distances are clustered using hclust and converted to a dendrogram using as.dendrogram.

Value

an invisible list with the following elements:

• val: the values plotted

• ddK: if a row dendrogram was requested, the row dendrogram

• ddG: if a column dendrogram was requested, the column dendrogram

• breaks: the breaks used for the color codes

• col: the colors used

See Also

tskrr, tune and link{impute_tskrr} to construct tskrr models.

Examples

data(drugtarget)
mod <- tskrr(drugTargetInteraction, targetSim, drugSim)

plot(mod)
plot(mod, dendro = "row", legend = FALSE)
plot(mod, col = rainbow(20), dendro = "none", which = "residuals")
plot(mod, labCol = NA, labRow = NA, margins = c(0.2,0.2))

Plot the grid of a tuned tskrr model

Description

With this function, you can visualize the grid search for optimal lambdas from a tskrrTune object. In the case of two-dimensional grid search, this function plots a contour plot on a grid, based on the functions image and contour. For one-dimensional grid search, the function creates a single line plot.

Usage

plot_grid(
  x,
  addlambda = TRUE,
  lambdapars = list(col = "red"),
  log = TRUE,
  opts.contour = list(nlevels = 10),
  ...
)

Arguments

Value

NULL invisibly

Examples

data(drugtarget)

## One dimensional tuning
tuned1d <- tune(drugTargetInteraction, targetSim, drugSim,
                lim = c(1e-4,2), ngrid = 40,
                fun = loss_auc, onedim = TRUE)

plot_grid(tuned1d)
plot_grid(tuned1d, lambdapars = list(col = "green",
                                     lty = 1, lwd = 2),
          log = FALSE, las = 2, main = "1D tuning")

## Two dimensional tuning
tuned2d <- tune(drugTargetInteraction, targetSim, drugSim,
                lim = c(1e-4,10), ngrid = 20,
                fun = loss_auc)

plot_grid(tuned2d)

predict method for tskrr fits

Description

Obtains the predictions from a tskrr model for new data. To get the predictions on the training data, use the function fitted or set both k and g to NULL.

Usage

## S3 method for class 'tskrr'
predict(object, k = NULL, g = NULL, testdim = TRUE, ...)

## S4 method for signature 'tskrr'
predict(object, k = NULL, g = NULL, testdim = TRUE, ...)

Arguments

Details

Predictions can be calculated between new vertices and the vertices used to train the model, between new sets of vertices, or both. Which predictions are given, depends on the kernel matrices passed to the function.

In any case, both the K and G matrix need the kernel values for every combination of the new vertices and the vertices used to train the model. This is illustrated for both homogeneous and heterogeneous networks in the examples.

To predict the links between a new set of vertices and the training vertices, you need to provide the kernel matrix for either the K or the G set of vertices. If you want to predict the mutual links between two new sets of vertices, you have to provide both the K and the G matrix. This is particularly important for homogeneous networks: if you only supply the k argument, you will get predictions for the links between the new vertices and the vertices on which the model is trained. So in order to get the mutual links between the new vertices, you need to provide the kernel matrix as the value for both the k and the g argument.

Value

a matrix with predicted values.

Warning

This function is changed in version 0.1.9 so it's more consistent in how it expects the K and G matrices to be ordered. Up to version 0.1.8 the new vertices should be on the rows for the K matrix and on the columns for the G matrix. This lead to confusion.

If you're using old code, you'll get an error pointing this out. You need to transpose the G matrix in the old code to make it work with the new version.

See Also

tskrr and tskrrTune for fitting the models.

