---
title: "Hipathia Package"
#author: "Marta R. Hidalgo, Francisco Salavert, Alicia Amadoz, Çankut Cubuk, José Carbonell-Caballero, Joaquín Dopazo"
date: "`r Sys.Date()`"
package: hipathia
abstract: >
  _Hipathia_ is a method for the computation of signal transduction along
  signaling pathways from transcriptomic data. The method is based on an 
  iterative algorithm which
  is able to compute the signal intensity passing through the nodes of a
  network by taking into account the level of expression of each gene and
  the intensity of the signal arriving to it. It also provides a new approach 
  to functional analysis allowing to compute the signal arriving to the 
  functions annotated to each pathway. 
output: 
  BiocStyle::pdf_document
vignette: >
  %\VignetteIndexEntry{Hipathia Package}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
toc_float: true
author:
- name: Marta R. Hidalgo
  affiliation: Unidad de Bioinformática y Bioestadística, Centro de Investigación Príncipe Felipe (CIPF), Valencia, 46012, Spain
  email: marta.hidalgo@outlook.es
- name: Francisco Salavert
  affiliation: BioBam Bioinformatics S.L., Valencia, 46012, Spain
- name: Alicia Amadoz
  affiliation: Department of Bioinformatics, Igenomix S.A., Valencia, 46980, Spain
- name: Çankut Cubuk
  affiliation: Clinical Bioinformatics Area, Fundación Progreso y Salud (FPS), Hospital Virgen del Rocio, Sevilla, 41013, Spain
- name: José Carbonell-Caballero
  affiliation: Chromatin and Gene expression Lab, Gene Regulation, Stem Cells and Cancer Program, Centre de Regulació Genòmica (CRG), The Barcelona Institute of Science and Technology, PRBB, Barcelona, 08003, Spain
- name: Joaquín Dopazo
  affiliation: 
  - Clinical Bioinformatics Area, Fundación Progreso y Salud (FPS), Hospital Virgen del Rocio, Sevilla, 41013, Spain 
  - Functional Genomics Node (INB), FPS, Hospital Virgen del Rocio, Sevilla, 41013, Spain. 
  - Bioinformatics in Rare Diseases (BiER), Centro de Investigación Biomédica en Red de Enfermedades Raras (CIBERER), FPS, Hospital Virgen del Rocio, Sevilla, 41013, Spain

---


\newpage
\section{Introduction}\label{sec:intro}

_Hipathia_ package implements the Canonical Circuit Activity Analysis method
for the quantification of the signaling pathways activity presented in 
[Hidalgo et al](https://www.ncbi.nlm.nih.gov/pubmed/28042959). This method 
has been implemented in the webtool http://hipathia.babelomics.org, allowing 
the user to compare signal propagation in an experiment, and train and use a 
predictor based on the activation of the canonical circuits or subpathways. 
The package _hipathia_ has been
conceived as a functional tool for R users which allows more control on the
analysis pipeline than the web implementation does.

This document will introduce you to the _hipathia_ package and how to use it to
analyze your data. 

![Visual representation of the package functionalities.](pics/package_guide.png)

<!-- The use of the package has three main steps: Data preprocessment, Pathway and function activation computation, and data analysis and visualization. -->

\section{Previous considerations}

_Hipathia_ is a method for the computation of signal transduction along
signaling pathways taking as input transcriptomics data. The method is 
independent on the pathways database, it only 
needs information about the topology of the graph and the genes included in each
node. 

However, due to computational cost, _hipathia_ needs to preprocess the graphs to 
be fully efficient. In the current implementation we have developed a module 
which has preprocessed 145 KEGG pathway KGML files, which are ready to be 
analyzed.

Further versions of the package will allow the user to preprocess their own 
graph pathways to be analyzed with _hipathia_.


\subsection{Instalation}\label{sec:instalation}

In order to install the _hipathia_ package, type on your R console

```{r, fig.show='hold', message=FALSE, warning=FALSE, eval=FALSE}
## try http:// if https:// URLs are not supported 
source("https://bioconductor.org/biocLite.R") 
biocLite("hipathia")
```


\subsection{Example data}

In order to illustrate the _hipathia_ package functionalities an example dataset
has been prepared. Data has been downloaded from 
[The Cancer Genome Atlas](https://cancergenome.nih.gov/) data
repository, from the BRCA-US project, release 20. 20 tumor and 20 normal samples 
of RNA-Seq data have been randomly selected and normalized. 

