| 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 | } |