Oblivious dimension reduction for k -means: beyond subspaces and the Johnson-Lindenstrauss lemma

Luca Becchetti (1) , Marc Bury , Vincent Cohen-Addad (2) , Fabrizio Grandoni (3) , Chris Schwiegelshohn

1 UNIROMA - Università degli Studi di Roma "La Sapienza" = Sapienza University [Rome]
2 RO - Recherche Opérationnelle
3 CNR | ISTI - CNR Istituto di Scienza e Tecnologie dell’Informazione “A. Faedo” [Pisa]

We show that for n points in d-dimensional Euclidean space, a data oblivious random projection of the columns onto m∈ O((logk+loglogn)ε−6log1/ε) dimensions is sufficient to approximate the cost of all k-means clusterings up to a multiplicative (1±ε) factor. The previous-best upper bounds on m are O(logn· ε−2) given by a direct application of the Johnson-Lindenstrauss Lemma, and O(kε−2) given by [Cohen et al.-STOC’15].

Domaines: Algorithme et structure de données [cs.DS]

Luca Becchetti, Marc Bury, Vincent Cohen-Addad, Fabrizio Grandoni, Chris Schwiegelshohn. Oblivious dimension reduction for k -means: beyond subspaces and the Johnson-Lindenstrauss lemma. STOC 2019 - 51st Annual ACM SIGACT Symposium on Theory of Computing, Jun 2019, Phoenix, United States. pp.1039-1050, ⟨10.1145/3313276.3316318⟩. ⟨hal-02169563⟩