objective.fun {matchFeat} | R Documentation |
Calculates the objective value in the multidimensional assignment problem with decomposable costs (MDADC). The dissimilarity function used in this problem is the squared Euclidean distance.
objective.fun(x, sigma = NULL, unit = NULL, w = NULL)
x |
data: matrix of dimensions |
sigma |
permutations: matrix of dimensions |
unit |
integer (=number of units) or vector mapping rows of |
w |
weights for loss function: single positive number,
|
Given n
datasets having each m
vectors of same size,
say {x_{11},...,x_{1m}},...,x_{n1},...,x_{nm}
, and permutations
\sigma_1,...,\sigma_n
of {1,...,m}
, the function calculates
1/(n(n-1)) sum_{i,j} sum_{k} || x_{i,sigma_i(k)- x_{j,\sigma_j(k) \|^2}}
where i
and n
run from 1 to n
and k
runs from 1 to m
. This is the objective value (1) of Degras (2021), up to the factor 1/(n(n-1))
.
Objective value
Degras (2022) "Scalable feature matching across large data collections." doi:10.1080/10618600.2022.2074429
data(optdigits)
m <- 10
n <- 100
sigma <- matrix(1:m,m,n) # identity permutations
objective.fun(optdigits$x, sigma, optdigits$unit)