[Scilab-users] spatial correlation coefficient: Is the MATLAB corrcoef function doing the job?

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Heinz Nabielek-3 Heinz Nabielek-3
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[Scilab-users] spatial correlation coefficient: Is the MATLAB corrcoef function doing the job?

Friends:

I need to compute the spatial correlation coefficient of my x,y,z data in
3d.

Question 1: Is the MATLAB corrcoef function doing the job?
Question 2: How do I get corrcoef running in SciLab or C?

Heinz

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Rafael Guerra Rafael Guerra
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Re: spatial correlation coefficient: Is the MATLAB corrcoef function doing the job?

Hi Heinz,

 

Scilab computes the covariance matrix and from which the correlation matrix can be obtained using formula in https://en.wikipedia.org/wiki/Covariance_matrix

 

Check implementation below:

 

//START OF CODE

// https://en.wikipedia.org/wiki/Covariance_matrix

function Y=corrmatrix(M)

    C = cov(M);  // covariance matrix

    D = sqrt(diag(C)); // standard deviations

    D = inv(diag(D));

    Y = D*C*D;  // correlation matrix

endfunction

 

M = grand(9,3,"def")

M(:,2) = M(:,1)*2;

Y = corrmatrix(M);

disp(M,"M")

disp(Y,"Y")

// END OF CODE

 

Regards,

Rafael


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Samuel GOUGEON Samuel GOUGEON
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Re: spatial correlation coefficient: Is the MATLAB corrcoef function doing the job?

In reply to this post by Heinz Nabielek-3
Hello Heinz,

Le 07/02/2018 à 23:13, Heinz a écrit :
> Friends:
>
> I need to compute the spatial correlation coefficient of my x,y,z data in 3d.
>
> Question 1: Is the MATLAB corrcoef function doing the job?
> Question 2: How do I get corrcoef running in SciLab or C?

Do you mean the autocorrelation of a data(x,y,z) sampled distribution?
Or the intercorrelation of data(x,y,z) with a mask(x,y,z) function
sampled on the same grid?
Or anything else?

Samuel

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mottelet mottelet
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Re: spatial correlation coefficient: Is the MATLAB corrcoef function doing the job?

Yes, a precise math formula would disambiguate the denomination.

S.

> Le 8 févr. 2018 à 19:18, Samuel Gougeon <[hidden email]> a écrit :
>
> Hello Heinz,
>
>> Le 07/02/2018 à 23:13, Heinz a écrit :
>> Friends:
>>
>> I need to compute the spatial correlation coefficient of my x,y,z data in 3d.
>>
>> Question 1: Is the MATLAB corrcoef function doing the job?
>> Question 2: How do I get corrcoef running in SciLab or C?
>
> Do you mean the autocorrelation of a data(x,y,z) sampled distribution?
> Or the intercorrelation of data(x,y,z) with a mask(x,y,z) function sampled on the same grid?
> Or anything else?
>
> Samuel
>
> _______________________________________________
> users mailing list
> [hidden email]
> http://lists.scilab.org/mailman/listinfo/users

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Re: spatial correlation coefficient: Is the MATLAB corrcoef function doing the job?

In reply to this post by Rafael Guerra

Thanks. While not giving me ONE number, the analysis shows that my random generated xyz positions are uncorrelated as they should. Can one estimate the error bars for the xy xz and yz correlations?

 

Now, I can use this approach for actual measurements in real objects

Heinz

 

//START

function Y=corrmatrix(M)

    C = cov(M);  // covariance matrix

    D = sqrt(diag(C)); // standard deviations

    D = inv(diag(D));

    Y = D*C*D;  // correlation matrix

endfunction

n=10000;

r=23;

radius = r*grand(n,1,'def').^(1/3);

phi = 2*%pi*grand(n,1, 'def');

costheta = 1 - 2*grand(n,1, 'def');

radsintheta = radius.*sin(acos(costheta));

X = [radsintheta.*cos(phi),radsintheta.*sin(phi), radius.*costheta];

Y = corrmatrix(X)

   1.          0.0058073   0.0078778

   0.0058073   1.          0.0014375

   0.0078778   0.0014375   1.      

//END

 

From: users [mailto:[hidden email]] On Behalf Of Rafael Guerra
Sent: 08 February 2018 18:55
To: Users mailing list for Scilab <[hidden email]>
Subject: Re: [Scilab-users] spatial correlation coefficient: Is the MATLAB corrcoef function doing the job?

