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dml (Distance Metric Learning in R)

R package for a collection of Distance Metric Learning algorithms, including global and local methods such as Relevant Component Analysis, Discriminative Component Analysis, Local Fisher Discriminant Analysis, etc. These distance metric learning methods are widely applied in feature extraction, dimensionality reduction, clustering, classification, information retrieval, and computer vision problems.


Install the current release from CRAN:


Or, try the latest development version from GitHub:



Relevant Component Analysis


# generate synthetic multivariate normal data

k <- 100L # sample size of each class
n <- 3L # specify how many classes
N <- k * n # total sample size

x1 <- mvrnorm(k, mu = c(-16, 8), matrix(c(15, 1, 2, 10), ncol = 2))
x2 <- mvrnorm(k, mu = c(0, 0), matrix(c(15, 1, 2, 10), ncol = 2))
x3 <- mvrnorm(k, mu = c(16, -8), matrix(c(15, 1, 2, 10), ncol = 2))
x <-, x2, x3)) # predictors
y <- gl(n, k) # response

# fully labeled data set with 3 classes
# need to use a line in 2D to classify
plot(x[, 1L], x[, 2L],
  bg = c("#E41A1C", "#377EB8", "#4DAF4A")[y],
  pch = rep(c(22, 21, 25), each = k)
abline(a = -10, b = 1, lty = 2)
abline(a = 12, b = 1, lty = 2)

# generate synthetic chunklets
chunks <- vector("list", 300)
for (i in 1:100) chunks[[i]] <- sample(1L:100L, 10L)
for (i in 101:200) chunks[[i]] <- sample(101L:200L, 10L)
for (i in 201:300) chunks[[i]] <- sample(201L:300L, 10L)

chks <- x[unlist(chunks), ]

# make "chunklet" vector to feed the chunks argument
chunksvec <- rep(-1L, nrow(x))
for (i in 1L:length(chunks)) {
  for (j in 1L:length(chunks[[i]])) {
    chunksvec[chunks[[i]][j]] <- i

# relevant component analysis
rcs <- rca(x, chunksvec)

# learned transformation of the data
#>           [,1]       [,2]
#> [1,] -3.181484 -0.8812647
#> [2,] -1.196200  2.3438640

# learned Mahalanobis distance metric
#>           [,1]     [,2]
#> [1,] 10.898467 1.740125
#> [2,]  1.740125 6.924592

# whitening transformation applied to the chunklets
chkTransformed <- as.matrix(chks) %*% rcs$A

# original data after applying RCA transformation
# easier to classify - using only horizontal lines
xnew <- rcs$newX
plot(xnew[, 1L], xnew[, 2L],
  bg = c("#E41A1C", "#377EB8", "#4DAF4A")[gl(n, k)],
  pch = c(rep(22, k), rep(21, k), rep(25, k))
abline(a = -15, b = 0, lty = 2)
abline(a = 16, b = 0, lty = 2)

Other Examples

For examples of Local Fisher Discriminant Analysis, please take a look at the separate package here. For examples of all other implemented algorithms, please take a look at the dml package reference manual.

Brief Introduction

Distance metric is widely used in the machine learning literature. We used to choose a distance metric according to a priori (Euclidean Distance , L1 Distance, etc.) or according to the result of cross validation within small class of functions (e.g. choosing order of polynomial for a kernel). Actually, with priori knowledge of the data, we could learn a more suitable distance metric with (semi-)supervised distance metric learning techniques. dml is such an R package aims to implement a collection of algorithms for (semi-)supervised distance metric learning. These distance metric learning methods are widely applied in feature extraction, dimensionality reduction, clustering, classification, information retrieval, and computer vision problems.


Algorithms planned in the first development stage:

  • Supervised Global Distance Metric Learning:

    • Relevant Component Analysis (RCA) - implemented
    • Kernel Relevant Component Analysis (KRCA)
    • Discriminative Component Analysis (DCA) - implemented
    • Kernel Discriminative Component Analysis (KDCA)
    • Global Distance Metric Learning by Convex Programming - implemented
  • Supervised Local Distance Metric Learning:

    • Local Fisher Discriminant Analysis - implemented
    • Kernel Local Fisher Discriminant Analysis - implemented
    • Information-Theoretic Metric Learning (ITML)
    • Large Margin Nearest Neighbor Classifier (LMNN)
    • Neighbourhood Components Analysis (NCA)
    • Localized Distance Metric Learning (LDM)

The algorithms and routines might be adjusted during developing.

Contribute & Code of Conduct

To contribute to this project, please take a look at the Contributing Guidelines first. Please note that this project is released with a Contributor Code of Conduct. By contributing to this project, you agree to abide by its terms.


Contact the maintainer of this package: Yuan Tang

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