Specifically, raw data has been
corrected for batch effect using the `ComBat` function from package 
`r Biocpkg("sva")`, then corrected for RNA
composition bias applying TMM normalization from package `r Biocpkg("edgeR")`, 
and finally log-transformed.

```{r, fig.show='hold', message=FALSE, warning=FALSE}
library(hipathia)
data("brca")
brca
```

The dataset `brca` is a `r Biocpkg("SummarizedExperiment")` object, including 
the gene expression of the 40 samples in the assay `raw`, and the information 
about whether each 
sample comes from _Tumor_ or _Normal_ tissues in the `group` columns of the 
`colData` dataFrame.

```{r, fig.show='hold', message=FALSE, warning=FALSE}
hhead(assay(brca), 4)
```
```{r, fig.show='hold', message=FALSE, warning=FALSE}
colData(brca)
```


\subsection{Accepted objects}

_Hipathia_ has been designed to work with matrices encapsulated as 
`r Biocpkg("SummarizedExperiment")` objects, in which also the experimental 
design has been included. However, it is also possible to work in _hipathia_ 
with matrix objects, as long as the experimental design is provided when needed. 

Imagine we have the expression data stored in a matrix object called `brca_data`
and the experimental design stored in a data frame with one column called 
`brca_design`. Then, in order to summarize this data in a `SummarizedExperiment`
object we should only run:

```{r, fig.show='hold', message=FALSE, eval=FALSE}
brca <- SummarizedExperiment(assays=SimpleList(raw=brca_data), 
                             colData=brca_design)
```

Note that the data frame object provided as `colData` parameter should be 
ordered as the columns in the matrix provided as assay. For further information 
on this kind of objects please refer to `r Biocpkg("SummarizedExperiment")`.

When executing a function which needs as input parameter the experimental design
(such as the Wilcoxon test in `do_wilcoxon`, or `heatmap_plot`), parameter 
`group` may take two different objects. In case parameter `data` is a 
matrix, `group` should be a vector giving the class to which each sample 
belongs, in the same order than the data matrix. In case parameter `data` is a
`SummarizedExperiment`, `group` may be either a vector as above, or the name
of the column in the `colData` `dataFrame` of the `SummarizedExperiment` storing
this information. 

In general, functions accepting both SummarizedExperiment and matrix objects as 
input data and returning a data matrix object, will give as output the same kind 
of object received. That is, if we 
apply function `translate_data` to a SummarizedExperiment object, we will obtain
a SummarizedExperiment, while applying the same function to a matrix object 
will result in a matrix object as output.


\subsection{How to cite}
_Hipathia_ is a free open-source software implementing the result of a research 
work. If you use it, please support the research project by citing:

Hidalgo, M. R., Cubuk, C., Amadoz, A., Salavert, F., Carbonell-Caballero, J., 
& Dopazo, J. (2017). High throughput estimation of functional cell activities 
reveals disease mechanisms and predicts relevant clinical outcomes.
Oncotarget, 8(3), 5160–5178.  http://doi.org/10.18632/oncotarget.14107


\newpage
\section{Preprocessment}\label{sec:pre}

<!-- \subsection{Preprocess data} -->

_Hipathia_ accepts as input data a gene expression matrix. Expression may have
been measured with any available sequencing technique. However, _hipathia_
assumes that data has been already normalized for correcting any possible
sequencing bias (which includes also batch effect correction). 

\subsection{Gene IDs translation}

The gene expression matrix must include samples as columns and genes as rows,
as shown in the `brca` dataset example. Rownames must be the Entrez IDs of the 
genes in the rows. In order to transform other gene IDs to Entrez IDs, function
`translate_data` can be used. Accepted IDs to be transformed to Entrez IDs
include:
    
**Human**
\begin{itemize}
    \item Affy HG U133A probeset
    \item Affy HG U133B probeset
    \item Affy HG U133-PLUS\_2 probeset
    \item Agilent SurePrint G3 GE 8x60k
    \item Agilent SurePrint G3 GE 8x60k v2
    \item Agilent Whole Genome 4x44k
    \item Agilent Whole Genome 4x44k v2
    \item CCDS
    \item Ensembl gene
    \item Ensembl transcript
    \item Entrez ID
    \item GenBank EMBL
    \item GenBank PID
    \item HGNC symbol
    \item RefSeq mRNA
    \item RefSeq mRNA PRED
    \item RefSeq ncRNA
    \item RefSeq ncRNA PRED
\end{itemize}