Examples

## Predictions for homogeneous networks

data(proteinInteraction)

idnew <- sample(nrow(Kmat_y2h_sc), 20)

trainY <- proteinInteraction[-idnew,-idnew]
trainK <- Kmat_y2h_sc[-idnew,-idnew]

testK <- Kmat_y2h_sc[idnew, - idnew]

mod <- tskrr(trainY, trainK, lambda = 0.1)
# Predict interaction between test vertices
predict(mod, testK, testK)

# Predict interaction between test and train vertices
predict(mod, testK)
predict(mod, g = testK)

## Predictions for heterogeneous networks
data("drugtarget")

idnewK <- sample(nrow(targetSim), 10)
idnewG <- sample(ncol(drugSim), 10)

trainY <- drugTargetInteraction[-idnewK, -idnewG]
trainK <- targetSim[-idnewK, -idnewK]
trainG <- drugSim[-idnewG, -idnewG]

testK <- targetSim[idnewK, -idnewK]
testG <- drugSim[idnewG, -idnewG]

mod <- tskrr(trainY, trainK, trainG, lambda = 0.01)

# Predictions for new targets on drugs in model
predict(mod, testK)
# Predictions for new drugs on targets in model
predict(mod, g = testG)
# Predictions for new drugs and targets
predict(mod, testK, testG)

Protein interaction for yeast

Description

A dataset for examining the interaction between proteins of yeast. The dataset consists of the following objects:

Usage

proteinInteraction

Format

• proteinInteraction: a numeric square matrix with 150 rows/columns

• Kmat_y2h_sc: a numeric square matrix with 150 rows/columns

Details

• proteinInteraction: the label matrix based on the protein network taken from the KEGG/PATHWAY database

• Kmat_y2h_sc: a kernel matrix indicating similarity of proteins.

The proteins in the dataset are a subset of the 769 proteins used in Yamanishi et al (2004). The kernel matrix used is the combination of 4 kernels: one based on expression data, one on protein interaction data, one on localization data and one on phylogenetic profile. These kernels and their combination are also explained in Yamanishi et al (2004).

Source

https://doi.org/10.1093/bioinformatics/bth910

References

Yamanishi et al, 2004: Protein network inference from multiple genomic data: a supervised approach.

calculate residuals from a tskrr model

Description

This function returns the residuals for an object inheriting from class tskrr

Usage

residuals(object, ...)

## S3 method for class 'tskrr'
residuals(
  object,
  method = c("predictions", "loo"),
  exclusion = c("interaction", "row", "column", "both"),
  replaceby0 = FALSE,
  ...
)

## S4 method for signature 'tskrr'
residuals(
  object,
  method = c("predictions", "loo"),
  exclusion = c("interaction", "row", "column", "both"),
  replaceby0 = FALSE,
  ...
)

Arguments

Details

The parameter exclusion defines what is left out. The value "interaction" means that a single interaction is removed. In the case of a homogeneous model, this can be interpreted as the removal of the interaction between two edges. The values "row" and "column" mean that all interactions for a row edge resp. a column edge are removed. The value "both" removes all interactions for a row and a column edge.

In the case of a homogeneous model, "row" and "column" don't make sense and will be replaced by "both" with a warning. This can be interpreted as removing vertices, i.e. all interactions between one edge and all other edges. Alternatively one can use "edges" to remove edges and "vertices" to remove vertices. In the case of a homogeneous model, the setting "edges" translates to "interaction", and "vertices" translates to "both". For more information, see Stock et al. (2018).

Replacing by 0 only makes sense when exclusion = "interaction" and the label matrix contains only 0 and 1 values. The function checks whether the conditions are fulfilled and if not, returns an error.

Value

a matrix(!) with the requested residuals

Examples

data(drugtarget)
mod <- tskrr(drugTargetInteraction, targetSim, drugSim,
             lambda = c(0.01,0.01))
delta <- response(mod) - loo(mod, exclusion = "both")
resid <- residuals(mod, method = "loo", exclusion = "both")
all.equal(delta, resid)

Getters for tskrr objects

Description

The functions described here are convenience functions to get information out of a tskrr object.

