How to Show "Fuzziness" in Fuzzy Clustering Plot Python

Question

I have a normally distributed 2D dataset, and I am using the fcmeans library to perform fuzzy c-means clustering. I am able to plot the clusters with the red point indicating the cluster center. However, I need to show a gradient where the fuzziness occurs. I am not sure how to implement this in Python and I haven't been able to find anything like it online.

from fcmeans import FCM

data = pd.read_csv("my_data.csv")

model = FCM(n_clusters=2) 
model.fit(data) 

cntrs = my_model.centers
hard_prediction_labels = my_model.predict(data)
soft_prediction_labels = my_model.soft_predict(data)

plt.scatter(data[:, 0], data[:, 1], c=hard_prediction_labels, s=30);

I believe that my mistake is coming from the fact that my labels are 1 or 0; however, I'm not sure how to define it in a way that would allow me to determine which points are borderline. I am able to obtain the probabilities from the soft prediction (as to the probability of the data point belonging to each cluster) using the soft_predict() function, but I am unsure of how to create a color gradient with it.

Answer 1

Let's say that you have computed the (n_points, n_clusters) array prob, that for n_clusters being 2, looks like

print(prob)
# 0.61 0.39
# 0.55 0.45
# .... ....
# 0.07 0.93

Then you can do the following, to have a point that is more opaque when you have a higher probability of belonging to its cluster, and more transparent when it has a lower probabilty. I think this is what you want...

n_clusters = 2
...
for cluster in range(n_clusters):
    plt.scatter(data[hard_prediction_labels==cluster, 0],
                data[hard_prediction_labels==cluster, 1],
                s=30,
                alpha=0.8*prob[hard_prediction_labels==cluster, cluster])
    plt.scatter(data[hard_prediction_labels==cluster, 0],
                data[hard_prediction_labels==cluster, 1],
                s=5,
                alpha=1.0)

NB I haven't fcmeans so my code is untested, and is essentially based on informed speculation. You may need to adjust something to make it work.

---

EDIT

plotting twice each data cluster, with different sizes and transparencies, possibly give you a better visualization of your data.