wasserstein {SBCK}

wasserstein distance

Description

Compute wasserstein distance between two dataset or SparseHist X and Y

Usage

wasserstein(X, Y, p = 2, ot = SBCK::OTNetworkSimplex$new())

Arguments

X

[matrix or SparseHist] If matrix, dim = ( nrow = n_samples, ncol = n_features)

Y

[matrix or SparseHist] If matrix, dim = ( nrow = n_samples, ncol = n_features)

p

[float] Power of the metric (default = 2)

ot

[Optimal transport solver]

Value

[float] value of distance

References

Wasserstein, L. N. (1969). Markov processes over denumerable products of spaces describing large systems of automata. Problems of Information Transmission, 5(3), 47-52.

Examples

X = base::cbind( stats::rnorm(2000) , stats::rnorm(2000)  )
Y = base::cbind( stats::rnorm(2000,mean=10)  , stats::rnorm(2000) )
bw = base::c(0.1,0.1)
muX = SBCK::SparseHist( X , bw )
muY = SBCK::SparseHist( Y , bw )

## The four are equals
w2 = SBCK::wasserstein(X,Y)
w2 = SBCK::wasserstein(muX,Y)
w2 = SBCK::wasserstein(X,muY)
w2 = SBCK::wasserstein(muX,muY)