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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