**Mouse**
\begin{itemize}
    \item Affy Mouse 430 2
    \item Ensembl gene
    \item Gene name
    \item Mouse Gene 1.0
\end{itemize}

**Rat**
\begin{itemize}
    \item Ensembl gene
    \item Gene name
\end{itemize}



The parameters needed by this function are the data matrix and the species
of the experiment.

```{r, fig.show='hold'}
data(brca_data)
trans_data <- translate_data(brca_data, "hsa")
```


\subsection{Data scaling \& normalization}

Apart from the necessary bias corrections, the expression data matrix must be 
scaled between 0 and 1 before computing the subpaths activation values. Function 
`normalize_data` is designed to this purpouse. 

```{r, fig.show='hold'}
exp_data <- normalize_data(trans_data)
```
```{r, fig.show='hold', fig.cap="BRCA data before scaling"}
boxplot(trans_data)
```
```{r, fig.show='hold', fig.cap="BRCA data after scaling"}
boxplot(exp_data)
```

Function `normalize_data` includes different parameters for normalization.
If option `by_quantiles` is `TRUE`, a previous normalization by quantiles
is performed.

```{r, fig.show='hold', fig.cap="BRCA data after a Quantiles normalization"}
exp_data <- normalize_data(trans_data, by_quantiles = TRUE)
boxplot(exp_data)
```

Other parameters of this function affect the way in which scaling
to the interval [0,1] is performed. Parameter `by_gene` indicates whether
to perform the scaling to [0,1] to each row of the matrix. If the option
`by_gene` is set to `TRUE`, the normalization between 0 and 1 is done for each
row of the matrix, meaning that the expression of each gene will have a range
between 0 and 1. If it is set to `FALSE`, the normalization is done for the 
whole matrix, meaning that only the genes with the maximum value of the 
matrix will have a normalized value of 1. It is recommended to keep it set
to `FALSE`, as the default value. 

Parameter `percentil` indicates whether to use the percentil to compute the
normalized value between 0 and 1. If it is set to `TRUE`, the function takes as
a value for the position `(i,j)` of the matrix the percentil of sample `j` in
the ditribution of gene `i`. If it is set to `FALSE`, the function applies a
direct transformation from the original interval to [0,1]. It is recommended
to keep it set to `FALSE` except for heavy-tailed distributions of the genes. 

```{r, fig.show='hold', fig.cap="BRCA data after normalizing by percentil"}
exp_data <- normalize_data(trans_data, percentil = TRUE)
boxplot(exp_data)
```

Parameter `truncation_percentil` gives the value of percentil `p` from which
all further values are truncated to percentil `p`. Symmetrically, values beyond
percentil `1-p` are also truncated to `1-p`.

```{r, fig.show='hold', fig.cap="BRCA data after truncating by percentil 0.95"}
exp_data <- normalize_data(trans_data, truncation_percentil = 0.95)
boxplot(exp_data)
```



\newpage

\section{Pathway activation computation}

_Hipathia_ aims to compute the level of activation of each subpathway in a
pathway for each of the samples from the experiment. This is done by function
`hipathia`, which takes as inputs the matrix of gene expression, the pathways
object and some additional parameters.

In this section we will see how to load the pathways object, how the _hipathia_ 
method works and how to apply function `hipathia` to the computation of the
values of activation of the loaded pathways.


\subsection{Loading pathways}

_Hipathia_ package is currently implemented to use preprocessed KEGG pathways.
The pathways have been processed and stored in a pathways object. This object
includes all the information that the different functions in the package need.
In order to load this object, use function `load_pathways` and select the
species to be analyzed. Available species include human ( _hsa_ ), mouse 
( _mmu_ ) and rat ( _rno_ ).

```{r, fig.show='hold'}
pathways <- load_pathways(species = "hsa")
```

Parameter `pathways_list` allows the user to specify the pathways to be loaded.
The different functions of the package will use all the pathways in the 
pathways object for its computations. In order to restrict the analysis to a
particular set of pathways, load only the required pathways to the pathway
object. By default, all pathways available for the specified species are
loaded.

```{r, fig.show='hold'}
pathways_only2 <- load_pathways(species = "hsa", pathways_list = c("hsa03320",
                                                                   "hsa04014"))
```

