1 Introduction

The aim of this vignette is to use struct to implement a small set of exemplar objects (i.e. class-based templates) that can be used to conduct exploratory and statistical analysis of a multivariate dataset (e.g. Metabolomics or other omics). A more extensive and advanced use of struct templates is provided in the structToolbox package, which included quality filters, normalisation, scaling, univariate and multivariate statistics and machine learning methods.

2 Getting started

The latest version of struct compatible with your current R version can be installed using BiocManager.

# install BiocManager if not present
if (!requireNamespace("BiocManager", quietly = TRUE))
  install.packages("BiocManager")

# install structToolbox and dependencies
BiocManager::install("struct")

# install ggplot if not already present
 if (!require('ggplot2')) {
  install.packages('ggplot2')
}

The ggplot2 package is also needed for this vignette.

suppressPackageStartupMessages({
  # load the package
  library(struct)
  
  # load ggplot
  library(ggplot2)
})

3 struct helper functions

‘struct’ provides a number of helper functions that can be used to create a new struct object from the command line, or in a script:

  • set_struct_obj()
    • Used to create a new struct object
  • set_obj_method()
    • Used to modify a method for a struct object
  • set_obj_show()
    • Used to modify the displayed output for a struct object

Examples of using these functions to create new struct objects based on the provided templates are included in section 5.1.

3.1 Creating a new struct object

To create a new struct object use the set_struct_obj() function. There are several inputs which are described below.

  • class_name
    • The name of the new struct object (character).
  • struct_obj
    • The type of struct object to create e.g. model, iterator, metric, etc.
  • stato
    • TRUE (default) or FALSE to add stato functionality to the object
  • params
    • A named vector of types for input slots. The names will become slots and the types will be used to determine what type of assignments are allowed to the named slot (e.g. integer, character etc).
  • outputs
    • As params, but for output slots.
  • private
    • As params and outputs but for slots that are used internally by the object and not intended for use by the user. These slots are only accessible using @.
  • prototype
    • A named list of default values for each input/output/private slot. It is good practice to set any initial values for private slots here. It also good practice to set the value for the predicted slot here to set the default output of the object.
  • where
    • Specifies the environment in which the class definition is created. Default is .GlobalEnv

Note that slots listed in params and outputs will be accessible using dollar syntax and are intended to be get/set by the user, while slots named in private are only available internally to the developer.

3.2 Changing the default methods

All struct objects have some default methods that are intended to be “overloaded” i.e. replaced to provide functionality specific to the new object being implemented. The helper function set_obj_method() provides this functionality with the following inputs:

  • class_name
    • The name of the to update the method for.
  • method_name
    • The name of the method to update. Must be an existing method for the object.
  • definition
    • The function to replace the method with. This function will be used when the method is called on the object.
  • signature
    • The classes required for the input arguments.

3.3 Changing the default show output

All struct objects have a default show output, which prints the name and description for an object.

If you want to provide additional information when printing an object then you can overload the show method using the set_obj_show() function, which has the following inputs:

  • class_name
    • the name of the class to update the show method for
  • extra_string:
    • a function that takes the class_name object as input and outputs a string

The string output from the extra_string function will be appended to the default show output.

4 Class-based templates and struct objects

struct provides S4 classes, which can be thought of as extendable templates, for a number of different types of objects. These objects are fundamental components of a data analysis workflow and include:

  • DatasetExperiment objects
    • An extension of SummarizedExperiment objects for holding data and meta data
  • model objects
    • Used for filtering, normalisation, transformation, classification and others.
  • model_seq objects
    • A sequence of model objects, used to connect models together.
  • iterator objects
    • Used for repetitive approaches applied to models and model sequences e.g. cross-validation, resampling, permutations etc.
  • metric objects
    • Used to define performance metrics for classifiers, regression models etc.
  • chart objects
    • Used to define model/iterator specific ggplot objects
  • entity objects
    • Used to define input and output parameters
  • enum objects
    • Similar to entity objects but with a fixed set of allowed values
  • stato objects
    • Used in combination with other objects this provided access to the STATO database in order to provide standardised definitions for methods and parameters.

