In your example Card(A Union B) is always = Card(A) =N and that's an issue.
What happens if B = {A + noisy points} (false positive)?
According to your calcul the score will be 1.0... and that's not right.
Actually I think the answer is actually trivial.
(but I didn't think to formulate the problem in algebra terms)
score = Card(A Intersection B)/Card(A Union B)
score = # corcordances/ (#discordances+#concordances)
score = # corcordances/ (# omissions (=Card(elements in A not included in
B))+ # false positives(=Card(elements in B not included in
A))+#concordances)
Best,
Nicolas
On Sun, Mar 6, 2011 at 3:33 AM, Younes Fadakar <yfa.st...@ymail.com> wrote:
> 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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