[MARKER]: Support FunctionalConnectivityLagged

[synchon]

Which marker do you want to include?

1. Compute Cross-Correlation:

For two time series X(t) and Y(t) from different brain regions:
CCF(τ)=∑tX(t)Y(t+τ)
CCF(τ)=t∑​X(t)Y(t+τ)

where τ represents a time lag (positive or negative shifts).

Compute cross-correlation for each ROI pair across a range of time lags τ (e.g., -10s to +10s).
The peak of the cross-correlation function indicates the optimal time lag (e.g., if peak at τ = 2s, Y lags behind X by 2s).

2. Construct a Lag-Based Functional Connectivity Matrix:

Identify the lag at which cross-correlation is maximal.
Store the peak correlation value and associated lag for each ROI pair.
Construct:

• A functional connectivity matrix (correlation values).
• A lag matrix (time lags at which correlation is maximal).

Is there any publication or available code?

https://pmc.ncbi.nlm.nih.gov/articles/PMC4097876

Do you have a sample code that implements this outside of junifer?

import numpy as np
import matplotlib.pyplot as plt
from scipy.signal import correlate

# Simulated fMRI data (example: 10 ROIs, 300 time points)
np.random.seed(42)
n_rois = 10
n_timepoints = 300
fmri_data = np.random.rand(n_rois, n_timepoints)  # Replace with real fMRI signals

# Define time lag range (e.g., -10 to +10 time points)
max_lag = 10
lags = np.arange(-max_lag, max_lag + 1)

# Initialize matrices
fc_matrix = np.zeros((n_rois, n_rois))  # Functional connectivity matrix
lag_matrix = np.zeros((n_rois, n_rois))  # Lag matrix

# Compute cross-correlation for each ROI pair
for i in range(n_rois):
    for j in range(n_rois):
        if i != j:
            # Compute cross-correlation
            ccf = correlate(fmri_data[i], fmri_data[j], mode='full', method='auto')
            ccf = ccf[len(ccf)//2 - max_lag : len(ccf)//2 + max_lag + 1]  # Limit lag range
            
            # Find peak correlation & corresponding lag
            peak_idx = np.argmax(np.abs(ccf))  # Peak correlation index
            peak_corr = ccf[peak_idx]  # Peak correlation value
            peak_lag = lags[peak_idx]  # Corresponding lag
            
            # Store in matrices
            fc_matrix[i, j] = peak_corr
            lag_matrix[i, j] = peak_lag

# Plot Functional Connectivity Matrix
plt.figure(figsize=(8,6))
plt.imshow(fc_matrix, cmap='coolwarm', aspect='auto')
plt.colorbar(label="Peak Cross-Correlation")
plt.title("Functional Connectivity Matrix")
plt.xlabel("ROI")
plt.ylabel("ROI")
plt.show()

# Plot Lag Matrix
plt.figure(figsize=(8,6))
plt.imshow(lag_matrix, cmap='jet', aspect='auto')
plt.colorbar(label="Lag (Time Points)")
plt.title("Lag Matrix")
plt.xlabel("ROI")
plt.ylabel("ROI")
plt.show()

Anything else to say?

No response

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