PCSF: Network-based interpretation of highthroughput data

#' Prize-collecting Steiner Forest (PCSF)
#'
#' \code{PCSF} returns a subnetwork obtained by solving the PCSF on the given interaction network.
#' 
#' @param ppi An interaction network, an \pkg{igraph} object.
#' @param terminals  A list of terminal genes with prizes to be analyzed in the PCSF context. 
#' A named \code{numeric} vector, where terminal genes are named same as in the interaction network 
#' and numeric values correspond to the importance of the gene within the study.
#' @param w A \code{numeric} value for tuning the number of trees in the output. A default value is 2.
#' @param b A \code{numeric} value for tuning the node prizes. A default value is 1.
#' @param mu A \code{numeric} value for a hub penalization. A default value is 0.0005.
#' @return The final subnetwork obtained by the PCSF. 
#' It return an \pkg{igraph} object with the node prize and edge cost attributes.
#' @import igraph 
#' @export
#' 
#' @details 
#'  
#' The PCSF is a well-know problem in graph theory. 
#' Given an undirected graph \emph{G = (V, E)}, where the vertices are labeled with prizes
#' \eqn{p_{v}} and the edges are labeled with costs \eqn{c_{e} > 0}, the goal is to identify
#' a subnetwork \emph{G' = (V', E')} with a forest structure. The target is to minimize
#' the total edge costs in \emph{E'}, the total node prizes left out of \emph{V'}, and the 
#' number of trees in \emph{G'}. This is equivalent to  minimization of the following 
#' objective function:
#' 
#' \deqn{F(G')= Minimize \sum_{ e \in E'} c_{e} + \beta*\sum_{v \not\in V'} p_v + \omega*k}
#' where, \emph{k} is the number of trees in the forest, and it is regulated by parameter \eqn{\omega}.
#' The parameter \eqn{\beta} is used to tune the prizes of nodes. 
#' 
#' This optimization problem nicely maps onto the problem of finding differentially
#' enriched subnetworks in the cell protein-protein interaction (PPI) network. 
#' The vertices of interaction network correspond to genes or proteins, and edges 
#' represent the interactions among them. We can assign prizes 
#' to vertices based on measurements of differential expression, copy number, or 
#' mutation, and costs to edges based on confidence scores for those intra-cellular 
#' interactions from experimental observation, yielding a proper input to the PCSF 
#' problem. Vertices that are assigned a prize are referred to \emph{terminal} nodes, 
#' whereas the vertices which are not observed in patient data are not assigned a 
#' prize and are called \emph{Steiner} nodes. After scoring the interactome, the 
#' PCSF is used to detect a relevant subnetwork (forest), which corresponds to a 
#' portion of the interactome, where many genes are highly correlated in terms of 
#' their functions and may regulate the differentially active biological process 
#' of interest. The PCSF aims to identify  neighborhoods in interaction networks 
#' potentially belonging to the key dysregulated pathways of a disease.

#' In order to avoid a bias towards the hub nodes of PPI networks to appear in solution 
#' of PCSF, we penalize the prizes of \emph{Steiner} nodes according to their degree 
#' distribution in PPI, and it is regulated by parameter \eqn{\mu}:
#' 
#'  \deqn{p'_{v} = p_{v} - \mu*degree(v)}
#'  
#'  The parameter \eqn{\mu} also affects the total number of \emph{Steiner} nodes in the solution. 
#'  Higher the value of \eqn{\mu} smaller the number of \emph{Steiners} in the subnetwork, 
#'  and vice-versa. Based on our previous analysis the recommended range of \eqn{\mu} 
#'  for biological networks is between 1e-4 and 5e-2, and users can choose the values 
#'  resulting subnetworks with vertex sets that have desirable \emph{Steiner/terminal} 
#'  node ratio and average \emph{Steiner/terminal} in-degree ratio 
#'  in the template interaction network.
#'  
#' @examples
#' \dontrun{
#' library("PCSF")
#' data("STRING")
#' data("Tgfb_phospho")
#' terminals <- Tgfb_phospho
#' ppi <- construct_interactome(STRING)
#' subnet <- PCSF(ppi, terminals, w = 2, b = 1, mu = 0.0005)}
#' 
#' @author Murodzhon Akhmedov
#'  
#' @seealso \code{\link{PCSF_rand}}, \code{\link{plot.PCSF}}
#' 
#' @references 
#' Akhmedov M., LeNail A., Bertoni F., Kwee I., Fraenkel E., and Montemanni R. (2017)
#' A Fast Prize-Collecting Steiner Forest Algorithm for Functional Analyses in Biological Networks.
#' \emph{Lecture Notes in Computer Science}, to appear.
    

