pkg/R/utils.R

   1 #' normalize
   2 #'
   3 #' Normalize a vector or a matrix (by columns), using euclidian norm
   4 #'
   5 #' @param X Vector or matrix to be normalized
   6 #'
   7 #' @return The normalized matrix (1 column if X is a vector)
   8 #'
   9 #' @export
  10 normalize = function(X)
  11 {
  12   X = as.matrix(X)
  13   norm2 = sqrt( colSums(X^2) )
  14   sweep(X, 2, norm2, '/')
  15 }
  16
  17 # Computes a tensor-vector product
  18 #
  19 # @param Te third-order tensor (size dxdxd)
  20 # @param w vector of size d
  21 #
  22 # @return Matrix of size dxd
  23 #
  24 .T_I_I_w = function(Te, w)
  25 {
  26   d = length(w)
  27   Ma = matrix(0,nrow=d,ncol=d)
  28   for (j in 1:d)
  29     Ma = Ma + w[j] * Te[,,j]
  30   Ma
  31 }
  32
  33 # Computes the second-order empirical moment between input X and output Y
  34 #
  35 # @param X matrix of covariates (of size n*d)
  36 # @param Y vector of responses (of size n)
  37 #
  38 # @return Matrix of size dxd
  39 #
  40 .Moments_M2 = function(X, Y)
  41 {
  42   n = nrow(X)
  43   d = ncol(X)
  44   M2 = matrix(0,nrow=d,ncol=d)
  45   matrix( .C("Moments_M2", X=as.double(X), Y=as.double(Y), pn=as.integer(n),
  46     pd=as.integer(d), M2=as.double(M2), PACKAGE="morpheus")$M2, nrow=d, ncol=d)
  47 }
  48
  49 # Computes the third-order empirical moment between input X and output Y
  50 #
  51 # @param X matrix of covariates (of size n*d)
  52 # @param Y vector of responses (of size n)
  53 #
  54 # @return Array of size dxdxd
  55 #
  56 .Moments_M3 = function(X, Y)
  57 {
  58   n = nrow(X)
  59   d = ncol(X)
  60   M3 = array(0,dim=c(d,d,d))
  61   array( .C("Moments_M3", X=as.double(X), Y=as.double(Y), pn=as.integer(n),
  62     pd=as.integer(d), M3=as.double(M3), PACKAGE="morpheus")$M3, dim=c(d,d,d) )
  63 }
  64
  65 #' computeMoments
  66 #'
  67 #' Compute cross-moments of order 1,2,3 from X,Y
  68 #'
  69 #' @inheritParams computeMu
  70 #'
  71 #' @return A list L where L[[i]] is the i-th cross-moment
  72 #'
  73 #' @export
  74 computeMoments = function(X, Y)
  75   list( colMeans(Y * X), .Moments_M2(X,Y), .Moments_M3(X,Y) )
  76
  77 # Find the optimal assignment (permutation) between two sets (minimize cost)
  78 #
  79 # @param distances The distances matrix, in columns (distances[i,j] is distance between i
  80 #   and j)
  81 #
  82 # @return A permutation minimizing cost
  83 #
  84 .hungarianAlgorithm = function(distances)
  85 {
  86   n = nrow(distances)
  87   .C("hungarianAlgorithm", distances=as.double(distances), pn=as.integer(n),
  88     assignment=integer(n), PACKAGE="morpheus")$assignment
  89 }
  90
  91 #' alignMatrices
  92 #'
  93 #' Align a set of parameters matrices, with potential permutations.
  94 #'
  95 #' @param Ms A list of matrices, all of same size DxK
  96 #' @param ref Either a reference matrix or "mean" to align on empirical mean
  97 #' @param ls_mode How to compute the labels assignment: "exact" for exact algorithm
  98 #'   (default, but might be time-consuming, complexity is O(K^3) ), or "approx1", or
  99 #'   "approx2" to apply a greedy matching algorithm (heuristic) which for each column in
 100 #'   reference (resp. in current row) compare to all unassigned columns in current row
 101 #'   (resp. in reference)
 102 #'
 103 #' @return The aligned list (of matrices), of same size as Ms
 104 #'
 105 #' @export
 106 alignMatrices = function(Ms, ref, ls_mode)
 107 {
 108   if (!is.matrix(ref) && ref != "mean")
 109     stop("ref: matrix or 'mean'")
 110   if (!ls_mode %in% c("exact","approx1","approx2"))
 111     stop("ls_mode in {'exact','approx1','approx2'}")
 112
 113   K <- ncol(Ms[[1]])
 114   if (is.character(ref)) #ref=="mean"
 115     m_sum = Ms[[1]]
 116   L <- length(Ms)
 117   for (i in ifelse(is.character(ref),2,1):L)
 118   {
 119     m_ref = if (is.character(ref)) m_sum / (i-1) else ref
 120     m = Ms[[i]] #shorthand
 121
 122     if (ls_mode == "exact")
 123     {
 124       #distances[i,j] = distance between m column i and ref column j
 125       distances = apply( m_ref, 2, function(col) ( sqrt(colSums((m-col)^2)) ) )
 126       assignment = .hungarianAlgorithm(distances)
 127       col <- m[,assignment]
 128       if (is.list(Ms)) Ms[[i]] <- col else Ms[,,i] <- col
 129     }
 130     else
 131     {
 132       # Greedy matching:
 133       #   approx1: li[[i]][,j] is assigned to m[,k] minimizing dist(li[[i]][,j],m[,k'])
 134       #   approx2: m[,j] is assigned to li[[i]][,k] minimizing dist(m[,j],li[[i]][,k'])
 135       available_indices = 1:K
 136       for (j in 1:K)
 137       {
 138         distances =
 139           if (ls_mode == "approx1")
 140           {
 141             apply(as.matrix(m[,available_indices]), 2,
 142               function(col) ( sqrt(sum((col - m_ref[,j])^2)) ) )
 143           }
 144           else #approx2
 145           {
 146             apply(as.matrix(m_ref[,available_indices]), 2,
 147               function(col) ( sqrt(sum((col - m[,j])^2)) ) )
 148           }
 149         indMin = which.min(distances)
 150         if (ls_mode == "approx1")
 151         {
 152           col <- m[ , available_indices[indMin] ]
 153           if (is.list(Ms)) Ms[[i]][,j] <- col else Ms[,j,i] <- col
 154         }
 155         else #approx2
 156         {
 157           col <- available_indices[indMin]
 158           if (is.list(Ms)) Ms[[i]][,col] <- m[,j] else Ms[,col,i] <- m[,j]
 159         }
 160         available_indices = available_indices[-indMin]
 161       }
 162     }
 163
 164     # Update current sum with "label-switched" li[[i]]
 165     if (is.character(ref)) #ref=="mean"
 166       m_sum = m_sum + Ms[[i]]
 167   }
 168   Ms
 169 }