Each of the templates has a similar structure and a number of template-specific methods defined. They have been designed with the development of data analysis workflows in mind and make it easy to incorporate new methods into the existing framework.

All struct objects have a number of common fields or “slots”, which are defined in the base struct_class object:

  • name
    • A short name for the object
  • description
    • A longer description of what the object does
  • type
    • A list of keywords for the object, such as ‘classifier’
  • libraries
    • A list of R packages needed for to use the object

All struct objects have a show method defined which summarises the object.

S = struct_class()
S
## A "struct_class" object
## -----------------------
## name:          
## description:

Slots can be set by including them as named inputs when the object is created.

S = struct_class(name = 'Example',
                 description = 'An example struct object')
S
## A "struct_class" object
## -----------------------
## name:          Example
## description:   An example struct object

Methods have also been defined so that the value for slots can be set and retrieved using dollar syntax.

# set the name
S$name = 'Basic example'

# get the name
S$name
## [1] "Basic example"

In addition to these publicly accessible slots two additional hidden, or internal, slots are defined. These slots are not intended for general access and therefore cannot be accessed using dollar syntax.

  • .params
    • a list of additional slots that are to be used as input parameters for a model, iterator or chart.
  • .outputs
    • a list of additional slots that will be used as outputs from a model or iterator.

Use of these slots will be covered in section 5 as they are only applicable when extending the base struct_class template.

4.1 DatasetExperiment objects

The DatasetExperiment object is an extension of SummarizedExperiment. It is used to hold measured data and the relevant meta data, such as group labels or feature/variable annotations. All struct objects expect the data to be in the DatasetExperiment format, with samples in rows and variables/features in columns. As well as the default slots, DatasetExperiment objects also have the following additional slots:

  • data
    • a data.frame containing the measured data. Samples in rows and variables in columns.
  • sample_meta
    • a data.frame containing meta data related to the samples, such as group labels. The number of rows must be equal to the number of samples.
  • variable_meta
    • a data.frame containing meta data related to the features, such as annotations. The number of rows must be equal to the number of features.

As for all struct objects these slots, as well as the slots from the base class can be assigned during object creation.

DE = DatasetExperiment(
  data = iris[,1:4],
  sample_meta=iris[,5,drop=FALSE],
  variable_meta=data.frame('idx'=1:4,row.names=colnames(data)),
  name = "Fisher's iris dataset",
  description = 'The famous one')
DE
## A "DatasetExperiment" object
## ----------------------------
## name:          Fisher's iris dataset
## description:   The famous one
## data:          150 rows x 4 columns
## sample_meta:   150 rows x 1 columns
## variable_meta: 4 rows x 1 columns

A formal version of the iris dataset is included in the struct package.

DE = iris_DatasetExperiment()
DE
## A "DatasetExperiment" object
## ----------------------------
## name:          Fisher's Iris dataset
## description:   This famous (Fisher's or Anderson's) iris data set gives the
##                measurements in centimeters of the variables
##                sepal length and width and petal length and
##                width, respectively, for 50 flowers from each of
##                3 species of iris. The species are Iris setosa,
##                versicolor, and virginica.
## data:          150 rows x 4 columns
## sample_meta:   150 rows x 1 columns
## variable_meta: 4 rows x 1 columns

Because DatasetExperiment extends SummarizedExperiment it inherits functionality such as subsetting, nrow, ncol, etc.

# number of columns
ncol(DE)
## [1] 4
# number of rows
nrow(DE)
## [1] 150
# subset the 2nd and 3rd column
Ds = DE[,c(2,3)]
Ds
## A "DatasetExperiment" object
## ----------------------------
## name:          Fisher's Iris dataset
## description:   This famous (Fisher's or Anderson's) iris data set gives the
##                measurements in centimeters of the variables
##                sepal length and width and petal length and
##                width, respectively, for 50 flowers from each of
##                3 species of iris. The species are Iris setosa,
##                versicolor, and virginica.
## data:          150 rows x 2 columns
## sample_meta:   150 rows x 1 columns
## variable_meta: 2 rows x 1 columns

The slots are also accessible using dollar syntax.