PCSF <-
function(ppi, terminals, w = 2, b = 1, mu = 0.0005){
  
  # Checking function arguments
  if (missing(ppi))
    stop("Need to specify an interaction network \"ppi\".")
  if (class(ppi) != "igraph")
    stop("The interaction network \"ppi\" must be an igraph object.")
  if (missing(terminals))
    stop("  Need to provide terminal nodes as a named numeric vector, 
    where node names must be same as in the interaction network.")
  if(is.null(names(terminals)))
    stop("  The terminal nodes must be provided as a named numeric vector, 
    where node names must be same as in the interaction network.")
  
  
  # Gather the terminal genes to be analyzed, and their scores
  terminal_names = names(terminals)
  terminal_values = as.numeric(terminals)
  
  # Incorporate the node prizes
  node_names = V(ppi)$name
  node_prz = vector(mode = "numeric", length = length(node_names))
  index = match(terminal_names, node_names)
  percent = signif((length(index) - sum(is.na(index)))/length(index)*100, 4)
  if (percent < 5)
    stop("  Less than 1% of your terminal nodes are matched in the interactome, check your terminals!")
  cat(paste0("  ", percent, "% of your terminal nodes are included in the interactome\n"))
  terminal_names = terminal_names[!is.na(index)]
  terminal_values = terminal_values[!is.na(index)]
  index = index[!is.na(index)]
  node_prz[index] =  terminal_values



  ## Prepare input file for MST-PCSF implementation in C++
  
  cat("  Solving the PCSF...\n")
  
  # Calculate the hub penalization scores
  node_degrees = igraph::degree(ppi)
  hub_penalization = - mu*node_degrees
  
  # Update the node prizes
  node_prizes = b*node_prz
  index = which(node_prizes==0)
  node_prizes[index] = hub_penalization[index]


  # Construct the list of edges 
  edges = ends(ppi,es = E(ppi))
  from = c(rep("DUMMY", length(terminal_names)), edges[,1])
  to = c(terminal_names, edges[,2])
  cost = c(rep(w, length(terminal_names)), E(ppi)$weight)

  
  ## Feed the input into the PCSF algorithm
  output = call_sr(from,to,cost,node_names,node_prizes)
  
  # Check the size of output subnetwork and print a warning if it is 0
  if(length(output[[1]]) != 0){
    
    #names(output) = c("from", "to", "cost", "terminal_names", "terminal_prizes")
    
    # Contruct an igraph object from the MST-PCSF output
    e = data.frame(output[[1]], output[[2]], output[[3]])
    #e = e[which(e[,1]!="DUMMY"), ]
    Ee = e[which(e[,2]!="DUMMY"), ]
    names(e) = c("from", "to", "weight")
    
    
    # Differentiate the type of nodes
    type = rep("Steiner", length(output[[4]]))
    index = match(terminal_names, output[[4]])
    index = index[!is.na(index)]
    type[index] = "Terminal"
    
    v = data.frame(output[[4]], output[[5]], type)
    names(v) = c("terminals", "prize", "type")
    subnet = graph.data.frame(e,vertices=v,directed=F)
    E(subnet)$weight=as.numeric(output[[3]])
    subnet = delete_vertices(subnet, "DUMMY")
    subnet = delete_vertices(subnet, names(which(degree(subnet)==0)))
    
    
    class(subnet) <- c("PCSF", "igraph")
    
    return (subnet)
    
  } else{
    
    stop("  Subnetwork can not be identified for a given parameter set.
    Provide a compatible b or mu value with your terminal prize list...\n\n")
    
  }

}