dca: Discriminative Component Analysis
In dml: Distance Metric Learning in R

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

Performs discriminative component analysis on the given data.

1	dca(data, chunks, neglinks, useD = NULL)

`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.
`chunks`	length `n` vector describing the chunklets: `-1` in the `i` th place means point `i` doesn't belong to any chunklet; integer `j` in place `i` means point `i` belongs to chunklet j. The chunklets indexes should be 1:(number of chunklets).
`neglinks`	`s * s` symmetric matrix describing the negative relationship between all the `s` chunklets. For the element neglinks_{ij}: neglinks_{ij} = 1 means chunklet `i` and chunklet j have negative constraint(s); neglinks_{ij} = 0 means chunklet `i` and chunklet j don't have negative constraints or we don't have information about that.
`useD`	Integer. Optional. When not given, DCA is done in the original dimension and B is full rank. When useD is given, DCA is preceded by constraints based LDA which reduces the dimension to useD. B in this case is of rank useD.

Put DCA function details here.

list of the DCA results:

`B`	DCA suggested Mahalanobis matrix
`DCA`	DCA suggested transformation of the data. The dimension is (original data dimension) * (useD)
`newData`	DCA transformed data

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

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

Put some note here.

Xiao Nan <http://www.road2stat.com>

Steven C.H. Hoi, W. Liu, M.R. Lyu and W.Y. Ma (2006). Learning Distance Metrics with Contextual Constraints for Image Retrieval. Proceedings IEEE Conference on Computer Vision and Pattern Recognition (CVPR2006).

## Not run: 
set.seed(123)
require(MASS)  # generate synthetic Gaussian data
k = 100        # sample size of each class
n = 3          # specify how many class
N = k * n      # total sample number
x1 = mvrnorm(k, mu = c(-10, 6), matrix(c(10, 4, 4, 10), ncol = 2))
x2 = mvrnorm(k, mu = c(0, 0), matrix(c(10, 4, 4, 10), ncol = 2))
x3 = mvrnorm(k, mu = c(10, -6), matrix(c(10, 4, 4, 10), ncol = 2))
data = as.data.frame(rbind(x1, x2, x3))
# The fully labeled data set with 3 classes
plot(data$V1, data$V2, bg = c("#E41A1C", "#377EB8", "#4DAF4A")[gl(n, k)],
     pch = c(rep(22, k), rep(21, k), rep(25, k)))
Sys.sleep(3)
# Same data unlabeled; clearly the classes' structure is less evident
plot(x$V1, x$V2)
Sys.sleep(3)

chunk1 = sample(1:100, 5)
chunk2 = sample(setdiff(1:100, chunk1), 5)
chunk3 = sample(101:200, 5)
chunk4 = sample(setdiff(101:200, chunk3), 5)
chunk5 = sample(201:300, 5)
chks = list(chunk1, chunk2, chunk3, chunk4, chunk5)
chunks = rep(-1, 300)
# positive samples in the chunks
for (i in 1:5) {
  for (j in chks[[i]]) {
    chunks[j] = i
  }
}

# define the negative constrains between chunks
neglinks = matrix(c(
		0, 0, 1, 1, 1,
		0, 0, 1, 1, 1,
		1, 1, 0, 0, 0,
		1, 1, 0, 0, 1,
		1, 1, 1, 1, 0),
		ncol = 5, byrow = TRUE)

dcaData = dca(data = data, chunks = chunks, neglinks = neglinks)$newData
# plot DCA transformed data
plot(dcaData[, 1], dcaData[, 2], bg = c("#E41A1C", "#377EB8", "#4DAF4A")[gl(n, k)],
     pch = c(rep(22, k), rep(21, k), rep(25, k)),
     xlim = c(-15, 15), ylim = c(-15, 15))

## End(Not run)