Why does calling FuzzyCMeans.predict_proba() alter the centroids of the fitted model?

[vnmabus]

Discussed in #625

^{Originally posted by ensley-nexant August 5, 2024}
I'm trying to understand why I can call .predict_proba() multiple times on the same fitted model, passing the same function, and get different predictions. Is this the intended behavior?

It looks like the centroids are being updated on every prediction, and I'm not sure why that would be the case. Here is an example:

from skfda import datasets
from skfda.ml.clustering import FuzzyCMeans

X, y = datasets.fetch_weather(return_X_y=True, as_frame=True)
fd = X.iloc[:, 0].values.coordinates[0]

kmeans = FuzzyCMeans(n_clusters=4, random_state=2)
kmeans.fit(fd)

print("Initial centroids")
print(kmeans.cluster_centers_.data_matrix[0][:4])

for i in range(1, 5):
    print("\nPrediction", i)
    print(kmeans.predict_proba(fd[1])[0])
    print("Centroids (head):")
    print(kmeans.cluster_centers_.data_matrix[0][:4])

Output:

Initial centroids
[[-7.48331886]
 [-7.69572714]
 [-8.33347371]
 [-8.2457692 ]]

Prediction 1
[0.81649987 0.04951254 0.12522585 0.00876174]
Centroids (head):
[[-4.4]
 [-4.2]
 [-5.3]
 [-5.4]]

Prediction 2
[0.2 0.2 0.2 0.4]
Centroids (head):
[[-4.4]
 [-4.2]
 [-5.3]
 [-5.4]]

Prediction 3
[0.28571429 0.28571429 0.28571429 0.14285714]
Centroids (head):
[[-4.4]
 [-4.2]
 [-5.3]
 [-5.4]]

Prediction 4
[0.25 0.25 0.25 0.25]
Centroids (head):
[[-4.4]
 [-4.2]
 [-5.3]
 [-5.4]]
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