In order to know which pathways are included in each pathways object,
function `get_pathways_list` can be used.

```{r, fig.show='hold'}
length(get_pathways_list(pathways))
get_pathways_list(pathways)[1:10]
```

```{r, fig.show='hold'}
length(get_pathways_list(pathways_only2))
get_pathways_list(pathways_only2)
```



\subsection{Computing the signal}\label{sec:signal}

In order for a protein to pass the signal, there are two important factors:
    first, the protein must be present, and second, some other protein must
activate it. Therefore, _hipathia_ is a method to compute signal transduction
based on two steps. First, it quantifies the presence of a particular gene
as a normalized value between 0 and 1. Then, it computes the signal value
passing through a node taking into account the level of expression of each
gene inside the node and the intensity of the signal arriving to it. The
signal value of the pathway is the signal value through the last node of the
pathway. 


\subsubsection{Subpathways}\label{sec:subs}

Pathways are represented by directed graphs, which include different input
and output nodes. The signal arrives to an initial node and is transmited
along the pathway following the direction of the interactions up to an output
node. Thus, the signal may follow many different paths along the pathway.
_Hipathia_ computes the intensity of this signal up to each output node of a
pathway separately.

Genes in the output nodes are also called *effector proteins*, since they
are the ones responsibles for performing the action the signal is seeking.
We define the *effector subpathway* ending in node *G* as the subgraph
including any node in a path leading to *G*. When applied to effector
subpathways, _hipathia_ returns the intensity of the signal arriving to the
effector protein *G*.

![Effector subpathway depicted in yellow](pics/ERBB_eff_mini.png)

Effector subpathways may have many different input nodes. In order to analyze
in detail which of the possible paths leading to node *G* is responsible for
the observed change, effector subpathays can be decomposed into several
subpathways including only one input node. We define the 
*decomposed subpathway* from *H* to *G* as the subgraph including any node
in a path from *H* to *G*.

![Decomposed subpathway depicted in red](pics/ERBB_decomposed_mini.png)


\subsubsection{Node expression}\label{sec:nodes}

Pathways are represented by graphs and composed by nodes and relations
among them. Some nodes may contain multiple genes representing different
isoforms of the protein or members of the same gene familiy, among others.
Since each gene has its own level of expression, the first step of the
method is to summarize this information into a score representing the
expression of the node as a whole. 

\subsubsection{Signal transduction}\label{sec:transduct}

The computation of the signal intensity across the pathway is performed by
means of an iterative algorithm beginning in the input nodes of the
subpathway. In order to initialize the pathway signal we assume an incoming
signal value of 1 in the input nodes of the subpathway. Then, for each node
$n$ of the network, the signal value $S_n$ is propagated along the nodes 
according to the following rule
\begin{equation}
\label{formula}
S_n = v_n\cdot(1-\prod_{s_i \in A_n}(1-s_i))\cdot\prod_{s_j\in I_n}(1-s_j)
\end{equation}

\noindent where $A_n$ is the set of signals arriving to the current node from an
activation edge, $I_n$ is the set of signals arriving to the current node from 
an inhibition edge, and $v_n$ is the normalized value of expression of the 
current node. 


\subsection{Using \emph{Hipathia} to compute the signal}\label{sec:using}

Function `hipathia` computes the level of activation of the subpathways, taking 
as inputs the matrix of gene expression, the pathways
object and some additional parameters.

Parameter `decompose` indicates whether to use effector subpathways or 
decomposed subpathways. Option `decompose=FALSE` uses effector subpathways while
option `decompose=TRUE` uses decomposed subpathways. For further information
on this, see Section \@ref(sec:subs). For further information on the
method used to compute the level of signal activity in the pathways, see
Section \@ref(sec:signal) or refer to 
[Hidalgo et al.](https://www.ncbi.nlm.nih.gov/pubmed/28042959).

```{r, fig.show='hold'}
results <- hipathia(exp_data, pathways, decompose = FALSE, verbose=FALSE)
```

The genes which are needed by `hipathia` to compute the signal and are not
present in the provided matrix are added by the function, assigning to each 
sample the median of the matrix. The number and percentage of added genes is
shown by the function. A high level of _added missing genes_ may indicate that 
the results are not representative of the actual analysis.

