Stairstep-like dendrogram cut: a permutation test approach Dario - PowerPoint PPT Presentation

Stairstep-like dendrogram cut: a permutation test approach Dario Bruzzese Umberto Giani Domenico Vistocco dbruzzes@unina.it ugiani@unina.it vistocco@unicas.it ————————————————————- —————————— Department of Department of Preventive Medical Sciences Economics U NIVERSITY OF N APLES U NIVERSITY OF C ASSINO ITALY ITALY D. Bruzzese, U. Giani, D. Vistocco ( ————————————————————- Stairstep-like dendrogram cut —————————— Sismec 2009 1 / 21

La Carte Motivation 1 The stairstep-like permutation procedure 2 Notation The outline The Core Some results 3 Real datasets Synthetic dataset ToDo List 4 D. Bruzzese, U. Giani, D. Vistocco ( ————————————————————- Stairstep-like dendrogram cut —————————— Sismec 2009 2 / 21

La Carte Motivation 1 The stairstep-like permutation procedure 2 Notation The outline The Core Some results 3 Real datasets Synthetic dataset ToDo List 4 D. Bruzzese, U. Giani, D. Vistocco ( ————————————————————- Stairstep-like dendrogram cut —————————— Sismec 2009 3 / 21

Motivation Automatically determine the optimal cut-off level of a dendrogram D. Bruzzese, U. Giani, D. Vistocco ( ————————————————————- Stairstep-like dendrogram cut —————————— Sismec 2009 4 / 21

Motivation Automatically determine the optimal cut-off level of a dendrogram Explore partitions different from those allowed by an horizontal cut D. Bruzzese, U. Giani, D. Vistocco ( ————————————————————- Stairstep-like dendrogram cut —————————— Sismec 2009 4 / 21

Motivation Automatically determine the optimal cut-off level of a dendrogram Explore partitions different from those allowed by an horizontal cut The rep1HighNoise dataset Yeung KY, Medvedovic M, Bumgarner KY: Clustering gene-expression data with repeated measurements. Genome Biology, 2003, 4:R34 n = 200 p = 20 It is a synthetic data set with error distributions derived from real array data. D. Bruzzese, U. Giani, D. Vistocco ( ————————————————————- Stairstep-like dendrogram cut —————————— Sismec 2009 4 / 21

Motivation Automatically determine the optimal cut-off level of a dendrogram Explore partitions different from those allowed by an horizontal cut Horizontal cut k = 3 D. Bruzzese, U. Giani, D. Vistocco ( ————————————————————- Stairstep-like dendrogram cut —————————— Sismec 2009 4 / 21

Motivation Automatically determine the optimal cut-off level of a dendrogram Explore partitions different from those allowed by an horizontal cut Horizontal cut k = 3 (green clusters) D. Bruzzese, U. Giani, D. Vistocco ( ————————————————————- Stairstep-like dendrogram cut —————————— Sismec 2009 4 / 21

Motivation Automatically determine the optimal cut-off level of a dendrogram Explore partitions different from those allowed by an horizontal cut An alternative cut k = 3 (rainbow clusters) D. Bruzzese, U. Giani, D. Vistocco ( ————————————————————- Stairstep-like dendrogram cut —————————— Sismec 2009 4 / 21

Motivation Automatically determine the optimal cut-off level of a dendrogram Explore partitions different from those allowed by an horizontal cut An alternative cut k = 3 (rainbow clusters) D. Bruzzese, U. Giani, D. Vistocco ( ————————————————————- Stairstep-like dendrogram cut —————————— Sismec 2009 4 / 21

Motivation Automatically determine the optimal cut-off level of a dendrogram Explore partitions different from those allowed by an horizontal cut Horizontal cut k = 4 (blue clusters) D. Bruzzese, U. Giani, D. Vistocco ( ————————————————————- Stairstep-like dendrogram cut —————————— Sismec 2009 4 / 21

Motivation Automatically determine the optimal cut-off level of a dendrogram Explore partitions different from those allowed by an horizontal cut Horizontal cut k = 4 (blue clusters) D. Bruzzese, U. Giani, D. Vistocco ( ————————————————————- Stairstep-like dendrogram cut —————————— Sismec 2009 4 / 21

