A conceptual view of clustering

(This collects together posts from an occasional series of essays on clustering: for all posts in this topic, click here)

1. Clustering: an occasional series
2. The "I don't like you" view.
3. $k$-means
4. Hierarchical methods
5. Correlation clustering: "I don't like you, but I like them"
6. Spectral Clustering
7. An interlude: time-series clustering by Sorelle Friedler.
8. Mixture models: classification versus clustering
9. Choosing the number of clusters I: The elbow method
10. Choosing the number of clusters II: Diminishing returns and the ROC method.
11. Choosing the number of clusters III: Phase transitions
12. An interlude: New results on learning mixtures of Gaussians
13. Clustering as compression
14. Clustering with outliers (by Sergei Vassilvitskii)
15. Axioms of clustering (by Sergei Vassilvitskii) 
16. Large-data clustering Part I: Clusters of clusters