The resulting object is a `r Biocpkg("MultiArrayExperiment")` object, which 
includes two different `r Biocpkg("SummarizedExperiment")` objects: `paths` and
`nodes`.

```{r, fig.show='hold'}
results
```

The `paths` object includes as assay a matrix with the level of activity of the 
signal in each subpathway. In order to
extract the object of signal activity values from this object use function
`get_paths_data`. By default, this function returns a 
`r Biocpkg("SummarizedExperiment")` object, but it can return just the matrix of 
subpaths values if parameter `matrix` is set to `TRUE`. 

```{r, fig.show='hold'}
path_vals <- get_paths_data(results, matrix = TRUE)
path_vals <- get_paths_data(results)
hhead(path_vals, 4)
```

Rownames of the matrix of pathway results are the IDs of the subpathways. The 
object `results` stores also the comprehensive names of the subpathways as
`rowData` of the assay `paths`. However, in case we need to transform subpath 
IDs to comprehensive subpath names, we can use `get_path_names`
function, see Section \@ref(sec:gpn) for further information on this. 
However, it is not recommended to change the row names of the
matrix of subpath values.

Notice that the matrix of subpathway activity values will include a value of
activity for each sample and for each possible subpathway of the pathways in
the pathway object. Depending on whether parameter `decompose` is set to `TRUE`
or `FALSE`, and on the number of pathways included in the object of pathways
given as attribute, the number of analyzed subpathways may vary. Currently
_hipathia_ includes up to the following number of pathways, effector subpathways
and decomposed subpathways per species: 
    
    
```{r, echo=FALSE, results='asis'}
tab <- t(sapply(c("hsa", "mmu", "rno"), function(species){
    p <- suppressMessages(load_pathways(species))
    effs <- sum(sapply(p$pathigraphs, function(pathi) length(
        pathi$effector.subgraphs)))
    decs <- sum(sapply(p$pathigraphs, function(pathi) length(pathi$subgraphs)))
    n <- length(p$pathigraphs)
    c(n, effs, decs)
}))
colnames(tab) <- c("Pathways", "Effector subpathways", "Decomposed subpathways")
knitr::kable(tab)
```



It is recommended to perform an initial _hipathia_ analysis with effector
subpathways, and use decomposed subpathways only for specific pathways in
which the user is highly interested.




\newpage

\section{Function activation computation}

Each effector protein of a pathway is responsible for performing a particular
function. Thus, from the matrix of effector subpathways we can infer the
functions matrix with the function `quantify_terms`, which computes an intensity 
value for each molecular function and for each sample. 

Different effector subpathways of different pathways may end in the same
effector protein, and also different effector proteins may have the same 
molecular
function. Therefore, for a particular function $f$, `quantify_terms` summarizes
the values of all the subpathways ending in an effector protein related to $f$ 
with a mean value.

Different function activity matrices can be computed depending on the
functional annotation given to the effector nodes. Function `quantify_terms`,
through parameter `dbannot`,
accepts any annotation defined by the user and it has also two default
annotations: Gene Ontology functions and Uniprot keywords. 

```{r, fig.show='hold'}
uniprot_vals <- quantify_terms(results, pathways, dbannot = "uniprot")
go_vals <- quantify_terms(results, pathways, dbannot = "GO")
```

The result of this function is a data object with the level of activity of each
annotated function for each sample. As before, the returned object is a 
`r Biocpkg("SummarizedExperiment")`, unless parameter `matrix` is set to `TRUE`
in which case a matrix is returned.

Notice that functions annotated to genes
which are not included in any effector node will be not computed.


\newpage
\section{Pathway/Function activation analysis}\label{sec:pf-ana}

\subsection{Two classes comparison}

Once the object data of desired features has been computed, either subpath 
values or function values, any kind of analysis
may be performed on it, in the same way as if it were the matrix of gene
expression. Specifically, comparison of the features across different groups
of samples is one of the keys. We can perform a comparison of two groups
applying the Wilcoxon test using function `do_wilcoxon`.

```{r, fig.show='hold'}
sample_group <- brca_design[colnames(path_vals),"group"]
comp <- do_wilcoxon(path_vals, sample_group, g1 = "Tumor", g2 = "Normal")
hhead(comp)
```

Function `get_pathways_summary` returns a summary by pathway of the results
from the Wilcoxon test, summaryzing the number of significant up- or
down-activated features.

```{r, fig.show='hold'}
pathways_summary <- get_pathways_summary(comp, pathways)
head(pathways_summary, 4)
```

In order to visualize the results of the comparison, see Section 
\@ref(sec:visual).


