R/background.predict.R

In mixOmics: Omics Data Integration Project

#############################################################################################################
# Author:
#   Florian Rohart, The University of Queensland, The University of Queensland Diamantina Institute, Translational Research Institute, Brisbane, QLD
#
# created: 22-02-2017
# last modified: 01-03-2017
#
# Copyright (C) 2017
#
# This program is free software; you can redistribute it and/or
# modify it under the terms of the GNU General Public License
# as published by the Free Software Foundation; either version 2
# of the License, or (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program; if not, write to the Free Software
# Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.
#############################################################################################################

# --------------------------------------------------------------------------------------
# calculation of the predicted area depending on a model. output to be passed to plotIndiv
# --------------------------------------------------------------------------------------

# object: plsda or splsda object
# comp.predicted: prediction based on either component 1 or component 1:2
# dist: distance used in the predict function
# xlim: limit on the x-axis of the simulated variates
# ylim: limit on the y-axis of the simulated variates
# resolution: a total of resolution*resolution variates are simulated


#can only do a 2D prediction: cannot project 3D surface on 2D because we can have multiple prediction for same point
# ex: variateXi_1 = variateXj_1 and variateXi_3 = variateXj_3 but variateXi_2 !=variate Xj_3
# projection on comp1 and comp3 gives the same point, but depending on variate_2, the prediction can be different

background.predict = function(object, comp.predicted = 1, dist = "max.dist", xlim = NULL, ylim = NULL, resolution = 100)
{
    
    if(!any(class(object)%in%c("plsda","splsda")))
    stop("'background.predict' can only be calculated for 'plsda' and 'splsda' objects")

    if (!any(dist %in% c("max.dist", "centroids.dist", "mahalanobis.dist")))
    stop("Choose one of the three following distances: 'max.dist', 'centroids.dist' or 'mahalanobis.dist'")

    if(!comp.predicted %in% c(1,2))
    stop("Can only show predicted background for 1 or 2 components")
    
    if(!is.null(xlim) && length(xlim)!=2)
    stop("'xlim' must be a vector of two values, indicating the min and max of the simulated data on variates 1 (x-axis)")
    
    if(!is.null(ylim) && length(ylim)!=2)
    stop("'ylim' must be a vector of two values, indicating the min and max of the simulated data on variates 2 (y-axis)")

    if(resolution<=0)
    stop("'resolution' must be a positive value")

    # ... = arg to pass to plotIndiv
    #plotIndiv(object, style = "graphics", ...)
    #plot(-10:10,-10:10,type="n")
    
    
    ####################################
    # ---- simulating new data
    ####################################
    X = object$X
    Y = object$Y
    
    # we only need to simulate variates
    lim = apply(object$variates$X, 2, range) *1.2
    if(is.null(xlim))
    xlim = lim[,1]
    if(is.null(ylim))
    ylim = lim[,2]
    
    lim = cbind(xlim,ylim)
    
    increment = apply(lim, 2, function(x){sum(abs(x))/resolution})
    incrementx = increment[1]
    incrementy = increment[2]#(abs(ylim[1]) + abs(ylim[2]))/resolution
    #incrementy = (abs(zlim[1]) + abs(zlim[2]))/resolution
    
    
    list.grid = lapply(1:2, function(x){seq(lim[1,x],lim[2,x],increment[x])})
    grid = as.matrix(expand.grid(list.grid))
    #grid[,1] = as.numeric(as.character(grid[,1])) # to get numbers for sure, seemed to have a problem with some numbers..
    #grid[,2] = as.numeric(as.character(grid[,2]))
    
    
    t.pred = list(grid)
    ncomp=comp.predicted
    J=1
    q=nlevels(Y)
    variatesX = list(object$variates$X)
    Y.prim=unmap(Y)
    
    
    
    ####################################
    # ---- estimate polygon
    ####################################
    poly.save = vector("list", length = nlevels(Y))
    G = cls = list()
    
    if(dist == "max.dist")
    {
        
        variatesX = list(X=object$variates [-2][[1]][, 1:comp.predicted, drop = FALSE])
        Y=object$ind.mat
        means.Y = matrix(attr(Y, "scaled:center"),nrow=nrow(t.pred[[1]]),ncol=q,byrow=TRUE);
        sigma.Y = matrix(attr(Y, "scaled:scale"),nrow=nrow(t.pred[[1]]),ncol=q,byrow=TRUE)
        
        Cmat = crossprod(Y, variatesX[[1]])
        
        Y = object$Y
        
        #print(variatesX)
        