Usage

## S4 method for signature 'tskrr'
response(x, ...)

## S4 method for signature 'tskrrHomogeneous'
lambda(x)

## S4 method for signature 'tskrrHeterogeneous'
lambda(x)

is_tskrr(x)

is_homogeneous(x)

is_heterogeneous(x)

symmetry(x)

get_eigen(x, which = c("row", "column"))

get_kernelmatrix(x, which = c("row", "column"))

has_hat(x)

get_kernel(x, which = c("row", "column"))

Arguments

Value

For response: the original label matrix

For lambda: a named numeric vector with one resp both lambda values used in the model. The names are "k" and "g" respectively.

For is_tskrr a logical value indicating whether the object is a tskrr object

For is_homogeneous a logical value indicating whether the tskrr model is a homogeneous one.

For is_heterogeneous a logical value indicating whether the tskrr model is a heterogeneous one.

For symmetry a character value indicating the symmetry for a homogeneous model. If the model is not homogeneous, NA is returned.

For get_eigen the eigen decomposition of the requested kernel matrix.

For get_kernelmatrix the original kernel matrix for the rows or columns.

For has_hat a logical value indicating whether the tskrr model contains the kernel hat matrices.

Warning

The function get_kernel is deprecated. Use get_kernelmatrix instead.

Examples

data(drugtarget)

mod <- tskrr(drugTargetInteraction, targetSim, drugSim)
is_homogeneous(mod)

EigR <- get_eigen(mod)
EigC <- get_eigen(mod, which = 'column')
lambda(mod)

test the symmetry of a matrix

Description

This function tells you whether a matrix is symmetric, skewed symmetric, or not symmetric. It's used by tskrr to determine which kind of homologous network is represented by the label matrix.

Usage

test_symmetry(x, tol = .Machine$double.eps)

Arguments

Value

a character value with the possible values "symmetric", "skewed" or "none".

See Also

tskrrHomogeneous for more information on the values for the slot symmetry

Examples

mat1 <- matrix(c(1,0,0,1),ncol = 2)
test_symmetry(mat1)
mat2 <- matrix(c(1,0,0,-1), ncol = 2)
test_symmetry(mat2)
mat3 <- matrix(1:4, ncol = 2)
test_symmetry(mat3)

Fitting a two step kernel ridge regression

Description

tskrr is the primary function for fitting a two-step kernel ridge regression model. It can be used for both homogeneous and heterogeneous networks.

Usage

tskrr(
  y,
  k,
  g = NULL,
  lambda = 1e-04,
  testdim = TRUE,
  testlabels = TRUE,
  symmetry = c("auto", "symmetric", "skewed"),
  keep = FALSE
)

Arguments

Value

a tskrr object

See Also

response, fitted, get_eigen, eigen2hat

Examples

# Heterogeneous network

data(drugtarget)

mod <- tskrr(drugTargetInteraction, targetSim, drugSim)

Y <- response(mod)
pred <- fitted(mod)

# Homogeneous network

data(proteinInteraction)

modh <- tskrr(proteinInteraction, Kmat_y2h_sc)

Yh <- response(modh)
pred <- fitted(modh)

Class tskrr

Description

The class tskrr represents a two step kernel ridge regression fitting object, and is normally generated by the function tskrr. This is a superclass so it should not be instantiated directly.

Slots

y

the matrix with responses

k

the eigen decomposition of the kernel matrix for the rows

lambda.k

the lambda value used for k

pred

the matrix with the predictions

has.hat

a logical value indicating whether the kernel hat matrices are stored in the object.

Hk

the kernel hat matrix for the rows.

labels

a list with two character vectors, k and g, containing the labels for the rows resp. columns. See tskrrHomogeneous and tskrrHeterogeneous for more details.

See Also

the classes tskrrHomogeneous and tskrrHeterogeneous for the actual classes.

Carry out a two-step kernel ridge regression

Description

This function provides an interface for two-step kernel ridge regression. To use this function, you need at least one kernel matrix and one label matrix. It's the internal engine used by the function tskrr.

Usage

tskrr.fit(y, k, g = NULL, lambda.k = NULL, lambda.g = NULL, ...)

