有哪些评估聚类相似性的方法？

Question

Suppose I have two ways of clustering the same dataset, and want to calculate the similarity of their outputs. I would have to calculate something akin to a correlation, but cluster labels are a categorical variable. I thought about using chi-square, but it's not advised to do so when multiple cells in the contingency table are <5 (and this will happen often when clusterings are very similar). Another clue was to use Fisher's exact test, but the Python scipy implementation works only for 2x2 contingency matrices, and I will likely be working with bigger matrices (10x10, or 8x6 for example).

Are there any other established methods of comparing clusterings in this way? Are there any Python implementations of them?

Answer 1

Excellent Python implementations exist at https://scikit-learn.org/stable/modules/clustering.html#clustering-performance-evaluation . Each has its own upsides and downsides. Both for comparing a clustering result to its ground truth labels (external) and evaluating a clustering result on criteria such as distance between cluster centroids (internal) and more. The contingency matrix gives an excellent insight into your clustering, but does not give a numerical value to 'prove your clustering was good'.

If your dataset is very large with many dimensions the internal validation measures might be prohibitively slow.