 

Hi Heinz,

 

Scilab computes the covariance matrix and from which the correlation matrix can be obtained using formula in https://en.wikipedia.org/wiki/Covariance_matrix

 

Check implementation below:

 

//START OF CODE

// https://en.wikipedia.org/wiki/Covariance_matrix

function Y=corrmatrix(M)

    C = cov(M);  // covariance matrix

    D = sqrt(diag(C)); // standard deviations

    D = inv(diag(D));

    Y = D*C*D;  // correlation matrix

endfunction

 

M = grand(9,3,"def")

M(:,2) = M(:,1)*2;

Y = corrmatrix(M);

disp(M,"M")

disp(Y,"Y")

// END OF CODE

 

Regards,

Rafael


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Re: spatial correlation coefficient: Is the MATLAB corrcoef function doing the job?

In reply to this post by Samuel GOUGEON
Sorry, I am lost.

I have 10,000 xyz data and want to know, if there is some regularity in them
or if they are more or less random. The concept of a mask does not come up
at all...
Best greetings
Heinz

What do you suggest should be used here?

-----Original Message-----
From: users [mailto:[hidden email]] On Behalf Of Samuel
Gougeon
Sent: 08 February 2018 19:19
To: Users mailing list for Scilab <[hidden email]>
Subject: Re: [Scilab-users] spatial correlation coefficient: Is the MATLAB
corrcoef function doing the job?

Hello Heinz,

Le 07/02/2018 à 23:13, Heinz a écrit :
> Friends:
>
> I need to compute the spatial correlation coefficient of my x,y,z data in
3d.
>
> Question 1: Is the MATLAB corrcoef function doing the job?
> Question 2: How do I get corrcoef running in SciLab or C?

Do you mean the autocorrelation of a data(x,y,z) sampled distribution?
Or the intercorrelation of data(x,y,z) with a mask(x,y,z) function sampled
on the same grid?
Or anything else?

Samuel


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Heinz Nabielek-3 Heinz Nabielek-3
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Re: spatial correlation coefficient: Is the MATLAB corrcoef function doing the job?

In reply to this post by Rafael Guerra

From: users [mailto:[hidden email]] On Behalf Of Rafael Guerra
Sent: 08 February 2018 18:55
To: Users mailing list for Scilab <[hidden email]>
Subject: Re: [Scilab-users] spatial correlation coefficient: Is the MATLAB corrcoef function doing the job?

 

Hi Heinz,

 

Scilab computes the covariance matrix and from which the correlation matrix can be obtained using formula in https://en.wikipedia.org/wiki/Covariance_matrix

 

Check implementation below:

 

//START OF CODE

// https://en.wikipedia.org/wiki/Covariance_matrix

function Y=corrmatrix(M)

    C = cov(M);  // covariance matrix

    D = sqrt(diag(C)); // standard deviations

    D = inv(diag(D));

    Y = D*C*D;  // correlation matrix

endfunction

 

M = grand(9,3,"def")

M(:,2) = M(:,1)*2;

Y = corrmatrix(M);

disp(M,"M")

disp(Y,"Y")

// END OF CODE

 

For random generated xyz positions, I get the matrix below and this looks fine with me:

1.000

-0.009

-0.003

-0.009

1.000

-0.001

-0.003

-0.001

1.000

 

 

 

               

 

But this here is a manufactured object and every singly xyz-value is obtained from X-ray tomography

https://www.dropbox.com/s/87osn38agn8jfzo/Measured%2016867%20data%20points%20in%203d.png?dl=0

 

and looks much more regular than the Monte-Carlo. However, the correlation analysis suggested here, gives much the same numbers.

1.000

-0.009

0.008

-0.009

1.000

-0.001

0.008

-0.001

1.000

 

Perhaps, I have asked the wrong question:

 

 

àwhat I need is one single figures that summarizes the spatial correlation.

 

Heinz


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Samuel GOUGEON Samuel GOUGEON
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Re: spatial correlation coefficient: Is the MATLAB corrcoef function doing the job?

In reply to this post by Heinz Nabielek-3
Le 08/02/2018 à 20:16, Heinz a écrit :
Sorry, I am lost.

I have 10,000 xyz data and want to know, if there is some regularity in them
or if they are more or less random. 

So you need and are speaking about the 3D autocorrelation of data(x,y,z).
Usually we compute it through a 3D convolution, that is easy to compute
through the FFT, noting that for an autocorrelation we just flip one of both
data array along x,y, and z before computing its FFT and going on with the algorithm.

Finally we use the inverse FFT to come back to the direct x,y,z space.
You may find good references on the web about the keyword 3D autocorrelation.