        Y.hat.temp = Y.hat = list()
        for(j in 1:ncomp)
        {
            Y.hat.temp[[j]] = ((as.matrix(t.pred[[1]][,1:j, drop = FALSE])/matrix( apply(variatesX[[1]][,1:j, drop = FALSE], 2,function(y){(norm(y, type = "2"))^2}),nrow=nrow(t.pred[[1]]),ncol=j,byrow=T))%*%t(Cmat)[1:j,, drop = FALSE])
            #                *sigma.Y+means.Y
        }
        Ypred = sapply(Y.hat.temp, function(x){x*sigma.Y + means.Y}, simplify = "array")
        Y.hat[[1]] = Ypred
        
        cls$max.dist = lapply(1:J, function(x){matrix(sapply(1:ncomp[x], ### List level
            function(y){apply(Y.hat[[x]][, , y, drop = FALSE], 1,  ### component level
                function(z){
                    paste(levels(Y)[which(z == max(z))], collapse = "/")
                }) ### matrix level
            }), nrow = nrow(t.pred[[x]]), ncol = ncomp[x])
        })
        cls$max.dist = lapply(1:J, function(x){colnames(cls$max.dist[[x]]) = paste(rep("comp", ncomp[x]), 1 : ncomp[[x]], sep = " ");
            rownames(cls$max.dist[[x]]) = rownames(t.pred[[x]]); return(cls$max.dist[[x]])})
        names(cls$max.dist)=names(X)
        
    }
    
    if(dist == "mahalanobis.dist" | dist == "centroids.dist")
    {
        for (i in 1 : J)
        {
            G[[i]] = sapply(1:q, function(x) {apply(as.matrix(variatesX[[i]][Y.prim[, x] == 1, 1:ncomp[i] , drop=FALSE]), 2, mean)})
            if (ncomp[i] == 1)
            G[[i]] = t(t(G[[i]]))
            else
            G[[i]] = t(G[[i]])
            colnames(G[[i]]) = paste("dim", c(1:ncomp[i]), sep = " ")
            rownames(G[[i]]) = levels(Y)
            
        }
        names(G)=names(X)
        
        
        # predicting class of simulated data
        if(dist == "centroids.dist")
        {
            
            ###Start: Centroids distance
            cl = list()
            centroids.fun = function(x, G, h, i) {
                q = nrow(G[[i]])
                x = matrix(x, nrow = q, ncol = h, byrow = TRUE)
                
                if (h > 1) {
                    d = apply((x - G[[i]][, 1:h])^2, 1, sum)
                }
                else {
                    d = (x - G[[i]][, 1])^2
                }
                cl.id = paste(levels(Y)[which(d == min(d))], collapse = "/")
            }
            
            for (i in 1 : J)
            {
                cl[[i]] = matrix(nrow = nrow(t.pred[[i]]), ncol = ncomp[i])
                
                for (h in 1 : ncomp[[i]])
                {
                    cl.id = apply(matrix(t.pred[[i]][, 1:h], ncol = h), 1, function(x) {centroids.fun(x = x, G = G, h = h, i = i)})
                    cl[[i]][, h] = cl.id
                }
            }
            
            cls$centroids.dist = lapply(1:J, function(x){colnames(cl[[x]]) = paste(rep("comp", ncomp[x]), 1 : ncomp[[x]], sep = " ");
                return(cl[[x]])})
            
        } else if (dist == "mahalanobis.dist") {
            
            ### Start: Mahalanobis distance
            cl = list()
            Sr.fun = function(x, G, Yprim, h, i) {
                q = nrow(G[[i]])
                Xe = Yprim %*% G[[i]][, 1:h]
                #Xr = object$variates$X[, 1:h] - Xe
                Xr = variatesX[[i]][, 1:h] - Xe
                Sr = t(Xr) %*% Xr/nrow(Yprim)
                Sr.inv = solve(Sr)
                x = matrix(x, nrow = q, ncol = h, byrow = TRUE)
                if (h > 1) {
                    mat = (x - G[[i]][, 1:h]) %*% Sr.inv %*% t(x - G[[i]][, 1:h])
                    d = apply(mat^2, 1, sum)
                } else {
                    d = drop(Sr.inv) * (x - G[[i]][, 1])^2
                }
                cl.id = paste(levels(Y)[which(d == min(d))], collapse = "/")
            }
            
            for (i in 1 : J){
                cl[[i]] = matrix(nrow = nrow(t.pred[[1]]), ncol = ncomp[i])
                
                for (h in 1:ncomp[[i]]) {
                    cl.id = apply(matrix(t.pred[[i]][, 1:h], ncol = h), 1, Sr.fun, G = G, Yprim = Y.prim, h = h, i = i)
                    cl[[i]][, h] = cl.id
                }
            }
            
