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Spectral clustering versus Watanabe theorem

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Kłopotek M. A.

Studia Informatica : systems and information technology

2024

tom vol. 1 (30)

21--34

We devote this paper to a special case of Graph Spectral Clustering of graphswith identical distances between nodes. This study is motivated by the special theorempresented by Watanabe which claims that given all derivable attributes are taken intoaccount, all distinct objects are at the same distance. As the multi-view clusteringbecomes popular, the mentioned Watanabe theorem may imply serious problems forrecovering the intrinsic structure of the collection of objects. We show that GraphSpectral Clustering should not be affected in the most favourable case that is blockstructure of similarity matrix in theory, but in practice the underlying𝑘-means algorithmintroduces up to 20% error rate in assignment of elements to clusters.