# get data frame 
head(DE$data)
##   Sepal.Length Sepal.Width Petal.Length Petal.Width
## 1          5.1         3.5          1.4         0.2
## 2          4.9         3.0          1.4         0.2
## 3          4.7         3.2          1.3         0.2
## 4          4.6         3.1          1.5         0.2
## 5          5.0         3.6          1.4         0.2
## 6          5.4         3.9          1.7         0.4
# sample meta
head(DE$sample_meta)
##   Species
## 1  setosa
## 2  setosa
## 3  setosa
## 4  setosa
## 5  setosa
## 6  setosa

Note that although technically it is possible to set data, sample_meta and variable_meta using dollar syntax, it is usually better to create a new DatasetExperiment and assign them during creation of the object due to the strict definition of a SummarizedExperiment.

5 model objects

Model objects are the most commonly used template as they are the main building block of data analysis workflows. They can be used to implement data processing methods for quality filtering, normalisation, and scaling, as well as methods for statistics and machine learning (e.g. classification, regression and clustering).

model objects have three unique slots defined, but they are all related to model sequences, so they are discussed in detail in section 6.

model objects also have four methods that are used to actually carry out the intended data analysis method.

  • model_train
    • A method used to train a model using a DatasetExperiment object.
  • model_predict
    • A method used to apply a trained model to a second DatasetExperiment object e.g. a test set.
  • model_apply
    • Used when training/testing doesn’t fit the type of model e.g. certain types of normalisation. By default this method calls model_train and model_predict sequentially on the same input data (sometimes called autoprediction).
  • model_reverse
    • A method generally only used for preprocessing methods where it is advantageous to be able to reverse the processing e.g. after regression so that the predictions are in the input units. For example, model_apply might subtract the mean, while model_reverse adds the mean back again.

For the base model template these methods function only as placeholder; they should be defined as part of extending the template, as described in the next section.

Model objects also make use of the .params and .outputs slots of the base class to allow flexibility when extending the template, as shown in the next section.

5.1 using the model template

The model object is intended as a template for creating new objects. In programming terms it is intended to be inherited by new objects derived from it. Methods have been defined so that they can be overloaded with new functionality.

In structToolbox a number of model objects have been defined using setClass and setMethod, which is the preferred way to extend the templates in a package.

struct also makes it possible to define new model objects as you go, which we will demonstrate here. We will define two new objects, one for mean centring and one for Principal Component Analysis. More complete versions of these objects are available as part of the structToolbox package.

The first step is to define the new model objects using the set_struct_object() function (see section 3).

# mean centre object
mean_centre = set_struct_obj(
  class_name = 'mean_centre', 
  struct_obj = 'model',       
  stato = FALSE,              
  params = character(0),            
  outputs = c(centred = 'DatasetExperiment',
              mean = 'numeric'),
  private = character(0),
  prototype=list(predicted = 'centred')
)

# PCA object
PCA = set_struct_obj(
  class_name = 'PCA', 
  struct_obj = 'model',       
  stato = TRUE,              
  params = c(number_components = 'numeric'),                
  outputs = c(scores = 'DatasetExperiment',
              loadings = 'data.frame'),
  private = character(0),
  prototype = list(number_components = 2,
                  stato_id = 'OBI:0200051',
                  predicted = 'scores')
)

The objects we have created (mean_centre and PCA) both extend the model object template. mean_centre is a fairly basic model with a single output slot centred while the PCA object has inputs, outputs and sets a some default values.

The new objects can be initialised like other struct, with named input parameter values.

M = mean_centre()
M
## A "mean_centre" object
## ----------------------
## name:          
## description:   
## outputs:       centred, mean 
## predicted:     centred
## seq_in:        data
P = PCA(number_components=4)
P
## A "PCA" object
## --------------
## name:          
## description:   
## input params:  number_components 
## outputs:       scores, loadings 
## predicted:     scores
## seq_in:        data

The new objects currently have the default methods, which need to be replaced using the either setMethod or the helper function set_obj_method() to provide the desired functionality.

We will need to define model_train and model_predict for both of our new objects. We will start with the mean_centre object.