\subsection{Principal Components Analysis}

Principal Components Analysis can be also performed by using function
`do_pca`. Notice that the number of rows must not exceed the number of
columns of the input matrix.

```{r, fig.show='hold'}
ranked_path_vals <- path_vals[order(comp$p.value, decreasing = FALSE),]
pca_model <- do_pca(ranked_path_vals[1:ncol(ranked_path_vals),])
```

PCA models can be visualized with a specific function called `pca_plot`.
See Section \@ref(sec:visual) for further information.


\newpage
\section{Visualization}\label{sec:visual}
                         
\subsection{Heatmap}

Function `heatmap_plot` plots a heatmap with the values of the given data 
object. This object may be a SummarizedExperiment object or a matrix. 
The experimental design can be provided to assign a class to each sample by
means of the parameter `group`. Notice that the classes must be in the
same order as the columns of the provided matrix. One can select whether to
cluster samples or variables setting parameters `variable_clust` and
`sample_clust` to `TRUE`. 

The colors of the different classes of samples can be selected
through parameter `sample_colors` with a vector of colors named after the
classes. The colors inside the heatmap can be also selected with parameter
`colors`. Personalized colors can be provided as a vector, or preselected
color schemes *classic* (default), *hipathia* or *redgreen* may be chosen. 

```{r, fig.show='hold', fig.cap="Heatmap plot", fig.small=TRUE}
heatmap_plot(path_vals, group = sample_group)
```

```{r, fig.show='hold', fig.cap="Heatmap plots with variable clustering", fig.small=TRUE}
heatmap_plot(uniprot_vals, group = sample_group, colors="hipathia", 
          variable_clust = TRUE)
```

```{r, fig.show='hold', fig.cap="Different colors of heatmaps: `redgreen`", fig.small=TRUE}
heatmap_plot(go_vals, group = sample_group, colors="redgreen", 
          variable_clust = TRUE)
```

<!-- ```{r, fig.show='hold', fig.cap="Different colors of heatmaps: `classic`", fig.small=TRUE} -->
<!-- heatmap_plot(ranked_path_vals[1:15,], group = sample_group,  -->
<!--           variable_clust = TRUE) -->
<!-- ``` -->

<!-- ```{r, fig.show='hold', fig.cap="Different colors of heatmaps: `hipathia`", fig.small=TRUE} -->
<!-- heatmap_plot(ranked_path_vals[1:15,], group = sample_group,  -->
<!--           colors="hipathia", variable_clust = TRUE) -->
<!-- ``` -->

<!-- ```{r, fig.show='hold', fig.cap="Different colors of heatmaps: `redgreen`", fig.small=TRUE} -->
<!-- heatmap_plot(ranked_path_vals[1:15,], group = sample_group,  -->
<!--           colors="redgreen", variable_clust = TRUE) -->
<!-- ``` -->


\subsection{PCA}

Function `pca_plot` plots two components of a PCA model computed with function
`do_pca` (see Section \@ref(sec:pf-ana)). The
experimental design can be provided to assign a class to each sample by means
of the parameter `group`. Notice that the classes must be in the same
order as the columns of the matrix provided to the PCA model. The colors of
the different classes of samples can be selected through parameter
`sample_colors` with a vector of colors named after the classes. If no such
parameter is provided, a predefined set of colors will be assigned. A main
title may be given to the plot through parameter `main`. The components to be
plotted can be selected through parameters `cp1` and `cp2` giving integer
number. If parameter `legend` is set to TRUE, the legend will be plotted.

```{r, fig.show='hold', fig.cap="PCA plot"}
pca_plot(pca_model, sample_group, legend = TRUE)
```
```{r, fig.show='hold', fig.cap="PCA plot with 5 random colors"}
pca_plot(pca_model, group = rep(1:5, 8), main = "Random types", 
      legend = TRUE)
```

Function `multiple_pca_plot` plots $n$ PCA components given by parameter
`comps=n` as an integer vector. By default, $n=3$. As before, the experimental 
design can be
provided to assign a class to each sample by means of the parameter
`group`. Notice that the classes must be in the same order as the
columns of the matrix provided to the PCA model. The colors of the different
classes of samples can be selected through parameter `sample_colors` with a
vector of colors named after the classes. If no such parameter is provided,
a predefined set of colors will be assigned. The cumulative explained variance
can be represented by setting `plot_variance` parameter to TRUE. If parameter
`legend` is set to TRUE, the legend will be plotted. A main title may be given
to the plot through parameter `main`. 