Arguments

Details

This function is mostly available for internal use. In most cases, it makes much more sense to use tskrr, as that function returns an object one can work with. The function tskrr.fit could be useful when doing simulations or fitting algorithms, as the information returned from this function is enough to use the functions returned by get_loo_fun.

Value

a list with three elements:

• k : the hat matrix for the rows

• g : the hat matrix for the columns (or NULL) for homogeneous networks.

• pred : the predictions

Examples

data(drugtarget)

K <- eigen(targetSim)
G <- eigen(drugSim)

res <- tskrr.fit(drugTargetInteraction,K,G,
                 lambda.k = 0.01, lambda.g = 0.05)

Class tskrrHeterogeneous

Description

The class tskrrHeterogeneous is a subclass of the superclass tskrr specifically for heterogeneous networks.

Slots

y

the matrix with responses

k

the eigen decomposition of the kernel matrix for the rows

lambda.k

the lambda value used for k

pred

the matrix with the predictions

g

the eigen decomposition of the kernel matrix for the columns

lambda.g

the lambda value used for g

has.hat

a logical value indicating whether the kernel hat matrices are stored in the object.

Hk

the kernel hat matrix for the rows.

Hg

the kernel hat matrix for the columns.

labels

a list with elements k and g (see tskrr-class). If any element is NA, the labels used are integers indicating the row resp column number.

Class tskrrHomogeneous

Description

The class tskrrHomogeneous is a subclass of the superclass tskrr specifically for homogeneous networks.

Slots

y

the matrix with responses

k

the eigen decomposition of the kernel matrix for the rows

lambda.k

the lambda value used for k

pred

the matrix with the predictions

symmetry

a character value that can have the possible values "symmetric", "skewed" or "not". It indicates whether the y matrix is symmetric, skewed-symmetric or not symmetric.

has.hat

a logical value indicating whether the kernel hat matrices are stored in the object.

Hk

the kernel hat matrix for the rows.

labels

a list with elements k and g (see tskrr-class). For homogeneous networks, g is always NA. If k is NA, the labels used are integers indicating the row resp column number.

Class tskrrImpute

Description

The class tskrrImpute is a virtual class that represents a tskrr model with imputed values in the label matrix Y. Apart from the model, it contains the following extra information on the imputed values.

Slots

imputeid

a vector with integer values indicating which of the values in y are imputed

niter

an integer value gving the number of iterations used

tol

a numeric value with the tolerance used

Class tskrrImputeHeterogeneous

Description

The class tskrrImputeHeterogeneous is a subclass of the class tskrrHeterogeneous and tskrrImpute specifically for heterogeneous networks with imputed values. It is the result of the function impute_tskrr.

Slots

y

the matrix with responses

k

the eigen decomposition of the kernel matrix for the rows

lambda.k

the lambda value used for k

pred

the matrix with the predictions

g

the eigen decomposition of the kernel matrix for the columns

lambda.g

the lambda value used for g

has.hat

a logical value indicating whether the kernel hat matrices are stored in the object.

Hk

the kernel hat matrix for the rows.

Hg

the kernel hat matrix for the columns.

labels

a list with elements k and g (see tskrr-class). If any element is NA, the labels used are integers indicating the row resp column number.

imputeid

a vector with integer values indicating which of the values in y are imputed

niter

an integer value gving the number of iterations used

tol

a numeric value with the tolerance used

Class tskrrImputeHomogeneous

Description

The class tskrrImputeHomogeneous is a subclass of the class tskrrHomogeneous and tskrrImpute specifically for homogeneous networks with imputed values. It is the result of the function impute_tskrr on a homogeneous network model.

Slots

y

the matrix with responses

k

the eigen decomposition of the kernel matrix for the rows

lambda.k

the lambda value used for k

pred

the matrix with the predictions

symmetry

a character value that can have the possible values "symmetric", "skewed" or "not". It indicates whether the y matrix is symmetric, skewed-symmetric or not symmetric.

has.hat

a logical value indicating whether the kernel hat matrices are stored in the object.

