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Difference between revisions of "Bilateral Trigeminal neuromotor organic symmetry"
Bilateral Trigeminal neuromotor organic symmetry (view source)
Revision as of 16:03, 8 March 2022
, 2 years ago→Artificial neural network model
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If organic symmetry exists, there would be a correlation coefficient between the EMG values of the right and left muscles. To test this assumption, we adopted the ANN model. First we created, configured, and initialized our multi-layer ANN.<ref name=":6" /> | If organic symmetry exists, there would be a correlation coefficient between the EMG values of the right and left muscles. To test this assumption, we adopted the ANN model. First we created, configured, and initialized our multi-layer ANN.<ref name=":6" /> | ||
We assumed that each layer is composed of a number of predefined neurons. The neurons in the input layer perform as a buffer which | ====The multi-layer ANN==== | ||
We assumed that each layer is composed of a number of predefined neurons. <br />The neurons in the input layer perform as a buffer which divides into portions and dispense the input signals <math>x_i</math> to the next neurons in the hidden layer without degrading the signal. Each neuron <math>j</math> in the hidden layer sums the input signals <math>x_i</math>, after weighting them with the strengths <math>w_{i,j}</math> of the respective connections from the input layer, and calculates its output <math>y_i</math> as a function <math>f</math> of the sum.<blockquote><math>y_j=\sum_{i=1}^N w_jx_i</math> <math>Eq.1</math></blockquote> | |||
Where, <math>w_{i,j}</math> is the weight of the ''<math>i^{th}</math>'' and ''<math>j^{th}</math>'' connection and ''<math>x_i</math>'' is the ''<math>i^{th}</math>'' input signal. <math>f</math> is the activation function which is needed to transform the weighted sum of all signals influencing a neuron.<ref name=":5">Akdenur B, Okkesum S, Kara S, Gunes S (2009) Correlation- and covariance- supported normalization method for estimating orthodontic trainer treatment for clenching activity. Proc Inst Mech Eng H 223: 991-1001.</ref> | Where, <math>w_{i,j}</math> is the weight of the ''<math>i^{th}</math>'' and ''<math>j^{th}</math>'' connection and ''<math>x_i</math>'' is the ''<math>i^{th}</math>'' input signal. <math>f</math> is the activation function which is needed to transform the weighted sum of all signals influencing a neuron.<ref name=":5">Akdenur B, Okkesum S, Kara S, Gunes S (2009) Correlation- and covariance- supported normalization method for estimating orthodontic trainer treatment for clenching activity. Proc Inst Mech Eng H 223: 991-1001.</ref> | ||
In our ANN model, | In our ANN model, a radial basis function (RBF) has been chosen as the activation function <math>f</math>. In the field of mathematical modelling, an artificial neural network that uses RBF as activation function is properly called a 'radial basis function network'. The output of this network is a linear combination of RBF of the inputs and neuron parameters. RBF has many application, and we choose this one because it is specific for function approximation tasks. | ||
====Going practical==== | |||
We decided to initialize two layers and define ten neurons in the hidden layer in order to increase the power of our network. We equipped our ANN with the Levenberg-Marquardt (LM) algorithm as training function to be used and trained with the normalized features computed from the EMG of the left muscles. With the LM algorithm, we were able to achieve the rapid execution of the network.<ref name=":6">Kara S, Dirgenali F, Okkesim S (2006) Detection of gastric dysrhythmia using WT and ANN in diabetic gastroparesis patients. Comput Biol Med 36: 276-290.</ref> | We decided to initialize two layers and define ten neurons in the hidden layer in order to increase the power of our network. We equipped our ANN with the Levenberg-Marquardt (LM) algorithm as training function to be used and trained with the normalized features computed from the EMG of the left muscles. With the LM algorithm, we were able to achieve the rapid execution of the network.<ref name=":6">Kara S, Dirgenali F, Okkesim S (2006) Detection of gastric dysrhythmia using WT and ANN in diabetic gastroparesis patients. Comput Biol Med 36: 276-290.</ref> | ||
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If values computed from Equation 2 are used as input to the ANN, inferences can be drawn according to the column with the highest correlation. Although the correlation is lower, the other columns show correlation well. If ANN equipped using only the highest correlation, the correlation of the other columns will be ignored. To prevent this kind of guidance, all the row values were normalized according to Equations 3.1, 3.2, and 3.3 for the features computed from the EMG traces of the left muscles, were the subscript ''n'' indicates the normalized value. After the first normalization, there was no unit belonging to a specific feature, and the second normalization procedure could be applied. <blockquote> | If values computed from Equation 2 are used as input to the ANN, inferences can be drawn according to the column with the highest correlation. Although the correlation is lower, the other columns show correlation well. If ANN equipped using only the highest correlation, the correlation of the other columns will be ignored. To prevent this kind of guidance, all the row values were normalized according to Equations 3.1, 3.2, and 3.3 for the features computed from the EMG traces of the left muscles, were the subscript ''n'' indicates the normalized value. After the first normalization, there was no unit belonging to a specific feature, and the second normalization procedure could be applied. <blockquote> | ||
<math>Ons-lat_n= \tfrac{Ons-lat}{\sqrt{ Ons-lat^2+Amp^2+Int-A^2}}</math> | |||
<math>Eq.3.1</math></blockquote><blockquote><math>Ons-lat_n= \tfrac{Amp}{\sqrt{ Ons-lat^2+Amp^2+Int-A^2}}</math> | |||
<math>Eq. 3.2</math></blockquote><blockquote><math>Ons-lat_n= \tfrac{Int-lat}{\sqrt{ Ons-lat^2+Amp^2+Int-A^2}}</math> | |||
<math>Eq.3.3</math></blockquote>The correlation coefficients (CC) were computed based on raw EMG values in Equations 4.1, 4.2 and 4.3, to obtain characteristics of the ANN output. | |||
<blockquote> | |||