Network Connection Determination in Sparse EEG Systems
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Solution Overview
Problem
Current methods for determining network connections in high-dimensional systems, particularly in EEG data, face challenges with accuracy and computational efficiency, leading to false positives and inability to handle sparse networks effectively.
Innovation Solution
A computer-implemented method that identifies probable zero connection coefficients and sets them to zero, improving parameter estimation by assuming sparseness in the network, reducing indirect links, and applying Granger-causality in high-dimensional systems.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If existing methods (coherence, partial coherence, directed partial correlation) are used to determine network connections, then the coupling structure can be estimated, but the methods become unacceptably long or computationally demanding and lose accuracy when the network exceeds 10 nodes
Solution Approach 1:
The method segments the network analysis by first identifying and removing indirect links through coherence and partial coherence calculations, then separately estimating direct connection coefficients. This segmentation allows the complex high-dimensional problem to be broken into manageable steps that maintain accuracy while improving computational efficiency
Solution Approach 2:
The method performs preliminary identification of probable zero connection coefficients using coherence and partial coherence thresholds before the main parameter estimation. This preliminary action removes indirect links in advance, reducing the dimensionality of the subsequent estimation problem and preventing computational burden from increasing with network size
2Reliability
If existing methods are used to determine network connections in high-dimensional systems, then connections can be identified, but false positives increase and the ability to handle sparse networks effectively is lost
Solution Approach 1:
The method performs preliminary filtering by calculating coherence and partial coherence and identifying probable zero connection coefficients before main estimation. This preliminary action removes indirect links and reduces false positives by establishing a cleaner set of candidate connections for subsequent Granger-causality analysis
Solution Approach 2:
The method changes parameters by applying sparsity assumptions and thresholding connection coefficients. By setting probable zero coefficients to zero and focusing estimation on non-zero coefficients, the method improves reliability in high-dimensional sparse networks while reducing false positives
3Quantity of substance
If the network dimension increases beyond 10 nodes, then more comprehensive coverage is achieved, but the methods start to significantly lose accuracy and become unacceptably long or computationally demanding
Solution Approach 1:
The method segments the computational task into distinct phases: identifying indirect links through coherence, removing them by setting coefficients to zero, and then estimating remaining direct connections. This segmentation prevents computational complexity from scaling poorly with network dimension
Solution Approach 2:
The method changes the parameter space by assuming sparsity and setting many connection coefficients to zero. This parameter change reduces the effective dimensionality of the estimation problem, allowing the method to handle networks with many more than 10 nodes without becoming computationally intractable
Data Source
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AI summary
This invention relates to methods and systems for determining network connections. It is particularly, but not exclusively, related to methods and systems for determining network connections in sparse networks, and has particular application to EEG data. An aspect of the invention provides a method for identifying, in a network of interacting nodes simultaneously producing signals,connections between said nodes andof estimating connection coefficients between nodesidentified as connected which includes the steps of setting to zero connection coefficients where the calculated coherence or partial coherence is below a first predetermined thresholdand subsequently setting to zero connection coefficients where the estimated connection coefficients are below a second predetermined threshold, and then re-estimatingthe connection coefficients for the combinations of nodes for which the connection coefficients have not already been set to zero.