~ Function: Frechet distance ~

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Description

Compute Frechet distance between two trajectories.

Usage

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distFrechet(Px,Py,Qx, Qy, timeScale=0.1, FrechetSumOrMax = "sum")
distFrechetR(Px,Py,Qx, Qy, timeScale=0.1, FrechetSumOrMax = "sum")
distFrechetRec(Px,Py,Qx, Qy, timeScale=0.1, FrechetSumOrMax = "sum")

Arguments

Px

[vector(numeric)] Times (abscisse) of the first trajectories.

Py

[vector(numeric)] Values of the first trajectories.

Qx

[vector(numeric)] Times of the second trajectories.

Qy

[vector(numeric)] Values of the second trajectories.

timeScale

[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.

FrechetSumOrMax

[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.

Details

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.

Value

A numeric value.

Author

Christophe Genolini
1. UMR U1027, INSERM, Universit<e9> Paul Sabatier / Toulouse III / France
2. CeRSM, EA 2931, UFR STAPS, Universit<e9> de Paris Ouest-Nanterre-La D<e9>fense / Nanterre / France

References

[1] Thomas Eiter & Heikki Mannila:
"Computing Discrete Fr<b4>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

See Also

distTraj

Examples

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   Px <- 1:20
   Py <- dnorm(1:20,12,2)
   Qx <- 1:20
   Qy <- dnorm(1:20,8,2)

   ### Function from Eiter and Mannila compiled in C
   system.time(cat("\n",distFrechet(Px,Py,Qx,Qy)))

   ### Same thing in R
   system.time(cat("\n",distFrechetR(Px,Py,Qx,Qy)))

   ### Frechet using sum instead of max.
   distFrechet(Px,Py,Qx,Qy,FrechetSumOrMax="sum")