Summary
In this chapter, we presented a soft-clustering method called Fuzzy C-means, which resembles the structure of standard K-means but allows managing membership degrees (analogous to probabilities) that encode the similarity of a sample with all cluster centroids. This kind of approach allows the processing of membership vectors in a more complex pipeline, where the output of a clustering process, for example, is fed into a classifier.
One of the most important limitations of K-means and similar algorithms is the symmetric structure of the clusters. This problem can be solved with methods such as spectral clustering, which is a very powerful approach based on the dataset graph and is quite similar to non-linear dimensionality reduction methods. We analyzed an algorithm proposed by Shi and Malik, showing how it can easily separate a non-convex dataset.
We also discussed a completely geometry-agnostic algorithm, DBSCAN, which is helpful when it's necessary to discover...
