GdmDiag: Global Distance Metric Learning
In road2stat/sdml: Supervised Distance Metric Learning with R

Description Usage Arguments Details Value Note Author(s) References Examples

Performs Global Distance Metric Learning (GDM) on the given data, learning a diagonal matrix.

1 2	GdmDiag(data, simi, dism, C0 = 1, S1 = NULL, D1 = NULL, threshold = 0.001)

`data`	`n * d` data matrix. `n` is the number of data points, `d` is the dimension of the data. Each data point is a row in the matrix.
`simi`	`n * 2` matrix describing the similar constrains. Each row of matrix is serial number of a similar pair in the original data. For example, pair(1, 3) represents the first observation is similar the 3th observation in the original data.
`dism`	`n * 2` matrix describing the dissimilar constrains as `simi`. Each row of matrix is serial number of a dissimilar pair in the original data.
`C0`	numeric, the bound of similar constrains.
`threshold`	numeric, the threshold of stoping the learning iteration.

Put GdmDiag function details here.

list of the GdmDiag results:

`newData`	GdmDiag transformed data
`diagonalA`	suggested Mahalanobis matrix
`dmlA`	matrix to transform data, square root of diagonalA
`error`	the precision of obtained distance metric by Newton-Raphson optimization

For every two original data points (x1, x2) in newData (y1, y2):

(x2 - x1)' * A * (x2 - x1) = || (x2 - x1) * B ||^2 = || y2 - y1 ||^2

Be sure to check whether the dimension of original data and constrains' format are valid for the function.

Tao Gao <http://www.gaotao.name>

Steven C.H. Hoi, W. Liu, M.R. Lyu and W.Y. Ma (2003). Distance metric learning, with application to clustering with side-information.

set.seed(602)
library(MASS)
library(scatterplot3d)

# generate simulated Gaussian data
k = 100
m <- matrix(c(1, 0.5, 1, 0.5, 2, -1, 1, -1, 3), nrow =3, byrow = T)
x1 <- mvrnorm(k, mu = c(1, 1, 1), Sigma = m)
x2 <- mvrnorm(k, mu = c(-1, 0, 0), Sigma = m)
data <- rbind(x1, x2)

# define similar constrains
simi <- rbind(t(combn(1:k, 2)), t(combn((k+1):(2*k), 2)))

temp <-  as.data.frame(t(simi))
tol <- as.data.frame(combn(1:(2*k), 2))

# define disimilar constrains
dism <- t(as.matrix(tol[!tol %in% simi]))

# transform data using GdmDiag
result <- GdmDiag(data, simi, dism)
newData <- result$newData
# plot original data
color <- gl(2, k, labels = c("red", "blue"))
par(mfrow = c(2, 1), mar = rep(0, 4) + 0.1)
scatterplot3d(data, color = color, cex.symbols = 0.6,
		  xlim = range(data[, 1], newData[, 1]),
		  ylim = range(data[, 2], newData[, 2]),
		  zlim = range(data[, 3], newData[, 3]),
		  main = "Original Data")
# plot GdmDiag transformed data
scatterplot3d(newData, color = color, cex.symbols = 0.6,
		  xlim = range(data[, 1], newData[, 1]),
		  ylim = range(data[, 2], newData[, 2]),
		  zlim = range(data[, 3], newData[, 3]),
		  main = "Transformed Data")