Fuzzy C-Means Clustering

Fuzzy c-means clustering partitions cases into a chosen number of clusters while giving each case a membership degree in every cluster rather than a single hard assignment.

퍼지 c-평균 군집은 사례를 정해진 수의 군집으로 나누되 하나에만 배정하지 않고 모든 군집에 대한 소속도를 부여하는 방법입니다.

Some of my customers seem to belong partly to two segments; is there a clustering method that allows partial membership?

일부 고객은 두 세그먼트에 걸쳐 있는 것 같은데, 부분적인 소속을 허용하는 군집 방법이 있나요?

Fuzzy c-means alternates between updating cluster centers as membership-weighted means and updating each case's memberships from its relative distances to the centers, with a fuzzifier m that controls softness. The partition coefficient and partition entropy summarize how crisp the resulting partition is.

When to use Fuzzy C-Means Clustering

• Cases may plausibly belong to more than one cluster to different degrees.
• Variables are continuous and clusters are roughly spherical.
• You want membership degrees for later analysis or targeting.

When to use something else

• You need a probabilistic model with likelihood-based fit criteria; use a Gaussian mixture model instead.
• Clusters are irregular in shape or contain noise; use HDBSCAN instead.

Assumptions and requirements

• Continuous variables on comparable scales (standardized).
• Clusters are roughly spherical and of similar size.
• The number of clusters is chosen in advance (default 3).

What the analysis reports

• Partition coefficient and partition entropy
• Cluster centers
• Hard-assignment cluster sizes
• Membership summary per cluster

How to report it

Fuzzy c-means clustering (c = [c], m = 2; N = [n]) yielded a partition coefficient of [value] and a partition entropy of [value].

Related methods

• K-Means Clustering
• Gaussian Mixture Model (GMM)
• Optimal Number of Clusters (Elbow, Silhouette, Gap)

Run Fuzzy C-Means Clustering on Quorant