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Compute Frechet distance between two trajectories.
distFrechet(Px,Py,Qx, Qy, timeScale=0.1, FrechetSumOrMax = "max")
A numeric value.
[vector(numeric)] Times (abscisse) of the first trajectories.
[vector(numeric)] Values of the first trajectories.
[vector(numeric)] Times of the second trajectories.
[vector(numeric)] Values of the second trajectories.
[numeric
]: allow to modify the time scale,
increasing or decreasing the cost of the horizontal shift. If timeScale is
very big, then the Frechet's distance is equal to the
euclidienne distance. If timeScale is very small, then it is equal to
the Dynamic Time Warping.
[character
]: The Frechet's distance can
be define using the 'sum' function or the 'max' function. This option
let the user to chose one or the other.
Christophe Genolini
1. UMR U1027, INSERM, Université Paul Sabatier / Toulouse III / France
2. CeRSM, EA 2931, UFR STAPS, Université de Paris Ouest-Nanterre-La Défense / Nanterre / France
Given two curve P and Q, Frechet distance between P and Q is define as
inf_{a,b} max_{t} d(P(a(t)),Q(b(t)))
. It's computation is a
NP-complex problem. When P and Q are trajectories (discrete curve), the
problem is polynomial.
The Frechet distance can also be define using a sum instead of a max:
inf_{a,b} sum_{t} d(P(a(t)),Q(b(t)))
The function distFrechet
is C compiled,
the function distFrechetR
is in R,
the function distFrechetRec
is in recursive (the slowest) in R.
[1] Thomas Eiter & Heikki Mannila:
"Computing Discrete Fr´echet Distance"
[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
distTraj
Px <- 1:20
Py <- dnorm(1:20,12,2)
Qx <- 1:20
Qy <- dnorm(1:20,8,2)
distFrechet(Px,Py,Qx,Qy)
### Frechet using sum instead of max.
distFrechet(Px,Py,Qx,Qy,FrechetSumOrMax="sum")
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