# mean centre training
set_obj_method(
  class_name = 'mean_centre',
  method_name = 'model_train',
  definition = function(M,D) {
    # calculate the mean of all training data columns
    m = colMeans(D$data)
    # assign to output slot
    M$mean = m
    # always return the modified model object
    return(M)
  }
)

# mean_centre prediction
set_obj_method(
  class_name = 'mean_centre',
  method_name = 'model_predict',
  definition = function(M,D) {
    # subtract the mean from each column of the test data
    D$data = D$data - rep(M$mean, rep.int(nrow(D$data), ncol(D$data)))
    # assign to output
    M$centred = D
    # always return the modified model object
    return(M)
  }
)

The mean_centre object can now be used with DatasetExperiment objects.

# create instance of object
M = mean_centre()

# train with iris data
M = model_train(M,iris_DatasetExperiment())

# print to mean to show the function worked
M$mean
## Sepal.Length  Sepal.Width Petal.Length  Petal.Width 
##     5.843333     3.057333     3.758000     1.199333
# apply to iris_data
M = model_predict(M,iris_DatasetExperiment())

# retrieve the centred data and show that the column means are zero
colMeans(M$centred$data)
##  Sepal.Length   Sepal.Width  Petal.Length   Petal.Width 
## -3.671137e-16  9.177844e-17 -3.256654e-17 -3.404684e-17

Now we define methods for the PCA object.

# PCA training
set_obj_method(
  class_name = 'PCA',
  method_name = 'model_train',
  definition = function(M,D) {
    
    # get number of components
    A = M$number_components
    
    # convert to matrix
    X=as.matrix(D$data)
    
    # do svd
    model=svd(X,A,A)

    # loadings
    P=as.data.frame(model$v)
    
    # prepare data.frame for output
    varnames=rep('A',1,A)
    for (i in 1:A) {
      varnames[i]=paste0('PC',i)
    }
    rownames(P)=colnames(X)
    colnames(P)=varnames
    output_value(M,'loadings')=P
    
    # set output
    M$loadings = P
    
    # always return the modified model object
    return(M)
  }
)

# PCA prediction
set_obj_method(
  class_name = 'PCA',
  method_name = 'model_predict',
  definition = function(M,D) {
    ## calculate scores using loadings
    
    # get number of components
    A = M$number_components
    
    # convert to matrix
    X=as.matrix(D$data)
    
    # get loadings
    P=M$loadings
    
    # calculate scores
    that=X%*%as.matrix(P)
    
    # convert scores to DatasetExperiment
    that=as.data.frame(that)
    rownames(that)=rownames(X)
    varnames=rep('A',1,A)
    for (i in 1:A) {
      varnames[i]=paste0('PC',i)
    }
    colnames(that)=varnames
    S=DatasetExperiment(
      data=that,
      sample_meta=D$sample_meta,
      variable_meta=varnames)
    
    # set output
    M$scores=S
    
    # always return the modified model object
    return(M)
  }
)

Like the mean_centre object the PCA object now has methods defined and can be used with DatasetExperiment objects.

# get the mean centred data
DC = M$centred

# train PCA model
P = model_apply(P,DC)

# get scores
P$scores
## A "DatasetExperiment" object
## ----------------------------
## name:          
## description:   
## data:          150 rows x 4 columns
## sample_meta:   150 rows x 1 columns
## variable_meta: 4 rows x 1 columns

Note that because we defined model_train and model_predict for the PCA object we didn’t need to explicitly define a model_apply method as it defaults to applying model_train and model_precict sequentially. For some methods defining a model_apply definition would be more appropriate (e.g. t-test) and model_train and model_predict left undefined.

6 model_seq objects

Model sequences are a special kind of list defined by the struct package. They can be created by symbolically “adding” models together to form a sequence. We will do that here using the mean_centre() and PCA() objects we created.

# create model sequence
MS = mean_centre() + PCA(number_components = 2)

# print summary
MS
## A model_seq object containing:
## 
## [1]
## A "mean_centre" object
## ----------------------
## name:          
## description:   
## outputs:       centred, mean 
## predicted:     centred
## seq_in:        data
## 
## [2]
## A "PCA" object
## --------------
## name:          
## description:   
## input params:  number_components 
## outputs:       scores, loadings 
## predicted:     scores
## seq_in:        data

The model_train and model_predict methods for model sequences will automatically pass data along the list of models. model_apply works in the same way as for models and will use model_train and model_predict sequentially for the model sequence.

