RCGA

Task: create FCM based on one input

We propose an evolutionary approach, based on the algorithm, introduced by Stach Stach (2010). RCGA creates an FCM which concepts, after a predefined number of simulation steps, will have values close to the desired values. In order to do so, the user has to provide: the initial values of the concepts (can be multiple input vectors) structured as a NumPy array of shape(number of input vectors x number of concepts), the desired values of concepts after n steps, and the number of times steps as an integer. The algorithm will do its best to create the weight matrix which will maximize the fitness function - minimize the difference between obtained and desired values (error). The learning process stops if (i) fitness function is greater than the maximum fitness (default 0.999) or (ii) the number of generations is greater than the maximum number of generations (default 100000).

Step 1. Crossover

• Given two chromosomes and their weights matrixes, we randomly switch n weights between these matrixes
• Many crossover methods are available
• used with probability of 90%

Step 2. Mutations

Value of randomly chosen weight in the chromosome is being change into new value with the same sign

Step 3. Selection

Selection is the stage of a genetic algorithm in which individual genomes are chosen from a population for later breeding (using the crossover operator).

Roulette wheel selection

Selecting with weight probability, depending on the fitness of the individual gene Fitness values [1, 2, 3, 4], then the sum is (1 + 2 + 3 + 4 = 10). Therefore, you would want the probabilities or chances to be [1/10, 2/10, 3/10, 4/10] or [0.1, 0.2, 0.3, 0.4] The chosen one is taken for the crossover

Tournament selection

Winner of the tournament is being selected for the crossover two variants of the selection: with and without replacement

Step 4. Fitness function

Fitness is calculated as difference between concept values on each step of the simulation

For more information about the algorithms, please check out LEARNING AND AGGREGATION OF FUZZY COGNITIVE MAPS – AN EVOLUTIONARY APPROACH by Wojciech Stach

from fcmpy.ml.genetic.rcga import rcga,reshapeW,simulateFCM
import numpy as np

2.2.1 Heart attack risk

We used initial FCM presented in the article from arcticle

Fuzzy cognitive map based approach for determining the risk of ischemic stroke Mahsa Khodadadi 1, Heidarali Shayanfar 2, Keivan Maghooli 3, Amir Hooshang Mazinan 1

https://pubmed.ncbi.nlm.nih.gov/31778126/

Do not worry about the empty plot, if you would run it in another IDE, such as VSCode, plot would interactivly display current fitness function

testc = 7
#

# test 2
nofsteps = 2

# go to the paper and create an initial A0 (shape (1,n)
# and weight matrix n x n

A0 = np.asarray([[0.47, 0.51, 0.13, 0, 1, 0.37, 0.1]])
W_init = np.asarray([[0,0,0.20,0.3,0,0,0.45],
    [0,0,0,0.40,0,0,0.35],
    [0,0,0,0.30,0,0,0.30],
    [0,0,0,0,0,0,0.40],
    [0.30,0,0.15,0.35,0,0,0.25],
    [0.20,0,0.25,0.30,0,0,0.20],
    [0,0,0,0,0,0,0]])

# we reshape weight matrix in such a way that 0 - filled - diagonal is removed and 
W_init = reshapeW(W_init,'in')

# we prepare the placeholder for historical data 

historicaldata = np.zeros((A0.shape[0],A0.shape[1]))
# we prepare the historical data for learning process 

for concepts,i in zip(A0,range(A0.shape[0])):
    historicaldata[i] = simulateFCM(concepts, W_init, nofsteps)
    

# run the learning algorithm
# %%capture
GA = rcga(A0,historicaldata=historicaldata,numberofsteps=nofsteps,maxfitness=0.97)
W_final = GA.run()

We are at 100/100000
max fitness function so far is 0.9416627800656449
We are at 200/100000
max fitness function so far is 0.9656261906515792

W = reshapeW(W_final[-1],'out')
W

array([[ 0.        ,  0.2392139 ,  0.0186609 , -0.22615999,  0.14688781,
         0.40326178,  0.01711518],
       [ 0.43515269,  0.        , -0.51941326,  0.17227596, -0.78192652,
        -0.26074009,  0.202243  ],
       [ 0.99645221, -0.74905677,  0.        ,  0.59727595,  0.70527696,
        -0.7515263 ,  0.60774873],
       [ 0.61203435,  0.73934232, -0.93735818,  0.        , -0.31688036,
        -0.86817381, -0.25375124],
       [ 0.3541491 , -0.05118418,  0.53135025,  0.97417019,  0.        ,
         0.04842812,  0.8999771 ],
       [-0.70795986,  0.16143704, -0.0915654 , -0.49343288,  0.81211933,
         0.        , -0.90462744],
       [-0.68661796, -0.23099666,  0.93660758, -0.06985412, -0.63285064,
        -0.10909749,  0.        ]])