Estimation of effective connectivity using multi-layer perceptron artificial neural network

Abstract

Studies on interactions between brain regions estimate effective connectivity, (usually) based on the causality inferences made on the basis of temporal precedence. In this study, the causal relationship is modeled by a multi-layer perceptron feed-forward artificial neural network, because of the ANN's ability to generate appropriate input-output mapping and to learn from training examples without the need of detailed knowledge of the underlying system. At any time instant, the past samples of data are placed in the network input, and the subsequent values are predicted at its output. To estimate the strength of interactions, the measure of "" is defined based on the network structure, the connecting weights and the parameters of hidden layer activation function. Simulation analysis demonstrates that the method, called "CREANN" (Causal Relationship Estimation by Artificial Neural Network), can estimate time-invariant and time-varying effective connectivity in terms of MVAR coefficients. The method shows robustness with respect to noise level of data. Furthermore, the estimations are not significantly influenced by the model order (considered time-lag), and the different initial conditions (initial random weights and parameters of the network). CREANN is also applied to EEG data collected during a memory recognition task. The results implicate that it can show changes in the information flow between brain regions, involving in the episodic memory retrieval process. These convincing results emphasize that CREANN can be used as an appropriate method to estimate the causal relationship among brain signals.

Estimation of brain connectivity through Artificial Neural Networks

“…where p is the model order and the vector E is the innovation process assumed to be white and uncorrelated. Independence between a pair of signals result in zero coefficients while dependence is reflected in nonzero values [10].…”

“…Only recently a new training algorithm, named stochastic gradient descent-L1 [9] (SGD-L1), was introduced in the literature, allowing to apply l1-norm during the training process directly on the estimated weights with the result of an efficient training process. The use of ANNs as MVAR model for the brain connectivity estimation has been proposed in [10]. However, the use of SGD-L1 algorithm has never been tested for the purposes of reducing collinearity in the estimation of MVAR parameters and performing the assessment of estimated connectivity patterns.…”

Accelerated Exploration for Long-Term Urban Water Infrastructure Planning through Machine Learning

“…one hidden layer is usually sufficient in most cases [14, 19-25, 33, 41-43] while sometimes multiple hidden layers shows better learning on certain problems [35]. The number of nodes in hidden layer is usually determined through trial-and-error method [19,23,43]. The range of attempts is usually within 1 to 20 [14,[19][20][21][22][23][24][25], or 3 times the number of input variables [43].…”

“…Simple networks maybe less accurate in learning the problem while complex networks may take excessively long training time. one hidden layer is usually sufficient in most cases [14,[19][20][21][22][23][24][25]33,[41][42][43] while sometimes multiple hidden layers shows better learning on certain problems [35].…”

“…For nodes in the hidden layer, most commonly used AFs are the logistic sigmoid function [34,38,41], the tanh function [35,43,45]. These two functions are similar in shape while different in output ranges (sigmoid: [0,1], tanh: [-1,1]).…”