Dear Nicolas,
Hope this can help you.
Let have a look at my implementation:
#-----the simplest implementation-----
N = 100 #number of ref points=Crad(A)
A.x = rand(N) #set A.x
A.y = rand(N) #set A.y: coordinate pairs
B.X = A.x[:-10] #set B = sampling
B.Y = A.y[:-10] # has 10 points less than A
# Card(B)-Card(A)=-10
M = PositionAccuracy(A,B) #as you defined=#concordances
Score = M/N*100 #my score=normalized based on N
# N=Card(A)
So the Score will be always in [0,1], here is 0.9 or 90.00%.
and
#-----the realistic implementation-----
N = 100 #
A.x = rand(N) #set A.x
A.y = rand(N) #set A.y: coordinate pairs
B.x = shake(A.x,10%) #slightly repositions points
B.y = shake(A.y,10%) # randomly with 10% move
B.x = B.x+rand(N/10) #adds extra 10% rand points
B.y = B.y+rand(N/10) #Card(B)=1.1*Card(A)
M = PositionAccuracy(A,B) #
Score = M/N*100 #my score=normalized based on N
#N=Card(A)
Again the Score will be always in [0,1].
This is what I used to generate the previously sent figures.
Best Regards,
Younes
yfa.st...@ymail.com
http://alghalandis.com
________________________________
________________________________
From: Nicolas Maisonneuve <n.maisonne...@gmail.com>
To: Younes Fadakar <yfa.st...@ymail.com>
Cc: Ask Geostatisticians <ai-geostats@jrc.it>
Sent: Wed, 2 March, 2011 6:27:48 PM
Subject: Re: AI-GEOSTATS: Estimation of the position accuracy of 2 set of
points
with different cardinalities
Thanks for your support Younges
my idea was inspired and adapted from the Kendall correlation coefficient
(http://en.wikipedia.org/wiki/Kendall_tau_rank_correlation_coefficient
) but with the pb of cardinality.
- number of concordances (accurate observations)
- number of discordances(omission + false positive)
and do a sum and then a normalisation to get something like 1.0 = max
corcordance max 0.0 = max discordance.
but I am not sure how to normalize:
- the range of concordance [0, Card(A)] is smaller than the
discordance [0, Card(A+B)] so anormalisation should be something like
(2Card(A)+Card(B)) but I am not sure about that , and I am not sure
the whole idea is right..
How did you normalize in your calcul?
On Wed, Mar 2, 2011 at 5:50 AM, Younes Fadakar <yfa.st...@ymail.com> wrote:
> Dear Nicolas,
>
> This is not the answer to your question but a try to implement your idea and
> to have an experience with it.
> Please see the attached, the output.
> It seems the total score provided by the method is very dependent to the
> 'r', the radius of search for neighbors around each ref point (A).
> However, being able to define the right 'r', the score seems a realistic
> measure of accuracy to me.
> Of course, this is just a practical understanding hoping the community could
> provide the statistical references.
> Anyway, I liked the idea.
>
> Best Regards,
> .
> Younes
> yfa.st...@ymail.com
> http://alghalandis.com
> ________________________________
>
>
> ________________________________
> From: Nicolas Maisonneuve <n.maisonne...@gmail.com>
> To: ai-geostats@jrc.it
> Sent: Mon, 28 February, 2011 6:21:49 PM
> Subject: AI-GEOSTATS: Estimation of the position accuracy of 2 set of points
> with different cardinalities
>
> Hi everyone,
>
> A simple question:
> I have 1 set of 2D location points A that I use as reference.
> I have another set of location points B generated by observations.
>
> Is there any standard method/measure to estimate a kind of position
> accuracy error knowing that
> - A and B dont have the same cardinality of elements e.g. B could have
> more points than A?
> - a point in A should be associated to only one point in B.
>
> For the moment I created my own error measure using 3 estimations.
> for a given accuracy rate (<20 meters) I compute:
> - O: number of omissions (when there is no observation in B closed
> enough of a point in A) ,
> - FP: number of false positive (when a B point has been observed but
> not closed to a A point - or already taken from another
> observation)
> - M: number of matching (when a B point is closed enought of a A point)
> and then I aggregate the result = M- (O+FP) to get an indicator..
>
> I am pretty sure there are other more traditional ways to do that.
>
> Thanks in advance
> -NM
> +
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