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laplacianMeanMap.R
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laplacianMeanMap.R
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library(doMC)
library(Matrix)
library(data.table)
library(FNN)
library(foreach)
registerDoMC()
#------------------------------------------------------------------------------
# Laplacian Mean Map
#
#The algorithm expects the data organized in data$bag and data$label (the proportions).
#The rest is the features vector.
#
#The file implements also all functions for building the Laplacian
#------------------------------------------------------------------------------
epsilon <- 0.0 #this refers to Eq. 8 in the paper
gs.graph <- function(N, bag.x.avg, sigma=1){
G <- matrix(0, nrow=N, ncol=N)
for (i in 1:(N-1)){
for (j in (i+1):N){
G[i,j] <- exp(-sqrt(sum((bag.x.avg[i,] - bag.x.avg[j,])^2))/sigma) # exp{ -|| mu_i - mu_j ||_2 / sigma }
G[j,i] <- G[i,j]
}
}
G
}
assoc.distance <- function(bag1,bag2){
N1 <- nrow(bag1)
N2 <- nrow(bag2)
sum <- 0
for (i in 1:N1)
for (j in 1:N2)
sum <- sum + sqrt(sum((bag1[i,] - bag2[j,])^2))
sum
}
nc.graph <- function(data, N, map.bag){
data <- data.table(data)
G <- matrix(0, nrow=N, ncol=N)
assoc <- matrix(0, nrow=N, ncol=N)
for (i in 1:N){
assoc[i,1:N] <- unlist(foreach(j=1:N) %do% {
if (j<i)
0.0
else{
val <- assoc.distance(as.matrix(data[data$bag==map.bag[i],-c(1,2), with=FALSE]),
as.matrix(data[data$bag==map.bag[j],-c(1,2), with=FALSE]))
}
})
}
#Fill the symmetric part
for (i in 1:(N-1))
for (j in (i+1):N)
assoc[j,i] <- assoc[i,j]
for (i in 1:N)
for (j in 1:N){
if (i==j)
next #Leave 0 when B1=B2
else
G[i,j] <- (1 / (1 + assoc[i,j]/assoc[i,i]) + 1 / (1 + assoc[i,j]/assoc[j,j]))
}
G
}
#The function computes the laplacian matrix of the graph represented as a matrix of nodes similarities, all >= 0
laplacian <- function(similarity="G,s", data, nbag, sigma){
#To build mapping with original bag numbers. Now select map.bag[j]
map.bag <- sort(unique(data$bag))
if (similarity == "G,s"){
X <- as.matrix(data[,-(1:2)])
#This computation is done by LMM too and might be factorise for efficiency
bag.x.avg <- foreach(bag = map.bag, .combine=rbind) %do% {
id <- which(data$bag==bag)
if (length(id)>1) { colMeans(X[id,]) } else { X[id,] }
}
graph <- gs.graph(nbag, bag.x.avg, sigma)
}else if (similarity == "NC"){
graph <- nc.graph(data, nbag, map.bag)
}
La <- diag(rowSums(graph)) - graph #The Laplacian matrix of the graph
bdiag(La,La) + diag(epsilon, 2*nrow(La))
}
#LMM algorithm
laplacian.mean.map <- function(data, L, lambda=10, gamma=10, weight=NULL) {
f <- function(w) {
xw <- X %*% w
ai <- log(exp(xw) + exp(-xw))
ai <- ifelse(is.finite(ai), ai, xw) # Handle numerical overflow for log(exp(..))
lterm <- sum(ai)
rterm <- w %*% (M*meanop)
loss <- as.numeric(lterm - rterm + (0.5*lambda*(w %*% w)))
loss
}
g <- function(w) {
xw <- as.vector(X %*% w)
lterm <- colSums(X*tanh(xw))
lterm - (M*meanop) + lambda*w
}
#number of samples
M <- nrow(data)
X <- as.matrix(data[,-(1:2)])
#number of features
K <- ncol(X)
#number of bags
N <- length(unique(data$bag))
bags <- 1:N
#To build mapping with original bag numbers. Now select map.bag[j]
map.bag <- sort(unique(data$bag))
# weights matrix
if (is.null(weight)) {
weight <- diag(1,N)
}
# extract proportions
proportions <- foreach(bag = map.bag, .combine=rbind) %do% {
id <- which(data$bag==bag)
data$label[id[1]]
}
pi <- cbind(diag(as.vector(proportions)), diag(as.vector(1-proportions)))
# compute the average feature vector for each bag
bag.x.avg <- foreach(bag = map.bag, .combine=rbind) %do% {
id <- which(data$bag==bag)
if (length(id)>1) { colMeans(X[id,]) } else { X[id,] }
}
#Estimate the probability of the label over the dataset
py <- sum(proportions) / N
#Estimate the probability of the bag given a label
p.j.pos <- proportions /sum(proportions)
p.j.neg <- (1-proportions) / sum(1-proportions)
psinv <- solve((t(pi) %*% weight) %*% pi + gamma * L, t(pi) %*% weight)
meanop <- unlist(foreach(k=1:K) %do% {
v <- psinv %*% bag.x.avg[, k]
sum(py * p.j.pos * v[1:N] - (1-py) * p.j.neg * v[(N+1):(2*N)])
})
w0 <- rep(0.001,K)
result <- optim(w0, fn=f, gr=g, method="L-BFGS-B")
result$par
}