Objective: Sliding and tapered sliding window methods are the most often used approaches in computing dynamic correlations in biomedical signals such as the brain resting-state fMRI  . However,  due to the discrete nature of windows, the window methods suffer spurious high-frequency fluctuations and the zig-zag pattern in dynamic correlations. Methods: To address the problem and obtain more stable correlation estimates, we propose a novel windowless approach for computing dynamic correlations via heat kernel smoothing. The heat kernel, the natural generalization of the Gaussian kernel to manifolds, is used to defined a smoothing kernel without boundary or end points. Results: We show that the proposed windowless approach smooths out the unwanted high-frequency noise in correlation estimations and is more stable in identifying and discriminating state spaces in resting-state fMRI. The proposed method is applied to the study of interhemispheric connectivity and whole-brain network analysis. Conclusion: We present a novel framework using heat kernel to compute the windowless dynamic correlation, which is more stable with less high-frequency fluctuations than windowed methods. Significance: The proposed windowless approach reduced the spurious rapid changes in the state space of brain connectivity, and identified the strongest connections in brain networks and symmetry in interhemispheric connectivity .
Recent studies have shown that functional brain brainwork is dynamic even during rest. A common approach to modeling the brain network in whole brain resting-state fMRI is to compute the correlation between anatomical regions via sliding windows . However, the direct use of the sample correlation matrices is not reliable due to the image acquisition, processing noises and the use of discrete windows that often introduce spurious high-frequency fluctuations and the zig-zag pattern in the estimated time-varying correlation measures. To address the problem and obtain more robust correlation estimates, we propose the heat kernel based dynamic correlations. We demonstrate that the proposed heat kernel method can smooth out the unwanted high-frequency fluctuations in correlation estimations and achieve higher accuracy in identifying dynamically changing distinct states. The method is further used in determining if such dynamic state change is genetically heritable using a large-scale twin study. Various methodological challenges for analyzing paired twin dynamic networks are addressed .
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Objective: Sliding and tapered sliding window methods are the most often used approaches in computing dynamic correlations in biomedical signals such as the brain
Recent studies have shown that functional brain brainwork is dynamic even during rest. A common approach to modeling the brain network in whole brain
A
is to compute the correlation between anatomical regions via sliding windows
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the direct use of the sample correlation matrices is not reliable
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discrete nature of windows, the window methods suffer
image acquisition, processing noises and the use of discrete windows that often introduce
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dynamic correlations. Methods:
the estimated time-varying correlation measures.
R
stable
robust
R
a novel windowless approach for computing dynamic correlations via heat kernel smoothing. The heat kernel, the natural generalization of the Gaussian kernel to manifolds, is used to defined a smoothing kernel without boundary or end points. Results: We show
the heat kernel based dynamic correlations. We demonstrate
R
windowless approach smooths
heat kernel method can smooth
R
noise
fluctuations
R
is more stable in identifying and discriminating state spaces in resting-state fMRI. The proposed method is applied to the study of interhemispheric connectivity and whole-brain network analysis. Conclusion: We present a novel framework using heat kernel to compute the windowless dynamic correlation, which is more stable with less high-frequency fluctuations than windowed methods. Significance: The proposed windowless approach reduced the spurious rapid changes in the state space of brain connectivity, and identified the strongest connections in brain networks and symmetry in interhemispheric connectivity
achieve higher accuracy in identifying dynamically changing distinct states. The method is further used in determining if such dynamic state change is genetically heritable using a large-scale twin study. Various methodological challenges for analyzing paired twin dynamic networks are addressed