Unless specified the default output named in the ‘predicted’ slot of the object will be used as the data input for the next object in the sequence.

For the PCA example, the data is input into the mean_centre object, mean centring is applied, and then the centred output is used an input into the PCA object to calculate the scores and loadings.

# apply model sequence to iris_data
MS = model_apply(MS,iris_DatasetExperiment())

# get default output from sequence (PCA scores with 2 components)
predicted(MS)
## A "DatasetExperiment" object
## ----------------------------
## name:          
## description:   
## data:          150 rows x 2 columns
## sample_meta:   150 rows x 1 columns
## variable_meta: 2 rows x 1 columns

To change the flow of data through a model sequence three slots can be set for each model:

  • predicted
    • The name of the output slot to output from the model when used in a model sequence.
  • seq_in
    • The name of an input parameter slot that receives the input from the previous model in the sequence, overriding any value set for the slot. The default value ‘data’ assumes the connecting object is a DatasetExperiment object and uses it as input for model_train and model_predict.
  • seq_fcn
    • Sometimes the default output isn’t in the correct format for the input. For example, a numerical output might need to be converted to a logical by applying threshold. This operation can be defined as a function in the seq_fcn slot.

There are examples of this advanced model sequence flow control in the vignettes of the structToolbox package.

7 iterator objects

Iterator objects are similar to model object templates in that they can be extended to have input parameters and outputs specified. They have some unique slots:

  • models
    • Can be a model or model_seq (model sequence) object. The iterator will call model_train and model_predict multiple times using this model.
  • result
    • operates in a similar fashion to the predicted slot for model objects and specifies the default output of the object. This is less useful than predicted at this time as iterators cannot be combined into a sequence (but this may be implemented in the future).

iterator objects are intended for resampling methods, where an input model is run multiple times by subsetting the data into training and test sets. Cross-validation and permutation tests are just two examples where iterator objects might be used.

The model to be run by the iterator can be get/set using the models method.

# create iterator
I = iterator()

# add PCA model sequence
models(I) = MS

# retrieve model sequence
models(I)
## A model_seq object containing:
## 
## [1]
## A "mean_centre" object
## ----------------------
## name:          
## description:   
## outputs:       centred, mean 
## predicted:     centred
## seq_in:        data
## 
## [2]
## A "PCA" object
## --------------
## name:          
## description:   
## input params:  number_components 
## outputs:       scores, loadings 
## predicted:     scores
## seq_in:        data

Models can also be ‘nested’ within an iterator by symbolically multiplying them by a model or model_seq. The implication is that the iterator will use the model multiple times. This can be combined with the symbolic adding of models to create sequences.

# alternative to assign models for iterators
I = iterator() * (mean_centre() + PCA())
models(I)
## A model_seq object containing:
## 
## [1]
## A "mean_centre" object
## ----------------------
## name:          
## description:   
## outputs:       centred, mean 
## predicted:     centred
## seq_in:        data
## 
## [2]
## A "PCA" object
## --------------
## name:          
## description:   
## input params:  number_components 
## outputs:       scores, loadings 
## predicted:     scores
## seq_in:        data

It is also possible to nest iterators within iterators e.g. to create a ‘permuted cross_validation’ using a similar approach.

I = iterator() * iterator() * (mean_centre() + PCA())

A run method is provided, which can be extended in a similar fashion to method_train etc to implement the desired functionality. It is up to the developer to ensure that the iterator can handle model, model_seq and iterator objects as input and as such iterator run methods can be quite complex. For brevity we do not demonstrate one here, but there are several examples in the structToolbox package and the corresponding vignettes.

8 metric objects

Metric objects calculate a scalar value by comparing true, known values to predicted outputs from a model, usually a classifier or a regression model. They are a required input for running iterators and may be calculated multiple times depending on the iterator. Metrics have a single unique slot.

  • value
    • The calculated value of the metric

The calculate method is provided for metric object templates, which can be extended using the same approach as for model_train etc. It takes three inputs:

  • M
    • The metric object to calculate.
  • Y
    • The true value for each each sample e.g. the group labels.
  • Yhat
    • The predicted value for each sample e.g. from a classification model.