Hk

the kernel hat matrix for the rows.

labels

a list with elements k and g (see tskrr-class). For homogeneous networks, g is always NA. If k is NA, the labels used are integers indicating the row resp column number.

imputeid

a vector with integer values indicating which of the values in y are imputed

niter

an integer value gving the number of iterations used

tol

a numeric value with the tolerance used

Class tskrrTune

Description

The class tskrrTune represents a tuned tskrr model, and is the output of the function tune. Apart from the model, it contains extra information on the tuning procedure. This is a virtual class only.

Slots

lambda_grid

a list object with the elements k and possibly g indicating the tested lambda values for the row kernel K and - if applicable - the column kernel G. Both elements have to be numeric.

best_loss

a numeric value with the loss associated with the best lambdas

loss_values

a matrix with the loss results from the searched grid. The rows form the X dimension (related to the first lambda), the columns form the Y dimension (related to the second lambda if applicable)

loss_function

the used loss function

exclusion

a character value describing the exclusion used

replaceby0

a logical value indicating whether or not the cross validation replaced the excluded values by zero

onedim

a logical value indicating whether the grid search was done in one dimension. For homogeneous networks, this is true by default.

See Also

• the function tune for the tuning itself

• the class tskrrTuneHomogeneous and tskrrTuneHeterogeneous for the actual classes.

Class tskrrTuneHeterogeneous

Description

The class tskrrTuneHeterogeneous represents a tuned Heterogeneous tskrr model. It inherits from the classes tskrrHeterogeneous and tskrrTune.

Class tskrrTuneHomogeneous

Description

The class tskrrTuneHomogeneous represents a tuned homogeneous tskrr model. It inherits from the classes tskrrHomogeneous and tskrrTune.

tune the lambda parameters for a tskrr

Description

This function lets you tune the lambda parameter(s) of a two-step kernel ridge regression model for optimal performance. You can either tune a previously fitted tskrr model, or pass the label matrix and kernel matrices to fit and tune a model in one go.

Usage

## S4 method for signature 'tskrrHomogeneous'
tune(
  x,
  lim = c(1e-04, 1),
  ngrid = 10,
  lambda = NULL,
  fun = loss_mse,
  exclusion = "edges",
  replaceby0 = FALSE,
  onedim = TRUE,
  ...
)

## S4 method for signature 'tskrrHeterogeneous'
tune(
  x,
  lim = c(1e-04, 1),
  ngrid = 10,
  lambda = NULL,
  fun = loss_mse,
  exclusion = "interaction",
  replaceby0 = FALSE,
  onedim = FALSE,
  ...
)

## S4 method for signature 'matrix'
tune(
  x,
  k,
  g = NULL,
  lim = c(1e-04, 1),
  ngrid = 10,
  lambda = NULL,
  fun = loss_mse,
  exclusion = "interaction",
  replaceby0 = FALSE,
  testdim = TRUE,
  testlabels = TRUE,
  symmetry = c("auto", "symmetric", "skewed"),
  keep = FALSE,
  onedim = is.null(g),
  ...
)

Arguments

Details

This function currently only performs a simple grid search for all (combinations of) lambda values. If no specific lambda values are provided, then the function uses create_grid to create an evenly spaced (on a logarithmic scale) grid.

In the case of a heterogeneous network, you can specify different values for the two parameters that need tuning. To do so, you need to provide a list with the settings for every parameter to the arguments lim, ngrid and/or lambda. If you try this for a homogeneous network, the function will return an error.

Alternatively, you can speed up the grid search by searching in a single dimension. When onedim = TRUE, the search for a heterogeneous network will only consider cases where both lambda values are equal.

The arguments exclusion and replaceby0 are used by the function get_loo_fun to find the correct leave-one-out function.

By default, the function uses standard mean squared error based on the cross-validation results as a measure for optimization. However, you can provide a custom function if needed, as long as it takes two matrices as input: Y being the observed interactions and LOO being the result of the chosen cross-validation.

