segTraj_EM.init_simultanee.R

# EM.init_simultanee
#' EM.init_simultanee proposes an initial value for the EM algorithm  based on a
#' hierarchical clustering  algorithm (ascending)
#' @param x the bivariate signal
#' @param rupt the  change point instants, data.frame
#' @param K number of segments
#' @param P number of clusters
#' @return phi0 : candidate for the EM algorithm
EM.init_simultanee <- function(x, rupt, K, P) {
  m <- apply(rupt, 1, FUN = function(y) rowMeans(x[, y[1]:y[2]]))
  v <- apply(rupt, 1, FUN = function(y) apply(x[, y[1]:y[2]], 1, stats::var))
  n <- apply(rupt, 1, diff) + 1

  Dist <- matrix(Inf, K, K)

  for (k in (1:(K - 1))) {
    for (r in ((k + 1):K)) {
      ybar <- (n[k] * m[, k] + n[r] * m[, r]) / (n[k] + n[r])
      varpool <- sum(n[r] * v[, r] +
                        n[k] * v[, k] +
                        n[r] * (m[, r] - ybar)^2 +
                        n[k] * (m[, k] - ybar)^2) /
         (n[r] + n[k])
      Dist[k, r] <- sum(-n[k] * log(v[, k]) - n[r] * log(v[, r])) +
         (n[k] + n[r]) * log(varpool)
    }
  }
  # Dist=matrix K*K = distance (associated to the log-likelihood)
  #  between the segments

  LR <- NULL

  if (nrow(Dist) > P) {
    for (indice in (1:K)) {
      # while (length(Dist) > P){

      if (nrow(as.matrix(Dist)) <= P) {
        break
      }

      out <- which(Dist == min(Dist), arr.ind = TRUE)
      imin <- out[1]
      jmin <- out[2]
      Dmin <- min(Dist)

      LR[nrow(Dist)] <- Dmin

      ntmp <- n[imin] + n[jmin]
      mtmp <- (n[imin] * m[, imin] + n[jmin] * m[, jmin]) / ntmp
      vtmp <- (n[imin] * v[, imin] +
                  n[jmin] * v[, jmin] +
                  n[imin] * (m[, imin] - mtmp)^2 +
                  n[jmin] * (m[, jmin] - mtmp)^2) / ntmp

      Dist <- Dist[-c(imin, jmin), -c(imin, jmin)]

      m <- m[, -c(imin, jmin)]
      v <- v[, -c(imin, jmin)]
      n <- n[-c(imin, jmin)]

      # update Dist N Nplus LogL
      m <- cbind(m, mtmp)
      v <- cbind(v, vtmp)
      n <- c(n, ntmp)

      Dtmp <- rep(Inf, times = nrow(as.matrix(Dist)))

      for (k in (seq_len(nrow(as.matrix(Dist))))) {
        ybar <- (n[k] * m[, k] + ntmp * mtmp) / (n[k] + ntmp)
        varpool <- sum(n[k] * v[, k] +
                          ntmp * vtmp + 
                          n[k] * (m[, k] - ybar)^2 +
                          ntmp * (mtmp - ybar)^2) /
           (n[k] + ntmp)
        Dtmp[k] <- sum(-n[k] * log(v[, k]) - ntmp * log(vtmp)) +
           (n[k] + ntmp) * log(varpool)
      }


      Dist <- rbind(cbind(Dist, Dtmp),
                    rep(Inf, times = (nrow(as.matrix(Dist)) + 1)))
    }
  }
  phi0 <- list(mu = m, sigma = sqrt(v), prop = n / sum(n))

  invisible(phi0)
}