The calculate method can be called manually, but usually it is called by an iterator during e.g. a cross-validation.

8.1 chart objects

Chart object templates are intended to produce a ggplot object from an input DatasetExperiment, model or iterator. The template has no unique slots but includes a chart_plot method to generate the ggplot object from the input object.

As a simple example we create a chart for plotting scores from the PCA object we created earlier. A more comprehensive pca_scores_plot object is included in the structToolbox as well several others for plotting the outputs of different methods.

We use the helper function set_struct_object() to define the new chart object.

# new chart object
set_struct_obj(
  class_name = 'pca_scores_plot',
  struct_obj = 'chart',
  stato = FALSE,
  params = c(factor_name = 'character'),
  prototype = list(
    name = 'PCA scores plot',
    description = 'Scatter plot of the first two principal components',
    libraries = 'ggplot2'
  )
)

The chart_plot method for our new object can then be replaced using the set_obj_method() helper function.

# new chart_plot method
set_obj_method(
  class_name = 'pca_scores_plot',
  method_name = 'chart_plot',
  signature = c('pca_scores_plot','PCA'),
  definition = function(obj,dobj) {
    
    if (!is(dobj,'PCA')) {
      stop('this chart is only for PCA objects')
    }
    
    # get the PCA scores data
    S = dobj$scores$data
    
    # add the group labels
    S$factor_name = dobj$scores$sample_meta[[obj$factor_name]]
    
    # ggplot
    g = ggplot(data = S, aes_string(x='PC1',y='PC2',colour='factor_name')) +
      geom_point() + labs(colour = obj$factor_name) 
    
    # chart objects return the ggplot object
    return(g)
  }
    
)

Note that we set signature = c('pca_scores_plot', 'PCA') to indicate that only PCA objects should be accepted as the second input for this chart.

The new chart object is now ready to be used with PCA objects.

# create chart object
C = pca_scores_plot(factor_name = 'Species')

# plot chart using trained PCA object from model sequence
chart_plot(C,MS[2]) + theme_bw() # add theme

9 entity and enum objects

These struct classes are used to make input params and outputs more informative and more flexible. The are not intednded to be an extendable template in the same way as model objects.

By specifying the type or class of a slot as an entity or enum object you can provide additional information about the slot, such as a more informative name and a description. entity and enum slots have some unique slots:

  • value
    • The value assigned to the input parameter / output.
  • max_length
    • The maximum length of the input value. e.g. setting to 1 ensures that the value cannot be set to c(1,2) for example. Default is Inf.
  • allowed
    • enum objects only. A list of allowed values for the input parameter / output.

Both objects also make use of the type slot to ensure the assigned value for a slot can only be of a certain class e.g. setting type = c('numeric', 'integer') will not allow the parameter value to be set to a character.

The name and description slots can be useful e.g. in report writing for providing a standard definition of a parameter.

enitity and enum objects have methods for getting/setting all slots. They are designed to work seamlessly with dollar syntax in the same way you would access the value of any non-entity slot.

As an example the number_components parameter for the PCA object could be defined as an entity object.

# define entity
npc = entity(
  name = 'Number of principal components',
  description = 'The number of principal components to calculate',
  type = c('numeric','integer'),
  value = 2,
  max_length = 1
)

# summary
npc
## A "entity" object
## -----------------
## name:          Number of principal components
## description:   The number of principal components to calculate
## value:         2
## type:          numeric, integer
## max length:    1

It can then be used with the set_struct_obj() function when creating the PCA object by using “entity” as the input type for params and including the entity object in the prototype for the object. It will function exactly as it did before, but has the additional information (name, description, etc) attached as well.

# PCA object
PCA = set_struct_obj(
  class_name = 'PCA', 
  struct_obj = 'model',       
  stato = TRUE,              
  params = c(number_components = 'entity'),                
  outputs = c(scores = 'DatasetExperiment',
              loadings = 'data.frame'),
  private = character(0),
  prototype = list(number_components = npc,
                  stato_id = 'OBI:0200051',
                  predicted = 'scores')
)

# create PCA model 
P = PCA(number_components = 3)

# get set value
P$number_components
## [1] 3
# get description
param_obj(P,'number_components')$description
## [1] "The number of principal components to calculate"

Both entity and enum objects have extended stato versions, which is discussed in the next section.

