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Soft (Fuzzy) Clustering

Traditional clustering is usually called hard clustering. Each data points belongs to exactly one cluster. Usually we have an assignment matrix and we use one-hot encoding. (See for example clustering (DSC)).

In fuzzy clustering we have that each data point can belong to multiple clusters at the same time, with different degrees of membership.

In this case we still have the assignment matrix, but each row contains probabilities or weights that sums to 1. Example (soft clustering for 3 clusters):

This means:

• 20% membership in cluster 1
• 70% membership in cluster 2
• 10% membership in cluster 3

Examples of fuzzy/soft clustering algorithms: Gaussian Mixture Models (GMMs), Fuzzy -means, variational clustering in deep learning.