Markov Cluster algorithm

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Markov Cluster algorithm

An attempt to implement the MCL (Markov Cluster) algorithm in APL.
I'm still a beginner in APL, any advice is welcome.

https://github.com/koteth/MCL_APL
koteth

Posts: 3
Joined: Wed Jan 17, 2018 5:58 pm

Re: Markov Cluster algorithm

Looks really cool. How did you generate the graphics? Would you be interested in automatically generating those from within APL? Posts: 63
Joined: Thu Jun 25, 2015 1:13 pm

Re: Markov Cluster algorithm

Code from https://github.com/koteth/MCL_APL/blob/master/MCL.dyalog:

Code: Select all
matrix ← ⎕csv 'PATH TO MATRIX/matrix.csv'
InflateCoef ← 2

M ← ⍎¨ matrix
id←{⍵ ⍵⍴1,⍵⍴0}
Nor←{+⌿⍵}
Nmat ← {( ( ⍴ ⍵) ⍴ (Nor ⍵)) }
NormColumn ← {( ⍴ ⍵ ) ⍴ ((×/⍴⍵) ⍴⍵)÷((×/⍴⍵)  ⍴ Nmat  ⍵ )}

Expand ← {⍵ +.× ⍵}
Inflate  ←  NormColumn {  (⍴⍺) ⍴ (  (×/⍴⍺) ⍴  ⍺) * ⍵ }

M2 ← NormColumn (M + id (≢ M))
Markov ←  { ( Expand (NormColumn ⍵) ) Inflate InflateCoef }

FP ← (Markov ⍣ ≡ ⊢ M2)

R ← ((+/FP) >0) ⌿ FP
ClustMap ← ⌽↑⍸R

"Improved" version of as follows.
• separate code to create the matrix and to do the Markov iteration
• trivial functions included in-line and left unnamed

Code: Select all
MCL3←{
⍺←2                                 ⍝ inflation coefficient default
id←{(⍵,⍵)⍴1,⍵⍴0}                    ⍝ identity matrix of order ⍵
NormColumn←{⍵÷⍤1+⌿⍵}
Markov←{⍺ *⍨ +.×⍨ NormColumn ⍵}     ⍝ one Markov iteration
FP←⍺ Markov⍣≡NormColumn ⍵+id≢⍵
⌽↑⍸(0<+/FP)⌿FP
}
Roger|Dyalog

Posts: 139
Joined: Thu Jul 28, 2011 10:53 am

Re: Markov Cluster algorithm

Since NormColumn is idempotent and is the first function to be applied in Markov, it is not necessary to apply it before launching the iteration. Whence NormColumn is used just once and can be inserted in-line. Therefore:

MCL4 ← {⍺←2 ⋄ ⌽↑⍸(0<+/FP)⌿FP← ⍺ {⍺ *⍨ +.×⍨ ⍵÷⍤1+⌿⍵}⍣≡ ⍵+∘.=⍨⍳≢⍵}
Roger|Dyalog

Posts: 139
Joined: Thu Jul 28, 2011 10:53 am

Re: Markov Cluster algorithm

Interesting rewriting. Now is more clear to me how to use the ⍨ operator , thanks.

Roger|Dyalog wrote:Since NormColumn is idempotent and is the first function to be applied in Markov, it is not necessary to apply it before launching the iteration. Whence NormColumn is used just once and can be inserted in-line. Therefore:

MCL4 ← {⍺←2 ⋄ ⌽↑⍸(0<+/FP)⌿FP← ⍺ {⍺ *⍨ +.×⍨ ⍵÷⍤1+⌿⍵}⍣≡ ⍵+∘.=⍨⍳≢⍵}
koteth

Posts: 3
Joined: Wed Jan 17, 2018 5:58 pm

Re: Markov Cluster algorithm

Adam|Dyalog wrote:Looks really cool. How did you generate the graphics? Would you be interested in automatically generating those from within APL?

For the image I've used python with networkx. It would be nice to use APL, i've never tried to generate graphics. I'm currently using Dyalog 16 for linux, would you be able to suggest some starting point?
koteth

Posts: 3
Joined: Wed Jan 17, 2018 5:58 pm

Re: Markov Cluster algorithm

koteth wrote:Interesting rewriting. Now is more clear to me how to use the ⍨ operator , thanks.

There are illuminating parallels between dyadic f⍨ and the passive case and monadic f⍨ and the reflexive case for verbs in natural languages.
Roger|Dyalog

Posts: 139
Joined: Thu Jul 28, 2011 10:53 am

Re: Markov Cluster algorithm

koteth wrote:For the image I've used python with networkx. It would be nice to use APL, i've never tried to generate graphics. I'm currently using Dyalog 16 for linux, would you be able to suggest some starting point?

Network graphs are documented in https://sharpplot.com/NetworkMap.htm
If you've never used SharpPlot, see https://sharpplot.com/Languages.htm which should help you translate the C# samples of the rest of the documentation.
Nicolas|Dyalog

Posts: 12
Joined: Wed Sep 10, 2008 9:39 am