# On the Interpolation Algorithm Ranking - PowerPoint PPT Presentation

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10th International Symposium on Spatial Accuracy Assessment in Natural Resources and Environmental Sciences from 10th to 13th July 2012, Florianópolis, SC, Brazil. On the Interpolation Algorithm Ranking. Carlos López-Vázquez LatinGEO – Lab SGM+Universidad ORT del Uruguay.

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On the Interpolation Algorithm Ranking

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10th International Symposium on Spatial Accuracy Assessment in Natural Resources and Environmental Sciences from 10th to 13th July 2012, Florianópolis, SC, Brazil.

## On the Interpolation Algorithm Ranking

Carlos López-Vázquez

LatinGEO – Lab

### What is algorithm ranking?

• There exist many interpolation algorithms

• Which is the best?

• Is there a general answer?

• Is there an answer for my particular dataset?

• How to define the better-than relation between two given methods?

• How confident should I be regarding such answer?

### What has been done?

• {A}

• {B}

• Many papers so far

• Permanent interest

• How is a typical paper?

• Takes a dataset as an example

• N points sampled somewhere

• Subdivide N in two sets: Training Set {A} and Test Set {B}

• A∩B=Ø; N=#{A}+#{B}

• Repeat for all available algorithms:

• Define interpolant using {A};

blindly interpolate at locations of {B}

• Compare known values at {B}with those interpolated ones

• Better-Than is equivalent to lower-RMSE

### Is RMSE/MAD/etc. suitable as a metric?

• Different interpolation algorithms lead to different look

• RMSE might not be representative. Why?

• Let’s consider spectral properties

Images from www.spatialanalysisonline.com

### Some spectral metric of agreement

• For example, ESAM metric

• U=fft2d(measured error field), U(i,j)≥0

• V=fft2d(interpolated error field), V(i,j)≥0

• ideally, U=V

• 0≤ESAM(U,V)≤1

• ESAM(W,W)=1

Hint!: There might be better options than ESAM

### How confident should I be regarding such answer?

• Given {A} and {B}a deterministic answer

• How to attach a confidence level? Or just some uncertainty?

• Perform Cross Validation (Falivene et al., 2010)

• Set #{B}=1, and leave the rest with {A}

• N possible choices (events) to select B

• Evaluate RMSE for each method and event

• Average for each method over N cases

• Better-than is now Average-run-better-than

• Simulate

• Sample {A} from N, #{A}=m, m<N

• Evaluate RMSE for each method and event, and create rank(i)

• Select confidence level, and apply Friedman’s Test to all rank(i)

n wines judges each rank k different wines

### The experiment

• DEM of Montagne Sainte Victoire (France)

• Sample {B}, 20 points, held fixed

Apply six algorithms

Evaluate ranking(i)

• Evaluate ranking of means over i

• Apply Friedman’s Test and compare

• Do 250 times:

Sample {A} points

### Results

• Ranking using mean of simulated values might be different from Friedman’s test

• Ranking using spectral properties might disagree with that of RMSE/MAD

• Friedman’s Test has a sound statistical basis

• Spectral properties of the interpolated field might be important for some applications

Thank you!

Questions?

### Results

• Other results, valid for this particular dataset

• Ranking using ESAM varies with #{A}

• According to ESAM criteria, Inverse Distance Weighting (IDW) quality degrades as #{A} increases

• According to RMSE criteria, IDW is the best

• With a significative difference w.r.t. the second

• With 95% confidence level

• Irrespective of #{A}

• According to ESAM criteria, IDW is NOT the best