<!-- multiple_pca_plot(pca_model, sample_group, plot_variance = FALSE,  -->
<!--                legend = FALSE) -->

```{r, fig.show='hold', fig.cap="Multiple PCA plot with acumulated explained variance"}
multiple_pca_plot(pca_model, sample_group, cex=3, plot_variance = TRUE)
```

<!-- multiple_pca_plot(pca_model, group = rep(1:5, 8),  -->
<!--                main = "Random sample types") -->


\subsection{Pathway comparison}

The results of a comparison are sometimes difficult to summarize. An easy
way to understand these results is to visualize them as an image. Function
`pathway_comparison_plot` creates an image of a pathway, with the same layout
from KEGG, including a color code representing the significant up- and
down-activated subpathways, and, if desired, the significant up- and
down-regulated nodes. 

```{r, fig.show='hold', fig.cap= "Pathway comparison plot without node colors"}
pathway_comparison_plot(comp, metaginfo = pathways, pathway = "hsa03320")
```

<!-- ```{r, fig.show='hold'} -->
<!-- pathway_comparison_plot(comp, metaginfo = pathways, pathway = "hsa04014") -->
<!-- ``` -->

In these plots, colored edges represent significant subpathways. Edges
belonging to subpathways which are significantly down-activated will be
depicted in blue and those belonging to subpathways which are significantly
up-activated will be depicted in red (as default). The *up* and *down* colors
may be changed by the user through the parameter `colors` by giving a vector
with three colors (representing down-activation, non-significance and
up-activation respectively) or a color scheme (either *classic* or *hipathia*).

In order to visualize the effect of the nodes expression differences in the
pathways, nodes can be colored by its differential expression. The color of
each node with respect to its differential expression must be previously
computed using function `node_color_per_de`. Note that
this fucntion computes differential expression on the nodes, not on the genes.
It uses function `eBayes` from package `r Biocpkg("limma")`, see the package
vignette for further information. 

When computed, the resulting object must be provided to the
`pathway_comparison_plot` function as parameter `node_colors`.

```{r, fig.show='hold', fig.cap="Pathway comparison plot with node colors: `classic`"}
colors_de <- node_color_per_de(results, pathways, sample_group, "Tumor", 
                            "Normal")
pathway_comparison_plot(comp, metaginfo = pathways, pathway = "hsa03320", 
                     node_colors = colors_de)
```

```{r, fig.show='hold', fig.cap="Pathway comparison plot with node colors: `hipathia`"}
colors_de_hipathia <- node_color_per_de(results, pathways, sample_group, 
                                     "Tumor", "Normal", colors = "hipathia")
pathway_comparison_plot(comp, metaginfo = pathways, pathway = "hsa03320", 
                     node_colors = colors_de_hipathia, colors = "hipathia")
```


\subsection{Visualization through a local server}

_Hipathia_ results can be viewed on a web browser interactivelly. In order to
save the files for their visualization, use function `create_report`. To 
visualize the created report, use function `visualize_report`. For the
interpretation of the results in this visualization, see Section 
\@ref(sec:interpret).

The
parameters to be provided to function `create_report` are the object of results,
the Wilcoxon comparison,
the pathways object and the path to the folder in which the files must be
saved. Optionally, the colors of the nodes showing their differential expression
can be also provided using an 
object returned by function `node_color_per_de` or a
similar data structure. 

```{r, fig.show='hold'}
report <- create_report(comp, pathways, "save_noColors")
report_colors <- create_report(comp, pathways, "save_colors", 
                               node_colors = colors_de)
```

Due to cross-origin security restrictions 
([CORS](https://en.wikipedia.org/wiki/Cross-origin_resource_sharing)), 
a web server is needed to serve the result files correctly.
The easiest way to run a web server to show the result files is with the
_hipathia_ function `visualize_report`. The user must specify the folder where
the report has been stored by function `create_report`. A web server developed
in R will be executed, serving the result files to the default URL
http://127.0.0.1:4000. Port 4000 may be changed through parameter `port`. 

```{r, fig.show='hold'}
visualize_report(report_colors)
```

```{r, fig.show='hold'}
visualize_report(report, port = 4001)
```

The function `visualize_report` uses the `r CRANpkg("servr")` package, please 
refer to the package documentation for further information.