In scilab, you will mainly need
fft(A,sign,dims,incr [,option] )
since xcorr(), conv() conv2() convol2d() .. work only in 1D or 2D
(with too often duplicates to do the same thing, without "simple" extension to do more...)

Best regards
Samuel


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mottelet mottelet
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Re: spatial correlation coefficient: Is the MATLAB corrcoef function doing the job?

In reply to this post by Heinz Nabielek-3
Hello,

There seems to be some statistical tests related to this, namely Moran’s
or Mantel tests :

https://stats.idre.ucla.edu/other/mult-pkg/faq/general/faq-how-can-i-detectaddress-spatial-autocorrelation-in-my-data/

http://www.petrkeil.com/?p=1050

hth

S.


Le 08/02/2018 à 20:16, Heinz a écrit :

> Sorry, I am lost.
>
> I have 10,000 xyz data and want to know, if there is some regularity in them
> or if they are more or less random. The concept of a mask does not come up
> at all...
> Best greetings
> Heinz
>
> What do you suggest should be used here?
>
> -----Original Message-----
> From: users [mailto:[hidden email]] On Behalf Of Samuel
> Gougeon
> Sent: 08 February 2018 19:19
> To: Users mailing list for Scilab <[hidden email]>
> Subject: Re: [Scilab-users] spatial correlation coefficient: Is the MATLAB
> corrcoef function doing the job?
>
> Hello Heinz,
>
> Le 07/02/2018 à 23:13, Heinz a écrit :
>> Friends:
>>
>> I need to compute the spatial correlation coefficient of my x,y,z data in
> 3d.
>> Question 1: Is the MATLAB corrcoef function doing the job?
>> Question 2: How do I get corrcoef running in SciLab or C?
> Do you mean the autocorrelation of a data(x,y,z) sampled distribution?
> Or the intercorrelation of data(x,y,z) with a mask(x,y,z) function sampled
> on the same grid?
> Or anything else?
>
> Samuel
>
>
> _______________________________________________
> users mailing list
> [hidden email]
> http://lists.scilab.org/mailman/listinfo/users

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Rafael Guerra Rafael Guerra
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Re: spatial correlation coefficient: Is the MATLAB corrcoef function doing the job?

In reply to this post by Heinz Nabielek-3

Q: "I have 10,000 xyz data and want to know, if there is some regularity in them or if they are more or less random"
A:  look for tests of spatial randomness (https://en.wikipedia.org/wiki/Complete_spatial_randomness ) . If The experimental nearest neighbor distribution obtained previously can be compared to the expected Poisson distribution.



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Re: spatial correlation coefficient: Is the MATLAB corrcoef function doing the job?

1 The nearest neighbour distribution of N points in a 3d-Volume with
radius R is given by
W(r) = 1 - exp[ - N (r/r)^3] and this is a Weibull distribution and not a
Poisson distribution. The WIKI article, while correct, is a typical case
where high level statisticians are trying to make simple things look very
complicated.

2 Comparing the experimental distribution with the above prediction is
made complicated as the manufactured object has small hard spheres that push
each other apart in the manufacturing process and the Weibull is modified
anyway.

3 I am sill searching for a 3d spatial characterization coefficient
that differentiates between purely random arrangements and gradual regular
arrangements.

Heinz

-----Original Message-----
From: users [mailto:[hidden email]] On Behalf Of Rafael
Guerra
Sent: 09 February 2018 10:17
To: Users mailing list for Scilab <[hidden email]>
Subject: Re: [Scilab-users] spatial correlation coefficient: Is the MATLAB
corrcoef function doing the job?


Q: "I have 10,000 xyz data and want to know, if there is some regularity in
them or if they are more or less random"
A:  look for tests of spatial randomness
(https://en.wikipedia.org/wiki/Complete_spatial_randomness ) . If The
experimental nearest neighbor distribution obtained previously can be
compared to the expected Poisson distribution.


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Rafael Guerra Rafael Guerra
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Re: spatial correlation coefficient: Is the MATLAB corrcoef function doing the job?

You may want to study this article:
https://pdfs.semanticscholar.org/574f/8f7347a258f6431fb8316716ca51b9b7eacb.pdf

it should give you a clue or two of what you may want to implement.


-----Original Message-----
From: users [mailto:[hidden email]] On Behalf Of Heinz
Sent: Friday, February 09, 2018 7:44 PM
To: 'Users mailing list for Scilab' <[hidden email]>
Subject: Re: [Scilab-users] spatial correlation coefficient: Is the MATLAB corrcoef function doing the job?