Value

a model of class tskrrTune

See Also

• loo, loo_internal and get_loo_fun for more information on how leave one out validation works.

• tskrr for fitting a twostep kernel ridge regression.

• loss_functions for different loss functions.

Examples

data(drugtarget)

mod <- tskrr(drugTargetInteraction, targetSim, drugSim)
tuned <- tune(mod, lim = c(0.1,1), ngrid = list(5,10),
              fun = loss_auc)

## Not run: 

# This is just some visualization of the matrix
# It can be run safely.
gridvals <- get_grid(tuned)
z <- get_loss_values(tuned)        # loss values

image(gridvals$k,gridvals$g,z, log = 'xy',
      xlab = "lambda k", ylab = "lambda g",
      col = rev(heat.colors(20)))


## End(Not run)

Update a tskrr object with a new lambda

Description

This function allows you to refit a tskrr with a new lambda. It can be used to do manual tuning/cross-validation. If the object has the hat matrices stored, these are updated as well.

Usage

update(object, ...)

## S4 method for signature 'tskrrHomogeneous'
update(object, lambda)

## S4 method for signature 'tskrrHeterogeneous'
update(object, lambda)

Arguments

Value

an updated tskrr object fitted with the new lambdas.

Examples

data(drugtarget)

mod <- tskrr(drugTargetInteraction, targetSim, drugSim)

# Update with the same lambda
mod2 <- update(mod, lambda = 1e-3)

# Use different lambda for rows and columns
mod3 <- update(mod, lambda = c(0.01,0.001))

# A model with the hat matrices stored
lambda <- c(0.001,0.01)
modkeep <- tskrr(drugTargetInteraction, targetSim, drugSim, keep = TRUE)
Hk_1 <- hat(modkeep, which = "row")
modkeep2 <- update(modkeep, lambda = lambda)
Hk_2 <- hat(modkeep2, which = "row")

# Calculate new hat matrix by hand:
decomp <- get_eigen(modkeep, which = "row")
Hk_byhand <- eigen2hat(decomp$vectors,
                       decomp$values,
                       lambda = lambda[1])
identical(Hk_2, Hk_byhand)

Functions to check matrices

Description

These functions allow you to check whether the dimensions of the label matrix and the kernel matrix (matrices) are compatible. valid_dimensions checks whether both k and g are square matrices, whether y has as many rows as k and whether y has as many columns as g. is_square checks whether both dimensions are the same.

Usage

valid_dimensions(y, k, g = NULL)

is_square(x)

Arguments

Value

a logical value indicating whether the dimensions of the matrices are compatible for a two step kernel ridge regression.

Note

The function is_square is not exported

Test the correctness of the labels.

Description

This function checks whether the labels between the Y, K, and G matrices make sense. This means that all the labels found as rownames for y can be found as rownames and column names of k, and all the colnames for y can be found as rownames and colnames of g (if provided).

Usage

valid_labels(y, k, g = NULL)

Arguments

Details

Compatible labels mean that it is unequivocally clear which rows and columns can be linked throughout the model. In case none of the matrices have row- or colnames, the labels are considered compatible. In all other cases, all matrices should have both row and column names. They should fulfill the following conditions:

• the row- and column names of a kernel matrix must contain the same values in the same order. Otherwise, the matrix can't be symmetric.

• the rownames of y should correspond to the rownames of k

• the colnames of y should correspond to the colnames of g if it is supplied, or the colnames of k in case g is NULL

Value

TRUE if all labels are compatible, an error otherwise.

Note

This is a non-exported convenience function.

Extract weights from a tskrr model

Description

This function calculates the weight matrix for calculating the predictions of a tskrr model.

Usage

## S4 method for signature 'tskrrHeterogeneous'
weights(object)

## S4 method for signature 'tskrrHomogeneous'
weights(object)

Arguments

Details

The weight matrix is calculated from the map matrices through the function eigen2map.

Value

a matrix with the weights for the tskrr model.

Note

The package xnet adds a S4 generic function for weights.