            cls$mahalanobis.dist = lapply(1:J, function(x){colnames(cl[[x]]) = paste(rep("comp", ncomp[x]), 1 : ncomp[[x]], sep = " ");
                return(cl[[x]])})
        }
    }
    
    for(ind.area in 1:nlevels(Y))
    {
        ind1 = which(cls[[dist]][[1]][,comp.predicted] == levels(Y)[ind.area])
        # points(t.pred[[1]][ind1,1:2],col = adjustcolor(color.mixo(ind.area), alpha = 0.1), cex=0.1)
        #}
        
        if(length(ind1) >0)
        {
            
            # if less than 8 direct neighbours, we keep the point => contour
            # from one point from the contour, we can only test the direct neighbours to speed up
            area = t.pred[[1]][ind1, 1:2, drop = FALSE]#can only do it in 2d
            contour = NULL
            for (i in 1: nrow(area))
            {
                
                areax = area[,1]#as.numeric(as.character(area[,1]))
                areay = area[,2]#as.numeric(as.character(area[,2]))
                
                a = areax[i]
                b = areay[i]
                
                
                res = 0
                for(x in c(a-incrementx, a, a+incrementx))
                {
                    for(y in c(b-incrementy, b, b+incrementy))
                    {
                        temp =  intersect(which(areax == as.numeric(as.character(x))), which(areay == as.numeric(as.character(y))))#which(area[,1]==as.numeric(x) & area[,2]==as.numeric(y))
                        if(length(temp)>0)
                        res = res + 1
                    }
                }
                
                if(res!=9)
                contour = c(contour, i)
                
                if(length(contour) ==2)
                break
            }
            
            # now that we have two point of the contour, we look for other in the direct neighbours.
            
            added = TRUE
            while(added) # as long as we're adding a point in contour, we keep looking for another one
            {
                added = FALSE
                i = length(contour)
                
                point = contour[i]
                
                areax = area[,1]#round(as.numeric(as.character(area[,1])),7)
                areay = area[,2]#round(as.numeric(as.character(area[,2])),7)
                
                a = areax[point]#round(areax[point],7)
                b = areay[point]#round(areay[point],7)
                
                # we want to add the point (x,y) that has the lowest number of neighbour (the more extreme on the edge)
                
                
                
                neighbour = contour.temp = NULL
                for(x in c(a-incrementx, a, a+incrementx)) # around the point that is in the contour
                {
                    for(y in c(b-incrementy, b, b+incrementy)) # around the point that is in the contour
                    {
                        # (x,y) is a neighbour of (a,b) and I want to see whether it has 8+1 neighbours or less
                        res = 0
                        for(xx in c(x-incrementx, x, x+incrementx))
                        {
                            for(yy in c(y-incrementy, y, y+incrementy))
                            {
                                # (xx,yy) is a neighbour of (x,y)
                                temp =  intersect(which(abs(areax - xx)< 1e-5), which(abs(areay - yy)<1e-5))#which(area[,1]==as.numeric(x) & area[,2]==as.numeric(y))
                                #print(xx)
                                #print(yy)
                                #print(temp)
                                
                                if(length(temp)>0)
                                res = res + 1
                            }
                        }
                        #print(res)
                        if(res!=9) # if (x,y) has less than 8+1 neighbour, then it's on the edge and I want it, only if it's not already in contour
                        {
                            # recover which indice in area the point is
                            ind = intersect(which(abs(areax - x)<1e-5), which(abs(areay - y)<1e-5))
                            
                            # check whether it is already in contour
                            if(length(ind)>0 && sum(contour == ind) == 0)
                            {
                                contour.temp = c(contour.temp, ind)
                                neighbour = c(neighbour, res)
                                #contour = c(contour, ind)
                                added = TRUE
                                #points(area[contour,], cex = 0.1)#, col=color.mixo(ind.area))
                            }
                        }
                        
                    }
                }
                
                if(length(contour.temp)>0)
                {
                    contour = c(contour, contour.temp[which.min(neighbour)])
                    #points3d(area[contour[length(contour)],,drop=FALSE], cex = 0.1, col= adjustcolor(color.mixo(ind.area), alpha=0.1),pch=15)
                    #                    points(area[contour[length(contour)],,drop=FALSE], cex = 0.1, col= adjustcolor(color.mixo(ind.area), alpha=0.1))
                } else {
                    added=FALSE
                }
                
            }
            #polygon(area[contour,], col = adjustcolor(color.mixo(ind.area), alpha=0.1), border=NA)
            
            poly = area[contour,]
            poly.save[[ind.area]] = poly
            
        }
        
    }
    names(poly.save) = levels(Y)#adjustcolor(color.mixo(ind.area), alpha.f=0.1)


    class(poly.save) = "background.predict"
    return(poly.save)
}