1 The nearest neighbour distribution of N points in a 3d-Volume with
radius R is given by
W(r) = 1 - exp[ - N (r/r)^3] and this is a Weibull distribution and not a Poisson distribution. The WIKI article, while correct, is a typical case where high level statisticians are trying to make simple things look very complicated.

2 Comparing the experimental distribution with the above prediction is
made complicated as the manufactured object has small hard spheres that push each other apart in the manufacturing process and the Weibull is modified anyway.

3 I am sill searching for a 3d spatial characterization coefficient
that differentiates between purely random arrangements and gradual regular arrangements.

Heinz

-----Original Message-----
From: users [mailto:[hidden email]] On Behalf Of Rafael Guerra
Sent: 09 February 2018 10:17
To: Users mailing list for Scilab <[hidden email]>
Subject: Re: [Scilab-users] spatial correlation coefficient: Is the MATLAB corrcoef function doing the job?


Q: "I have 10,000 xyz data and want to know, if there is some regularity in them or if they are more or less random"
A:  look for tests of spatial randomness (https://en.wikipedia.org/wiki/Complete_spatial_randomness ) . If The experimental nearest neighbor distribution obtained previously can be compared to the expected Poisson distribution.


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Re: spatial correlation coefficient: Is the MATLAB corrcoef function doing the job?

In reply to this post by mottelet
Thanks for the many pointers. At this stage, although R is installed on my
computer, I would hesitate learning R just to run the Nathan Mantel test.
Can someone give me a helping hand in defining a spatial coordination index?
Using - in the first place - the random xyz coordinates below that we had
been using before for the nearest neighbour distribution which had worked
out very well in accordance theoretical predictions.

Apllication of covariance/correlance analysis turned out to be useless,
because this investigates a search into linear dependencies of the x, y, z
vectors and this is not of interest.

Now, with the numbers generated below, the spatial coordination index
looking for clusters and holes in 3d space should come out near zero.
Somebody trying to run the numbers?

For an xy projection, see <
https://www.dropbox.com/s/0sv1ak9zwk5f8rv/16%2C867%20points%20in%203d%20spac
e.pptx?dl=0>.

Heinz

// START OF CODE FOR RANDOM x, y, z NUMBER GENERATION
n=16867;
r=25046;
radius = r*grand(n,1,'def').^(1/3);
phi = 2*%pi*grand(n,1, 'def');
costheta = 1 - 2*grand(n,1, 'def');
radsintheta = radius.*sin(acos(costheta));
x=radsintheta.*cos(phi);
y=radsintheta.*sin(phi);
z=radius.*costheta;
// END OF CODE

-----Original Message-----
From: users [mailto:[hidden email]] On Behalf Of Stéphane
Mottelet
Sent: 09 February 2018 09:47
To: Users mailing list for Scilab <[hidden email]>
Subject: Re: [Scilab-users] spatial correlation coefficient: Is the MATLAB
corrcoef function doing the job?

Hello,

There seems to be some statistical tests related to this, namely Moran’s or
Mantel tests :

https://stats.idre.ucla.edu/other/mult-pkg/faq/general/faq-how-can-i-detecta
ddress-spatial-autocorrelation-in-my-data/

http://www.petrkeil.com/?p=1050

hth

S.


Le 08/02/2018 à 20:16, Heinz a écrit :

> Sorry, I am lost.
>
> I have 10,000 xyz data and want to know, if there is some regularity
> in them or if they are more or less random. The concept of a mask does
> not come up at all...
> Best greetings
> Heinz
>
> What do you suggest should be used here?
>
> -----Original Message-----
> From: users [mailto:[hidden email]] On Behalf Of
> Samuel Gougeon
> Sent: 08 February 2018 19:19
> To: Users mailing list for Scilab <[hidden email]>
> Subject: Re: [Scilab-users] spatial correlation coefficient: Is the
> MATLAB corrcoef function doing the job?
>
> Hello Heinz,
>
> Le 07/02/2018 à 23:13, Heinz a écrit :
>> Friends:
>>
>> I need to compute the spatial correlation coefficient of my x,y,z
>> data in
> 3d.
>> Question 1: Is the MATLAB corrcoef function doing the job?
>> Question 2: How do I get corrcoef running in SciLab or C?
> Do you mean the autocorrelation of a data(x,y,z) sampled distribution?
> Or the intercorrelation of data(x,y,z) with a mask(x,y,z) function
> sampled on the same grid?
> Or anything else?
>
> Samuel
>
>
> _______________________________________________
> users mailing list
> [hidden email]
> http://lists.scilab.org/mailman/listinfo/users

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