trend analysis - computation of δ (balanced distance of diagonal)

[schlichtanders]

in

RecurrenceAnalysis.jl/src/rqa/rqa.jl

Line 285 in 48df04b

δ = d - b/2

δ seems to be defined by comparing the current dimension with the "mean dimension", analogous to how the tau_recurrence value of the current dimension is compared to the mean recurrence value in

RecurrenceAnalysis.jl/src/rqa/rqa.jl

Line 286 in 48df04b

numerator += δ*(rr_τ[d] - mean_rr)

However the mean is taken from a:b only

RecurrenceAnalysis.jl/src/rqa/rqa.jl

Line 283 in 48df04b

mean_rr = mean(@view rr_τ[a:b])

so shouldn't it be

δ = d - (a+b)/2

?

[Datseris]

@felixcremer do you have any idea? @schlichtanders sorry, its been so long since I've done any meaningful science with RQA that I don't have the expertise to answer right away, I would need more background information.

[Datseris]

Oh perhaps @pucicu has an idea as well?

[schlichtanders]

I followed the literatur, and this is a standard computation of the slope of a linear regression.

This indeed requires the correct mean

See for instance https://en.wikipedia.org/wiki/Ordinary_least_squares#Simple_linear_regression_model

[heliosdrm]

The current implementation is based on the formula given here: http://www.recurrence-plot.tk/rqa.php

But it's true that that formula considers no Theiler window, (i.e. a=1), so it might be necessary to adapt it. However, even in that case it shouldn't be

δ = d - (a+b)/2

but

δ = d - (b+theiler)/2

(a and theiler differ by 1)

[pucicu]

simply do not use the trend measure. it does not make much sense. there was never a mathematical definition given by the inventors of this measure. at http://www.recurrence-plot.tk/rqa.php tried to formulate one, which seems to fit the original idea quite well.

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Am 09.01.2025 um 11:13 schrieb Stephan Sahm ***@***.***>: in https://github.com/JuliaDynamics/RecurrenceAnalysis.jl/blob/48df04ba38c6a14fc7153cd5dfac1fbb9d3a8eb8/src/rqa/rqa.jl#L285 δ seems to be defined by comparing the current dimension with the "mean dimension", analogous to how the tau_recurrence value of the current dimension is compared to the mean recurrence value in https://github.com/JuliaDynamics/RecurrenceAnalysis.jl/blob/48df04ba38c6a14fc7153cd5dfac1fbb9d3a8eb8/src/rqa/rqa.jl#L286 However the mean is taken from a:b only https://github.com/JuliaDynamics/RecurrenceAnalysis.jl/blob/48df04ba38c6a14fc7153cd5dfac1fbb9d3a8eb8/src/rqa/rqa.jl#L283 so shouldn't it be δ = d - (b-a)/2 ? — Reply to this email directly, view it on GitHub <#167>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/AAHNNEDPYFV7E6AMYY6EMN32JZDVRAVCNFSM6AAAAABU3ZPQZCVHI2DSMVQWIX3LMV43ASLTON2WKOZSG43TOMZZG4ZDAOI>. You are receiving this because you are subscribed to this thread.

[schlichtanders]

Here https://www.nsf.gov/pubs/2005/nsf05057/nmbs/nmbs.pdf (search for TREND) the trend is defined as the slope of a linear regression between diagonal offset and percentage of local recurrence, which I find quite intuitive as a measure.

[pucicu]

indeed, including the theiler window would make some sense. but there is not any study, as far as i know, which has used it in this way.

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Am 09.01.2025 um 15:04 schrieb Helios De Rosario ***@***.***>: The current implementation is based on the formula given here: http://www.recurrence-plot.tk/rqa.php But it's true that that formula considers no Theiler window, (i.e. a=1), so it might be necessary to adapt it. However, even in that case it shouldn't be δ = d - (a+b)/2 but δ = d - (b+theiler)/2 (a and theiler differ by 1) — Reply to this email directly, view it on GitHub <#167 (comment)>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/AAHNNEB6IAHAZU3YCTANFPL2JZ6WJAVCNFSM6AAAAABU3ZPQZCVHI2DSMVQWIX3LMV43OSLTON2WKQ3PNVWWK3TUHMZDKOBQGI4DENZRHA>. You are receiving this because you were mentioned.

[pucicu]

the problem with this measure is that it depends strongly on the size of the RP (or the used windows), on the initial conditions, and it does not have a clear physical meaning. regarding the windowing, see here: https://www.worldscientific.com/doi/abs/10.1142/S0218127411029008 it uses the tau-RR (although not stated in the original paper or the mentioned tutorial). tau-RR has a nice meaning, but used for different purposes. if you are interested in a qualitative measure for homogeneity of RPs, you can consider lacunarity: https://doi.org/10.1007/s11071-021-06457-5 if you need a pdf of the papers, send me an email.

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Am 10.01.2025 um 10:08 schrieb Stephan Sahm ***@***.***>: Here https://www.nsf.gov/pubs/2005/nsf05057/nmbs/nmbs.pdf (search for TREND) the trend is defined as the slope of a linear regression between diagonal offset and percentage of local recurrence, which I find quite intuitive as a measure. — Reply to this email directly, view it on GitHub <#167 (comment)>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/AAHNNECZR2CCX4SXWFTEU7D2J6EZFAVCNFSM6AAAAABU3ZPQZCVHI2DSMVQWIX3LMV43OSLTON2WKQ3PNVWWK3TUHMZDKOBSGEZDENRTGU>. You are receiving this because you were mentioned.

[Datseris]

Right, so what's the status now with this issue? Is there a change that should be done, or should it be closed?

[heliosdrm]

I would fix trend as I suggested above

δ = d - (b+theiler)/2

So that it is balanced with theiler windows, keeping the same result as the formula published in recurrence-plot.tk when theiler==0, as assumed there.
I'm doing the corresponding PR.

[pucicu]

thanks! but please include a clear documentation on this.

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Am 11.01.2025 um 06:18 schrieb Helios De Rosario ***@***.***>: I would fix trend as I suggested above δ = d - (b+theiler)/2 So that it at least gives the same result as the formula published in recurrence-plot.tk when theiler==0, as assumed there. I'm doing the corresponding PR. — Reply to this email directly, view it on GitHub <#167 (comment)>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/AAHNNEBKXTMM4RGRCBVTCL32KCSTPAVCNFSM6AAAAABU3ZPQZCVHI2DSMVQWIX3LMV43OSLTON2WKQ3PNVWWK3TUHMZDKOBVGA3TMNJRGI>. You are receiving this because you were mentioned.