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 > > + > > + To post a message to the list, send it to ai-geost...@jrc.ec.europa.eu > > + To unsubscribe, send email to majordomo@ jrc.ec.europa.eu with no > subject > > and "unsubscribe ai-geostats" in the message body. 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