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Generate a network for the entropy values

Alex Teymouri
Posted 6 years ago

Dear all,

I calculated the entropy values for the time series of 44 cities. Is it possible to define a simple or complex network for these values? I attached a related reference for getting more information.

shannonEntropy[data_, binWidth_] := 
 Module[{iter, n = Length[data], pi, pi1},
  iter = {Min[data], Max[data] + binWidth, binWidth};
  pi = N[BinCounts[data, iter]/n];
  pi1 = DeleteCases[pi, 0.];
  -pi1.Log[pi1]]

entr = {1.21`, 0.55`, 0.84`, 1.06`, 1.33`, 0.82`, 1.51`, 0.27`, 1.21`,
    1.14`, 0.92`, 1.23`, 1.37`, 0.82`, 0.69`, 1.46`, 0.1`, 0.09`, 
   1.63`, 1.58`, 0.89`, 0.21`, 0.93`, 1.33`, 1.31`, 1.09`, 0.46`, 
   0.54`, 0.94`, 0.04`, 0.88`, 0.87`, 1.24`, 1.62`, 0.96`, 1.35`, 
   1.43`, 0.9`, 0.72`, 1.07`, 1.02`, 1.16`, 1.38`, 0.07`};

lat = {36.37`, 35.44`, 35.44`, 36.69`, 37.`, 35.75`, 36.69`, 34.81`, 
   36.06`, 36.69`, 35.13`, 36.37`, 36.37`, 34.81`, 33.56`, 37.`, 
   33.25`, 32.63`, 36.37`, 36.69`, 35.44`, 33.88`, 35.44`, 36.37`, 
   36.37`, 36.06`, 35.75`, 33.25`, 35.75`, 32.`, 35.73`, 35.75`, 
   34.81`, 36.06`, 35.13`, 37.`, 36.37`, 35.44`, 35.13`, 35.44`, 
   36.69`, 35.44`, 36.69`, 33.25`};

lon = {1.875`, 2.5`, -0.9375`, 3.125`, 7.8125`, 6.25`, 5.`, 5.625`, 
   4.6875`, 3.4375`, 4.0625`, 0.9375`, 6.5625`, 3.125`, 0.9375`, 
   8.125`, 6.875`, 3.75`, 7.5`, 5.625`, 7.1875`, 2.8125`, 0.3125`, 
   2.8125`, 6.25`, 0.`, 4.6875`, -0.3125`, -0.3125`, 5.625`, 7.3693`, 
   0.625`, 0.3125`, 5.3125`, -0.625`, 6.875`, 7.8125`, 
   7.8125`, -1.875`, 1.25`, 2.5`, 1.5625`, 3.75`, 5.9375`};
Attachments:
ordinet.pdf
POSTED BY: Alex Teymouri
13 Replies
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Alex Teymouri
Alex Teymouri
Posted 6 years ago

Thank you so much, Henrik. Good job!

I tried to run the code again and got a different kind of graphs (I use Mathematica 11.3).

Where am I wrong?

Attachments:
Untitled-2.nb
POSTED BY: Alex Teymouri

Hi Alex,

Yes, strange, on Mathematica 11.3 I get the same results/graphs as in your notebook. For the above Mathematica 12.0 was used - maybe some algorithm for calculating graph communities has changed (i.e. improved).
POSTED BY: Henrik Schachner

Hello Alex,

Maybe I do not jet fully understand this seemingly interesting concept. Is it this you are having in mind? (I have no idea on how to use your position data ...)

v4 = Partition[entr, 4, 1];
order4 = FromDigits@*Ordering /@ v4;
rels = UndirectedEdge @@@ Partition[order4, 2, 1];
Graph[rels, VertexLabels -> Automatic]

EDIT:

I guess the partition of the data should be done differently and my code should rather read like so: 

v4 = Partition[entr, 4];
order4 = FromDigits@*Ordering /@ v4;
rels = UndirectedEdge @@@ Partition[order4, 2, 1];
Graph[rels, VertexLabels -> Automatic]

enter image description here
POSTED BY: Henrik Schachner

Henrik you did an incredible job. Congratulations!

Is there any concept behind the this network.? What does this network give us from the mathematical or application view?

POSTED BY: M.A. Ghorbani

Thank you Mohammad - but there is definitely no reason for any congratulations! I simply tried to follow the idea/concept in the above attached publication.
POSTED BY: Henrik Schachner

Dear Henrik,

I plotted for different orders and got interesting results. Thank you.

Attachments:
Henrik Entropy.nb
POSTED BY: M.A. Ghorbani
Alex Teymouri
Alex Teymouri
Posted 6 years ago
Attachments:
bracis14.pdf
POSTED BY: Alex Teymouri

Hi Alex, thank you for this publication! I will try to find time looking into it. Regards -- Henrik
POSTED BY: Henrik Schachner
Alex Teymouri
Alex Teymouri
Posted 6 years ago

Hi Henrik,

Did you have time to take a look at the paper that I sent you a few days ago? I got Oberpfaffenhofen Airport air temperature time series, may be it be useful for the method.

Oberpfaffenhofen Airport
ICAO code | EDMO

tt0 = WeatherData["EDMO", "MeanTemperature", {{2000}, {2018}, "Day"}];

temp0 = Last[tt0\[Transpose]];

Normal[temp0];

DateListPlot[temp0]
Attachments:
bracis14.pdf
POSTED BY: Alex Teymouri
POSTED BY: Henrik Schachner

Hi Henrik,

Please take a look at the attached manuscript. Studying periodicity using the complex network is a novel approach in water engineering, so I decided to apply this concept for 44 rain stations in the northern region of Algeria.If you remember, you have extracted a graph for one of the stations about two months ago (Figure 6). I need your help in providing graphs for all stations. We will write the section related to complex network and also the results and other details. May I send you data from all the stations?

It's my pleasure and honor to work with you.

Regards, Mohammad

Attachments:
Algeria_Manuscri...docx
POSTED BY: M.A. Ghorbani

Dear Prof. Ghorbani,

oops - I nearly missed that post, sorry! I will try to contact you via ResearchGate.net

Regards -- Henrik
POSTED BY: Henrik Schachner

Dear Henrik,

I hope your Christmas is filled with joy this year!

I applied your program for the hourly river water temperature time series of the Skokomish river in the USA. If possible, please have a look at the notebook and let me know the output is correct or not?

Have a nice weekend

Attachments:
Henrik.nb
data.xlsx
POSTED BY: M.A. Ghorbani
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