New paper:

Studying Complex Adaptive Systems With Internal States: A Recurrence Network Approach to the Analysis of Multivariate Time-Series Data Representing Self-Reports of Human Experience

with @AMTBosman

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https://www.frontiersin.org/articles/10.3389/fams.2020.00009/full

Supp.">https://www.frontiersin.org/articles/... Material: #supplementary-material">https://www.frontiersin.org/articles/10.3389/fams.2020.00009/full #supplementary-material">https://www.frontiersin.org/articles/...

We cover 4 topics:

1. Dealing with time series that represent internal state dynamics: The change profile
2. Weighted Recurrence Networks (wRN)-Scaling of Strength distribution
3. Spiral Graph network layout for recurrence networks
4. Multiplex RN of multivariate timeseries

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1. The Change Profile (CP)

Self-ratings will be relative to some reference level partially based on previous ratings, within some time window. The CP turns the bounded series into an unbounded profile and emphasizes different dynamical regimes, see: #supplementary-material">https://www.frontiersin.org/articles/10.3389/fams.2020.00009/full #supplementary-material

3/8">https://www.frontiersin.org/articles/...

2. Scaling of wRN

Vertices represent time points, edges whether a value recurs at some other point in time. Recurrent values (and network degree) are based on a thresholded distance matrix. We add recurrence times as edge weights and show a scaling of strength~degree

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3. Spiral Graphs

RNs are plotted according to some spring-layout algorithm. We wanted to preserve the temporal order and came up with the Spiral Grap layout.
Different layouts are possible: Archimedean, Fermat, Bernoulli, Euler

See package casnet: https://fredhasselman.com/casnet/ 

5/8">https://fredhasselman.com/casnet/&q...

4. Multiplex wRN

We analyze multivariate time series of self-esteem ratings (6 vars, N=4) by Delignieres et al. (2004) https://didierdelignieresblog.wordpress.com/recherche/databank/
Create">https://didierdelignieresblog.wordpress.com/recherche... 6 wRNs and add them together in a multiplex network! Edge weights represent Inter-layer Mutual Information & Edge-overlap

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Take home messages:

1. Adjust your analyses to your data, not the other way around! Embrace long-range dependence and nonstationarity, do not avoid it by short observ. times
2. No need to aggregate subsets of multivariate series to reduce dimensions, use Multiplex Networks!

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Stay tuned for more (applied) recurrence-based analyses:
- Directed RNs for real-time prediction
- https://fredhasselman.com/casnet/ ">https://fredhasselman.com/casnet/&q... will be updated often!

More on long-range dependence in EMA/ESM data with @OlthofMerlijn, @MaartenWijnants and @AnnaLichtwarck
https://twitter.com/FredHasselman/status/1250088196194603008?s=20

8/8">https://twitter.com/FredHasse...