The servers will be active until function `daemon_stop` from package `servr`
is executed. Information about how to stop each server individually is given
as an output of each `visualize_report` function. To stop all servers at a
time, use

```{r, fig.show='hold'}
servr::daemon_stop()
```


Alternatively, if you have already a web server installed in your computer,
just link or move the output folder to your web server http document root
and then open it on your web browser.


\subsection{Visualization through a local server with different groupings}

Effector subpathway results are shown by default grouped by the pathway to which
they belong. However, if our interest is to see the comparison of all the 
subpathways arriving to a particular function, we can group the subpathways by
Uniprot or GO functions. Moreover, if we want to see the results of all the 
subpathways containing a particular gene, we can group the subpathways by
genes.

In order to do that, we must use the `group_by` parameter of functions 
`node_color_per_de` and `create_report`. 
Available `group_by` parameter values include: `uniprot`, to group subpathways 
arriving to the same Uniprot functions, `GO`, to group subpathways arriving to 
the same GO terms, and `genes`, to group subpathways containing each particular 
gene.

```{r, fig.show='hold', eval=FALSE}
colors_de_uni <- node_color_per_de(results, pathways, sample_group, "Tumor", 
                                "Normal", group_by = "uniprot")
create_report(comp, pathways, "save_colors_uniprot", 
           node_colors = colors_de_uni, group_by = "uniprot")
visualize_report("save_colors_uniprot", port = 4002)
```

As before, to stop the server and free the port, use the information about how 
to stop each server individually in the output of each `visualize_report` 
function or stop all servers at a time, using

```{r, fig.show='hold'}
servr::daemon_stop()
```


\subsection{Interpreting HTML results}\label{sec:interpret}

The interactive visualization of _hipathia_ results includes three panels and
a legend. The legend is on top of the page resuming the main information
depicted in the images. The left panel is the pathways panel, where the
currently selected pathway is shown. The layout of the pathway is similar
to the layout shown in KEGG. 

![Interactive Hipathia report visualization](pics/hipathia_report_1.png)


As before, edges belonging to significant down-activated pathways are depicted
in blue, those belonging to significant up-activated subpathways are depicted
in red, and those belonging to non-significant subpathways are depicted in
grey. Similarly, when nodes are colored by their differential expression,
down-regulated nodes are colored in blue, up-regulated nodes are colored in
red and non-significant nodes are colored in white. Different shades of the
colors indicate different levels of significance with respect to the p-value
of the differential expression. 

The selected pathway to be shown can be modified through the pathway list in
the top right panel. Arrows pointing up and down to the left of the names of
the pathways indicates that the pathways contain up- or down-activated
subpathways, respectively. When the arrows are colored in red or blue, it
means that there are significant up- or down-regulated subpathways,
respectively. The pathways list can be filtered through the *Filter...* box,
or ordered by means of the buttons in the top right part of the panel.

All computed subpathways of the currently selected pathway are listed in the
subpathways list in the bottom right panel. Arrows pointing up and down by the
names of the subpathways indicates that they are up- or down-activated,
respectively. When the arrows are colored in red or blue, it means that they
are significantly up- or down-regulated, respectively. When a subpathway is
selected from the list, only the arrows and nodes belonging to this subpathway
will be highlighted. Clicking again on this subpathway will deselect it.


\newpage
\section{Utilities}
\subsection{Functions}

We have developed some simple functions to ease the use of data in _hipathia_.

\subsubsection{hhead}

Function `hhead` has been conceived as a generalization of function `head` to
matrices, dataframes and SummarizedExperiment objects. It returns the values of 
the $n$ first rows and columns of the matrix. In case the object is a 
SummarizedExperiment, it returns the values of the $n$ first rows and columns 
of the (first) assay included in it. In case the object is not a matrix, 
dataframe or SummarizedExperiment object, it returns the result of applying
function `head` to the object.

```{r, fig.show='hold', message=FALSE, warning=FALSE}
class(brca)
hhead(brca, 4)
```

```{r, fig.show='hold', message=FALSE, warning=FALSE}
class(assay(brca))
hhead(assay(brca), 4)
```

\subsubsection{get\_path\_name}\label{sec:gpn}

The results object returned by function `hipathia` includes the names of the 
subpathways, and they are shown in the table returned by function `do_wilcoxon`.
However, in case we need to transform subpath 
IDs to comprehensive subpath names, we can use `get_path_names`
function:


```{r, fig.show='hold'}
get_path_names(pathways, c("P-hsa03320-37", "P-hsa04010-15"))
```

