Identification of Heart Sounds with an Interpretable Evolving Fuzzy Neural Network

. 2020 Nov 12;20(22):6477. doi: 10.3390/s20226477

Algorithm 1 EFNN-SOF training and update algorithm.

Initial Batch Learning Phase (Input: data matrix X with K samples):

1:
Extract L clouds in the first layer using the SOF approach (L is automatically estimated therein).
2:
Estimate center values $\vec{c}$ and widths $\vec{σ}$ for the L clouds derived from SOF.
3:
Calculate the combination (feature) weights $\vec{w}$ for neuron construction using Equation (20).
4:
Construct L logic neurons on the second layer of the network by welding the L fuzzy neurons of the first layer, using logical neurons concept and weights $\vec{w}$ .
5:
6:
for $i = 1, \dots, K$ do
7:
Calculate the regression vector $z ({\vec{x}}_{i})$ by activation levels of all neurons in ${\vec{x}}_{i}$ .
8:
Store it as one row entry into the activation level matrix Z.
9:
end for
10:
Extract reduced activation level matrix $Z_{r u l}$ according to the $L_{s} < L$ selected neurons.
11:
Estimate the weights ${\vec{v}}_{k}$ of the output layer for all classes $k = 1, \dots, c$ by Equation (23) using $Z_{r u l}$ and indicator vectors ${\vec{y}}_{k}$ .

Update Phase (Input: single data sample ${\vec{x}}_{t}$ ):

1:
Update $L_{s}$ clouds and evolving new ones on demand in the first layer using evolving SOF approach (→ $L_{s, u p d}$ clouds).
2:
Update the feature weights $\vec{w}$ by updating the within- and between-class scatter matrix and recalculating Equation (20).
3:
Perform Steps 2 and 4 with $L_{s, u p d}$ clouds.
4:
Calculate the degree of change of all neurons (rules) by Equation (29).
5:
Calculate the regression vector $z ({\vec{x}}_{t})$ by activation levels of all neurons in ${\vec{x}}_{t}$ .
6:
Update the weights ${\vec{v}}_{k}$ of the output layer by Equation (26).