Inconsistency between nk.entropy_multiscale and nk_entropy_sample within a loop of coarse-graining procedures

[neurothew]

Hi, thanks a lot for developing the package, I am just exploring the packages and see how it can be used to analyze some EEG signals.

I tried to compare the nk.entropy_multiscale and nk_entropy_sample within a loop of coarse-graining procedures to confirm my understanding of the computation. My codes look like the following:

# Loop over the scale parameter and compute sample entropy
list_sampen_cg = []
list_sampen_cg_info = []
max_scale = 40

for this_scale in range(1, max_scale+1):
    signal_cg = nk.complexity_coarsegraining(signal, scale=this_scale)

    sampen_cg, sampen_cg_info = nk.entropy_sample(signal_cg, delay=1, dimension=3)

    list_sampen_cg.append(sampen_cg)
    list_sampen_cg_info.append(sampen_cg_info)

# Directly compute multiscale entropy
this_mse, this_mse_info = nk.entropy_multiscale(signal, scale=np.arange(1, max_scale+1, 1), show=False, method="MSEn")

# Plot
plt.plot(list_sampen_cg, label='Custom MSE')
plt.plot(this_mse, label='NK MSE')
plt.legend()

As you can see, it shows striking difference after certain scale. For more information, the signal is a 245-second long recording with sampling rate of 512 Hz.

At first I thought it was because of the mismatch between the default dimension parameter between the two functions, but it remained like this even after I set both dimension to be 3. Please let me know if I am misunderstanding sth, any help is appreciated.

[welcome]

Hi 👋 Thanks for reaching out and opening your first issue here! We'll try to come back to you as soon as possible. ❤️

[DominiqueMakowski]

I'm not sure from the top of my head what's the difference, you can inspect the code here: https://github.com/neuropsychology/NeuroKit/blob/master/neurokit2/complexity/entropy_multiscale.py

I'd be happy to hear if you find the difference!

[neurothew]

I'm not sure from the top of my head what's the difference, you can inspect the code here: https://github.com/neuropsychology/NeuroKit/blob/master/neurokit2/complexity/entropy_multiscale.py

I'd be happy to hear if you find the difference!

@DominiqueMakowski Sorry for responding late, just getting back to this issue today after working on some other stuffs in the past month.

I figured out why, and it's because the nk.entropy_multiscale would use a global tolerance, which is computed only once before any coarse-graining procedures. And if we do the coarse-graining and entropy computation via nk.complexity_coarsegraining and nk.entropy_sample separately, the tolerance would change every time.

When I substitute the tolerance with the global tolerance within every coarse-graining loop, the results are then equal.

It's one of the issues raised in Kosciessa et al., (2020), whereas the authors argued that using the global tolerance would introduce a bias. According to them, over 90% of existing studies were using a global tolerance and they investigated comprehensively on that.

From my previous plot, the differences are pretty obvious and significant though.

Kosciessa, J. Q., Kloosterman, N. A., & Garrett, D. D. (2020). Standard multiscale entropy reflects neural dynamics at mismatched temporal scales: What’s signal irregularity got to do with it? PLOS Computational Biology, 16(5), e1007885. https://doi.org/10.1371/journal.pcbi.1007885