[DOC] Hierarchical, spectral, or density-based clustering using sklearn and aeon distance metrics

[CodeLionX]

Describe the issue linked to the documentation

The clustering component in aeon currently supports only partition-based methods. However, there are also hierarchical, spectral, and density-based clustering methods [1].

Suggest a potential alternative/fix

Using the distance metrics in aeon, we can pre-compute the distance matrix for traditional clustering methods. Some methods are already implemented in sklearn, which is a core dependency of eaon and, thus, available to users. I think we should at least link to the sklearn-clusterers in the documentation. With a bit more effort, we could provide examples on how to use sklearn's clusterers with aeon's distance measures (here).

• hierarchical clustering:
  • sklearn.cluster.AgglomerativeClustering with metric="precomputed"
• density-based clustering:
  • sklearn.cluster.DBSCAN with metric="precomputed"
  • sklearn.cluster.OPTICS with metric="precomputed"
  • Density Peaks? https://doi.org/10.1007/s10115-018-1189-7
• spectral clustering:
  • sklearn.cluster.SpectralClustering with affinity="precomputed" and the inverse of the distance matrix (large values indicate greater similarity)

I did not yet test this approach.

[1]: Paparrizos, John, and Luis Gravano. "Fast and Accurate Time-Series Clustering." ACM Transactions on Database Systems 42, no. 2 (2017): 8:1-8:49. https://doi.org/10.1145/3044711.

[TonyBagnall]

thanks for this, we have some examples I think of using precomputed with scikit, but if its not clear it would be great if it was clearer. I would like to get density peaks in, iirc we have a java implementation.