## [ai-geostats] natural neighbor applied to indicator transforms

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• Dear list members I would like to have some comments, suggestions or critics about the following topic: building a (preliminary) local uncertainty model of the
Message 1 of 7 , Aug 30, 2005
Dear list members

I would like to have some comments, suggestions or critics about the following topic:
building a (preliminary) local uncertainty model of the spatial distribution of discrete (categorical) variables by means of natural neighbor interpolation method applied to indicator transforms.

From my perspective, interpolating  indicator variables (well, at the end an indicator variable is the probability of occurrence of a given class) by means of a method like natural neighbor is an easy and quick way to build a (preliminary) model of local uncertainty of the studied properties, avoiding problems of order relation violations.
In my specific case I apply natural neighbor interpolation to indicator transforms representing lithological classes in the same way in which direct indicator kriging is applied. In this way, looking at the spatial distribution of the probability of occurrence of lithologies (or at the distribution of the lithological classes, if some classification algorithm is applied) I can have a first idea of the spatial distribution of lithologies. Clearly this method is utilized only as an explorative and preliminary data analysis tool.

S. Trevisani
• I try to reformulate my question..... When performing direct (i.e. without crossvariogram) indicator kriging, practically we interpolate probability values by
Message 2 of 7 , Sep 2, 2005

I try to reformulate my question.....
When performing direct (i.e. without crossvariogram) indicator kriging, practically we interpolate probability values by means of ordinary kriging. These probability values could represent the probability of occurrence of some category or the probability to overcome some threshold.
My question is: is there anything wrong to interpolate these probability values with other interpolating algorithm like, for example natural neighbor (or triangulation)?
In my opinion is all ok ..... considering also that we have no problem of order relation violations.
Again, this technique is applied only for a preliminary data analysis

Then a short consideration directed about the importance of boundaries:
Quoting Nicolas Gilardi
"My personnal feeling about the distinction between using a classification algorithm or a regression one is the importance you put on the boundaries.If you look for smooth boundaries, with uncertainty estimations, etc., then a regression algorithm (like indicator kriging) is certainly a good approach."

Well, if you use fuzzy classification the boundaries become continuos...fuzzy.

Bye

S. Trevisani
• Ciao Sebastiano, I realized nobody replied to your question (sorry for have added confusion here). I don t see any objection in applying any interpolator to
Message 3 of 7 , Sep 5, 2005
Message
Ciao Sebastiano,

I realized nobody replied to your question (sorry for have added confusion here).

I don't see any objection in applying any interpolator to probability values.
However, you should better use exact interpolators to avoid getting probabilities of occurences > 1 (or smaller than 0)

Cheers

Gregoire

-----Original Message-----
From: seba [mailto:sebastiano.trevisani@...]
Sent: 02 September 2005 10:07
To: ai-geostats@...
Cc: ai-geostats@...; 'Nicolas Gilardi'
Subject: RE: [ai-geostats] natural neighbor applied to indicator transforms

I try to reformulate my question.....
When performing direct (i.e. without crossvariogram) indicator kriging, practically we interpolate probability values by means of ordinary kriging. These probability values could represent the probability of occurrence of some category or the probability to overcome some threshold.
My question is: is there anything wrong to interpolate these probability values with other interpolating algorithm like, for example natural neighbor (or triangulation)?
In my opinion is all ok ..... considering also that we have no problem of order relation violations.
Again, this technique is applied only for a preliminary data analysis

Then a short consideration directed about the importance of boundaries:
Quoting Nicolas Gilardi
"My personnal feeling about the distinction between using a classification algorithm or a regression one is the importance you put on the boundaries.If you look for smooth boundaries, with uncertainty estimations, etc., then a regression algorithm (like indicator kriging) is certainly a good approach."

Well, if you use fuzzy classification the boundaries become continuos...fuzzy.

Bye

S. Trevisani
• Dear Pierre and Gregorie Thank you for your help ..... Concluding (considering that natural neighbor method should be a convex and an exact interpolator) it
Message 4 of 7 , Sep 5, 2005
Dear Pierre and Gregorie

Thank you for your help .....
Concluding (considering that natural neighbor method should be a convex and
an exact interpolator) it seems that the approach has not side effects !!!!!!

Sincerely
Sebastiano

At 17.19 05/09/2005, you wrote:
>Content-Class: urn:content-classes:message
>Content-Type: text/plain;
> charset="utf-8"
>
>Hi,
>
>In fact, as long as the weights are all positive and sum up to one, your
>interpolated probability
>will always be between 0 and 1; so you should be all right..
>The approach proposed by Sebastiano is similar to median indicator kriging
>in the sense
>that the weights assigned to the observations will be the same across all
>a single indicator semivariogram used to compute the kriging weights, the
>same weighting set
>will be applied to all indicators since the data configuration, hence the
>size of the Thiessen polygons,
>doesn't change among indicators). Because all the weights are positive and
>remain the same
>for the different indicators, this approach should eliminate all order
>relation deviations
>(all estimated probabilities will be between 0 and 1, and at each location
>their sum will be one).
>
>
>Pierre
>
> -----Original Message-----
> From: Gregoire Dubois [mailto:gregoire.dubois@...]
> Sent: Mon 9/5/2005 7:00 AM
> To: 'seba'; ai-geostats@...
> Cc:
> Subject: RE: [ai-geostats] natural neighbor applied to indicator
> transforms
>
>
> Ciao Sebastiano,
>
> I realized nobody replied to your question (sorry for have added
> confusion here).
>
> I don't see any objection in applying any interpolator to
> probability values.
> However, you should better use exact interpolators to avoid
> getting probabilities of occurences > 1 (or smaller than 0)
>
> Cheers
>
> Gregoire
>
>
>
> -----Original Message-----
> From: seba [mailto:sebastiano.trevisani@...]
> Sent: 02 September 2005 10:07
> To: ai-geostats@...
> Cc: ai-geostats@...; 'Nicolas Gilardi'
> Subject: RE: [ai-geostats] natural neighbor applied to
> indicator transforms
>
>
>
> I try to reformulate my question.....
> When performing direct (i.e. without crossvariogram)
> indicator kriging, practically we interpolate probability values by means
> of ordinary kriging. These probability values could represent the
> probability of occurrence of some category or the probability to overcome
> some threshold.
> My question is: is there anything wrong to interpolate
> these probability values with other interpolating algorithm like, for
> example natural neighbor (or triangulation)?
> In my opinion is all ok ..... considering also that we
> have no problem of order relation violations.
> Again, this technique is applied only for a preliminary
> data analysis
>
> Then a short consideration directed about the importance
> of boundaries:
> Quoting Nicolas Gilardi
> "My personnal feeling about the distinction between using
> a classification algorithm or a regression one is the importance you put
> on the boundaries.If you look for smooth boundaries, with uncertainty
> estimations, etc., then a regression algorithm (like indicator kriging)
> is certainly a good approach."
>
> Well, if you use fuzzy classification the boundaries
> become continuos...fuzzy.
>
> Bye
>
> S. Trevisani
>
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