R/LMLogisticLossIterations.R

In mertayD/CodingProject2: coding project Linear Models

#' LMLogisticLossIterations
#'
#' calculates the LM Logistic Loss Iterations
#'
#' @param X.mat numeric input feature matrix [n x p]
#' @param Y.vec numeric input label vetor [n]
#' @param max.iterations scalar integer > 1, max number of iterations
#' @param step.size 
#'
#' @return W.mat matrix of weight vectors, one for each iteration, n_features+1 x max.iterations. (the first element of the weight vector should be the intercept term).
#' @export
#'
#' @examples
#'    library(codingProject2)
#'    data(spam, package = "ElemStatLearn")
#'    X.mat<-spam[1:100,-58]
#'    y.vec<-spam[1:100, 58]
#'    max.iterations <- 50
#'    step.size <- 0.1
#'    k <- sigmoid(0)
#'    res <- LMLogisticLossIterations(X.mat, y.vec, 50, 0.1)
LMLogisticLossIterations <- function(
  X.mat, 
  y.vec, 
  max.iterations,
  step.size
){
  
  if(nrow(X.mat) <= 0 || ncol(X.mat) <= 0 || nrow(y.vec) <= 0 || ncol(y.vec) <= 0)  
  {
    error("Feature matrix or Label vec has unexpected dimensions")
  }
  
  zero_variance_indices <- vector()
  
  #Scaling of the Input Matrix
  mean.mat <- matrix(rep(colMeans(X.mat)),nrow = ncol(X.mat), ncol = 1)
  zero_mean <- sweep(X.mat,2, as.vector(mean.mat),"-")
  zero_mean_col_means <- colMeans(zero_mean)
  
  count <- 1 
  for(index in 1:ncol(X.mat))
  {
    if(zero_mean_col_means[index] == 0)
    {
      zero_variance_indices[count] <- index
      count <- count + 1
    }
    
  }
  squared_zero_mean <- (zero_mean)^2
  squared.means = colMeans(squared_zero_mean)
  S.vec <- sqrt((squared.means))
  S.diagonal.mat <- diag(S.vec^-1, nrow = ncol(X.mat), ncol = ncol(X.mat))
  X.scaled <- sweep(zero_mean,2,S.vec,"/")
  
  X.scaled.wozero_variance <- X.scaled[,-zero_variance_indices]
  weights_scaled_mat <- matrix(0, ncol(X.scaled.wozero_variance) ,max.iterations)
  weight_vec <- seq(0,0, length.out = ncol(X.scaled.wozero_variance))
  weights_scaled_mat[,1] = as.vector(weight_vec)
  n <- nrow(X.scaled.wozero_variance)
  if("spam" %in% y.vec)
  {
    y.vec <- ifelse(y.vec == "spam", 1,0)
  }
  for (iteration in 2:max.iterations) { 
    pred <- as.matrix(X.scaled.wozero_variance) %*% as.matrix(weight_vec)
    sig <- sigmoid(pred)
    cost <- t(sig) - y.vec
    y_binary_vec <- ifelse(y.vec == "spam", 1,0)
    for (iteration in 2:max.iterations) { 
      pred <- as.matrix(X.scaled.wozero_variance) %*% as.matrix(weight_vec)
      sig <- sigmoid(pred)
      cost <- t(sig) - y.vec
      gradient <- t(X.scaled.wozero_variance) %*% as.vector(cost)
      weight_vec <- weight_vec - (step.size) * gradient  
      weights_scaled_mat[,iteration] = as.vector(weight_vec)
    }
    
    S.wo.zeromean <- S.diagonal.mat[-zero_variance_indices,-zero_variance_indices]
    weigts_wo_zeromean <- t(weights_scaled_mat) %*% S.wo.zeromean
    weights_transpose <- t(weigts_wo_zeromean)
    w_head <- matrix(,nrow = nrow(weights_transpose)+length(zero_variance_indices), ncol = ncol(weights_transpose))
    w_head[-zero_variance_indices,] <- weights_transpose
    w_head[zero_variance_indices,] <- rep(0, ncol(weights_transpose))
    b <- -t(w_head) %*% mean.mat
    weights_mat <- cbind(b,t(w_head))
    return(t(weights_mat))
  } 
  
  #' Title
  #'
  #' @param z 
  #'
  #' @return g
  #' @export
  #'
  #' @examples
  sigmoid <- function(z)
  {
    g <-exp(-z)  + 1
    inv <- g^-1
    return(inv)
  }
}