Sliding Window Channel Capacity (swcc - matlab)

MATLAB reference implementation of the Sliding-Window Channel Capacity (and Prediction Correlation) framework for estimating the time-varying strength (prediction-correlation) and duration (how long directed influence persists across windows) of directed interactions between ROI time series (e.g., fMRI BOLD).

1. data input: data.mat
2. main script to run swcc: main_script2run_swcc.m
3. functions that execute swcc: ./swccv0226/sliding_pcorr_cc_window.m & ./swccv0226/pcorr_cc_x2y.m

Contents

• main_script2run_swcc.m — demo driver script (load data → run SWCC and Pcorr → save outputs)
• data.mat — demo input data
• swccv0226/
  • sliding_pcorr_cc_window.m — sliding-window wrapper
  • pcorr_cc_x2y.m — core estimator (fit + order selection + correlation)

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Requirements

• MATLAB
• Statistics and Machine Learning Toolbox (aicbic)
• Optimization Toolbox only if using positivity constraint (lsqlin via Constraint='p')

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Quick start

In MATLAB (repo root):

run('main_script2run_swcc.m')

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Using your own data

SWpC is called on two vectors per direction:

• tc1 (source): (T x 1)
• tc2 (target): (T x 1)

To use more ROIs, construct input as (nroi x T) and loop over ROI pairs (as in the demo script).

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Key parameters (in main_script2run_swpc.m)

• TR (sec)
  Sampling interval.

• windowsize_duration (sec)
  Window duration in seconds. Window length in samples is computed from TR and forced even:

  • windowsize = floor(windowsize_duration/TR/2)*2

• overlap (samples)
  Window overlap. The demo uses near full overlap:

  • overlap = windowsize - 1

• maxDur (sec) and maxLag (samples)
  Maximum lag/order search range:

  • maxLag = floor(maxDur/TR)

• Constraint
  Regression mode used to estimate the impulse response:

  • 'p' : positivity-constrained least squares (uses lsqlin)
  • 'all': unconstrained least squares (uses lsqr)

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Method overview

Within each sliding window, SWCC estimates directed influence tc1 → tc2 by:

1. Constructing a lag-embedded predictor matrix from the source window (tc1) up to candidate model orders (Nh = 1..maxLag).
2. Fitting a finite impulse response (FIR) filter h (lag weights) to predict the target window (tc2) from the lagged source.
3. Selecting the model order Nh per window using information criteria (BIC and AIC/AICc).
4. Quantifying directed interaction strength in that window as the prediction correlation between the observed target (tc2) and the model-predicted target (tc2_hat).

Running this window-by-window yields a time series of directed strength for each ROI pair and direction.

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Strength vs. duration

How to interpret SWCC outputs:

• Strength: the SWCC value per window (e.g., cc_bic or cc_aic) is the instantaneous directed interaction strength at that window.
• Duration: duration is not returned as a single primitive value; it is derived from the temporal persistence of directed strength across windows. For example, you can compute duration as:
  • the total number of windows where cc_* exceeds a threshold, and/or
  • the length of contiguous above-threshold segments (then convert windows → seconds using TR and the window step).

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AIC vs AICc

This implementation computes both AIC and AICc (small-sample corrected AIC).

The returned AIC-based choice (Nh_aic, cc_aic) should be interpreted as:

• AICc-selected in short-window regimes (when the sample size per window is not large relative to the number of fitted parameters),
• otherwise AIC-selected.

AICc is recommended for short windows because it penalizes model complexity more strongly and tends to yield more stable (less overfit) order selection.

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Outputs

What sliding_pcorr_cc_window returns (per direction)

Calling:

[cc_bic, corr_bic, Nh_bic, cc_aic, corr_aic, Nh_aic, corr_std, corr0, H, nmaps] = ...
    sliding_pcorr_cc_window(tc1, tc2, windowsize, overlap, maxLag, Constraint);

Returns (typically) 1 × nWindows vectors (unless otherwise noted):

• cc_bic — channel capacity using BIC-selected order (per window)
• corr_bic — prediction correlation using BIC-selected order (per window)
• Nh_bic — BIC-selected order Nh (per window)
• cc_aic — channel capacity using AIC/AICc-selected order (per window)
• corr_aic — prediction correlation using AIC/AICc-selected order (per window)
• Nh_aic — AIC/AICc-selected order Nh (per window)
• corr_std — baseline correlation (see pcorr_cc_x2y.m for exact definition used)
• corr0 — prediction correlation using order Nh = 1
• H — estimated impulse responses per window (stacked across windows)
• nmaps — number of windows

What main_script2run_swcc.m saves (per subject)

The demo script saves one file per subject:

• ./output/subj<k>.mat

Key saved arrays are shaped:

• (nroi x nroi x nWindows) with index order: [sourceROI, targetROI, window]

Saved variables include:

• slcc_BIC, slpcorr_BIC, slNh_BIC
• slcc_AIC, slpcorr_AIC, slNh_AIC (AIC/AICc per the rule above)
• slpcorr_STD
• slpcorr1 (stores corr0)

Both directions are computed and stored (i→j and j→i).