# Distance for curves Calculates distance matrix for two samples of curves using minimax metric. The function can be particularly useful for parallel computation of a big distance matrix. ```r dist.curves.asymm(curvesRows, curvesCols, oneWay = FALSE, verbosity = 0L) ``` ## Arguments - `curvesRows`: A list where each element is a function being a list containing a matrix `coords` (values, d columns). - `curvesCols`: A list where each element is a function being a list containing a matrix `coords` (values, d columns). - `oneWay`: Whether curves should be condisered as a one-directional, `FALSE` by default. - `verbosity`: Level of reporting messages, the higher the more progress reports are printed, set `0` (default) for no messages. ## Returns A matrix `length(curvesRows) x length(curvesCols)` with each entry being the distance between two corresponding curves. ## Examples ```r library(curveDepth) # Pixel-grid filling function for an image plotGridImage <- function(dims){ redDims1 <- dims[1] - 1 redDims2 <- dims[2] - 1 for (i in 1:(dims[1] - 1)){ lines(c(i / redDims1 - 0.5 / redDims1, i / redDims1 - 0.5 / redDims1), c(0 - 0.5 / redDims2, 1 + 0.5 / redDims2), lwd = 1, lty = 3, col = "lightgray") lines(c(0 - 0.5 / redDims1, 1 + 0.5 / redDims1), c(i / redDims2 - 0.5 / redDims2, i / redDims2 - 0.5 / redDims2), lwd = 1, lty = 3, col = "lightgray") } rect(0 - 0.5 / redDims1, 0 - 0.5 / redDims2, 1 + 0.5 / redDims1, 1 + 0.5 / redDims2) } # Load two Sevens and one One, plot them, # and transform to curves data("mnistShort017") # First Seven firstSevenDigit <- mnistShort017$`7`[, , 5] image(as.matrix(rev(as.data.frame(firstSevenDigit))), col = gray((255:0) / 256), asp = 1, xlim = c(0 - 1 / 27, 1 + 1 / 27), ylim = c(0 - 1 / 27, 1 + 1 / 27)) plotGridImage(dim(firstSevenDigit)[1:2]) firstSevenCurve <- images2curves(array( firstSevenDigit, dim = c(28, 28, 1)))[[1]] # Second Seven secondSevenDigit <- mnistShort017$`7`[, , 6] image(as.matrix(rev(as.data.frame(secondSevenDigit))), col = gray((255:0) / 256), asp = 1, xlim = c(0 - 1 / 27, 1 + 1 / 27), ylim = c(0 - 1 / 27, 1 + 1 / 27)) plotGridImage(dim(secondSevenDigit)[1:2]) secondSevenCurve <- images2curves(array( secondSevenDigit, dim = c(28, 28, 1)))[[1]] # A One aOneDigit <- mnistShort017$`1`[, , 1] image(as.matrix(rev(as.data.frame(aOneDigit))), col = gray((255:0) / 256), asp = 1, xlim = c(0 - 1 / 27, 1 + 1 / 27), ylim = c(0 - 1 / 27, 1 + 1 / 27)) plotGridImage(dim(aOneDigit)[1:2]) aOneCurve <- images2curves(array( aOneDigit, dim = c(28, 28, 1)))[[1]] # Caculate distances between all the curves distMatrix <- matrix(0, 3, 3) distMatrix[3, 1:2] <- distMatrix[1:2, 3] <- dist.curves.asymm(list( firstSevenCurve, secondSevenCurve), list(aOneCurve)) distMatrix[2, 1] <- distMatrix[1, 2] <- dist.curves.asymm( list(firstSevenCurve), list(secondSevenCurve)) # Print distance matrix print(distMatrix) ``` ## References Lafaye De Micheaux, P., Mozharovskyi, P. and Vimond, M. (2018). Depth for curve data and applications.

dist.curves.asymm function