longitudinalData (version 2.1.2)

distTraj: ~ Function: distance for trajectories ~

Description

This function computes and returns the distance computed by using the specified distance measure between two trajectorie.

Usage

distTraj(x, y, method = "euclidean", p = 2)

Arguments

x

[vector(numeric)]: first trajectories

y

[vector(numeric)]: second trajectories

method

[character]: the distance measure to be used. This must be one of "euclidean", "maximum", "manhattan", "canberra", "binary" or "minkowski". Unambiguous substring can not be given.

p

[numeric]: The power of the Minkowski distance.

Value

• A numeric value.

Author

Christophe Genolini 1. UMR U1027, INSERM, Universit� Paul Sabatier / Toulouse III / France 2. CeRSME, EA 2931, UFR STAPS, Universit� de Paris Ouest-Nanterre-La D�fense / Nanterre / France

Details

This function compute the same distances than the dist function but is optimized for trajectories. It can compute only a single distance at a time (whereas dist can return a matrix of distances) but on a single couple of trajectories, it is arround 5 times faster. Available distance measures are (written for two vectors x and y):

• 'euclidean': Usual square distance between the two vectors (2 norm).
• 'maximum': Maximum distance between two components of x and y (supremum norm)
• 'manhattan': Absolute distance between the two vectors (1 norm).
• 'canberra': sum(|x_i - y_i| / (|x_i| + |y_i|)). Terms with zero numerator and denominator are omitted from the sum and treated as if the values were missing.
• 'binary': (aka _asymmetric binary_): The vectors are regarded as binary bits, so non-zero elements are 'on' and zero elements are 'off'. The distance is the _proportion_ of bits in which only one is on amongst those in which at least one is on.
• 'minkowski': The p norm, the pth root of the sum of the pth powers of the differences of the components.

Missing values are allowed, and are excluded from all computations involving the column within which they occur. Further, when 'Inf' values are involved, all pairs of values are excluded when their contribution to the distance gave 'NaN' or 'NA'. If some columns are excluded in calculating a Euclidean, Manhattan, Canberra or Minkowski distance, the sum is scaled up proportionally to the number of columns used (Gower adjustement). If all pairs are excluded when calculating a particular distance, the value is 'NA'.

References

[1] Brian Everitt, Sabine Landau & Morven Leese "Cluster Analysis" [2] C. Genolini and B. Falissard "KmL: k-means for longitudinal data" Computational Statistics, vol 25(2), pp 317-328, 2010 [3] C. Genolini and B. Falissard "KmL: A package to cluster longitudinal data" Computer Methods and Programs in Biomedicine, 104, pp e112-121, 2011

See Also

dist

Examples

x <- -1+rnorm(25);x[floor(runif(5,1,26))] <- NA
    y <- 1+rnorm(25);y[floor(runif(5,1,26))] <- NA

    plot(x,type="b",col=2,ylim=c(-5,5))
    lines(y,type="b",col=3)

    system.time(for(i in 1:10000)dist(rbind(x,y)))
    system.time(for(i in 1:10000)distTraj(x,y))

    system.time(for(i in 1:10000)dist(rbind(x,y),method="maximum"))
    system.time(for(i in 1:10000)distTraj(x,y,method="maximum"))

    system.time(for(i in 1:10000)dist(rbind(x,y),method="manhattan"))
    system.time(for(i in 1:10000)distTraj(x,y,method="manhattan"))