9.1 stato objects.

STATistics Ontology (STATO) is incorporated into the struct package. By using entity_stato and enum_stato objects in place of entity and enum objects a STATO identifier can be included to provide standardised definitions for input and output parameters.

model and iterator objects can also be extended by the stato class to provide similar functionality. For example, a STATO id was included in the PCA object we created.

P = PCA()

# verify PCA is a stato object
is(P, 'stato')
## [1] TRUE
# get stato id
stato_id(P)
## [1] "OBI:0200051"
# stato name
stato_name(P)
## [1] "principal components analysis dimensionality reduction"
# stato definition
stato_definition(P)
## [1] "A principal components analysis dimensionality reduction is a dimensionality reduction achieved by applying principal components analysis and by keeping low-order principal components and excluding higher-order ones. "

10 Session Info

sessionInfo()
## R version 4.0.0 (2020-04-24)
## Platform: x86_64-pc-linux-gnu (64-bit)
## Running under: Ubuntu 18.04.4 LTS
## 
## Matrix products: default
## BLAS:   /home/biocbuild/bbs-3.11-bioc/R/lib/libRblas.so
## LAPACK: /home/biocbuild/bbs-3.11-bioc/R/lib/libRlapack.so
## 
## locale:
##  [1] LC_CTYPE=en_US.UTF-8       LC_NUMERIC=C              
##  [3] LC_TIME=en_US.UTF-8        LC_COLLATE=C              
##  [5] LC_MONETARY=en_US.UTF-8    LC_MESSAGES=en_US.UTF-8   
##  [7] LC_PAPER=en_US.UTF-8       LC_NAME=C                 
##  [9] LC_ADDRESS=C               LC_TELEPHONE=C            
## [11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C       
## 
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base     
## 
## other attached packages:
## [1] ggplot2_3.3.0    struct_1.0.0     BiocStyle_2.16.0
## 
## loaded via a namespace (and not attached):
##  [1] SummarizedExperiment_1.18.0 tidyselect_1.0.0           
##  [3] xfun_0.13                   purrr_0.3.4                
##  [5] lattice_0.20-41             colorspace_1.4-1           
##  [7] vctrs_0.2.4                 htmltools_0.4.0            
##  [9] stats4_4.0.0                yaml_2.2.1                 
## [11] rlang_0.4.5                 pillar_1.4.3               
## [13] glue_1.4.0                  withr_2.2.0                
## [15] BiocGenerics_0.34.0         matrixStats_0.56.0         
## [17] GenomeInfoDbData_1.2.3      lifecycle_0.2.0            
## [19] stringr_1.4.0               zlibbioc_1.34.0            
## [21] munsell_0.5.0               gtable_0.3.0               
## [23] evaluate_0.14               labeling_0.3               
## [25] Biobase_2.48.0              knitr_1.28                 
## [27] IRanges_2.22.0              GenomeInfoDb_1.24.0        
## [29] parallel_4.0.0              ontologyIndex_2.5          
## [31] Rcpp_1.0.4.6                scales_1.1.0               
## [33] BiocManager_1.30.10         DelayedArray_0.14.0        
## [35] S4Vectors_0.26.0            magick_2.3                 
## [37] XVector_0.28.0              farver_2.0.3               
## [39] digest_0.6.25               stringi_1.4.6              
## [41] bookdown_0.18               dplyr_0.8.5                
## [43] GenomicRanges_1.40.0        grid_4.0.0                 
## [45] tools_4.0.0                 bitops_1.0-6               
## [47] magrittr_1.5                RCurl_1.98-1.2             
## [49] tibble_3.0.1                crayon_1.3.4               
## [51] pkgconfig_2.0.3             ellipsis_0.3.0             
## [53] Matrix_1.2-18               assertthat_0.2.1           
## [55] rmarkdown_2.1               R6_2.4.1                   
## [57] compiler_4.0.0