Motivation Automatically determine the optimal cut-off level of a dendrogram Explore partitions different from those allowed by an horizontal cut An alternative cut k = 4 (rainbow clusters) D. Bruzzese, U. Giani, D. Vistocco ( ————————————————————- Stairstep-like dendrogram cut —————————— Sismec 2009 4 / 21

Motivation Automatically determine the optimal cut-off level of a dendrogram Explore partitions different from those allowed by an horizontal cut An alternative cut k = 4 (rainbow clusters) D. Bruzzese, U. Giani, D. Vistocco ( ————————————————————- Stairstep-like dendrogram cut —————————— Sismec 2009 4 / 21

Motivation Automatically determine the optimal cut-off level of a dendrogram Explore partitions different from those allowed by an horizontal cut An alternative cut k = 5 (rainbow clusters) D. Bruzzese, U. Giani, D. Vistocco ( ————————————————————- Stairstep-like dendrogram cut —————————— Sismec 2009 4 / 21

Motivation Automatically determine the optimal cut-off level of a dendrogram Explore partitions different from those allowed by an horizontal cut An alternative cut k = 5 (rainbow clusters) D. Bruzzese, U. Giani, D. Vistocco ( ————————————————————- Stairstep-like dendrogram cut —————————— Sismec 2009 4 / 21

La Carte Motivation 1 The stairstep-like permutation procedure 2 Notation The outline The Core Some results 3 Real datasets Synthetic dataset ToDo List 4 D. Bruzzese, U. Giani, D. Vistocco ( ————————————————————- Stairstep-like dendrogram cut —————————— Sismec 2009 5 / 21

Notation Let: D. Bruzzese, U. Giani, D. Vistocco ( ————————————————————- Stairstep-like dendrogram cut —————————— Sismec 2009 6 / 21

Notation Let: n the number of objects to classify; � �� � D. Bruzzese, U. Giani, D. Vistocco ( ————————————————————- Stairstep-like dendrogram cut —————————— Sismec 2009 6 / 21

Notation Let: n the number of objects to classify; C k L and C k R the two classes merged at level k (k=1,...,n-1) D. Bruzzese, U. Giani, D. Vistocco ( ————————————————————- Stairstep-like dendrogram cut —————————— Sismec 2009 6 / 21

Notation Let: n the number of objects to classify; C k L and C k R the two classes merged at level k (k=1,...,n-1) C 1 C 1 L R D. Bruzzese, U. Giani, D. Vistocco ( ————————————————————- Stairstep-like dendrogram cut —————————— Sismec 2009 6 / 21

Notation Let: n the number of objects to classify; C k L and C k R the two classes merged at level k (k=1,...,n-1) C 2 C 2 L R D. Bruzzese, U. Giani, D. Vistocco ( ————————————————————- Stairstep-like dendrogram cut —————————— Sismec 2009 6 / 21

Notation Let: n the number of objects to classify; C k L and C k R the two classes merged at level k (k=1,...,n-1) C 3 C 3 L R D. Bruzzese, U. Giani, D. Vistocco ( ————————————————————- Stairstep-like dendrogram cut —————————— Sismec 2009 6 / 21

Notation Let: n the number of objects to classify; C k L and C k R the two classes merged at level k (k=1,...,n-1) “ ” C k L ∪ C k h the height necessary to merge R C k L and C k R D. Bruzzese, U. Giani, D. Vistocco ( ————————————————————- Stairstep-like dendrogram cut —————————— Sismec 2009 6 / 21

Notation “ ” C 1 L ∪ C 1 h R Let: n the number of objects to classify; C k L and C k R the two classes merged at level k (k=1,...,n-1) “ ” C k L ∪ C k h the height necessary to merge R C k L and C k R C 1 C 1 L R D. Bruzzese, U. Giani, D. Vistocco ( ————————————————————- Stairstep-like dendrogram cut —————————— Sismec 2009 6 / 21

Notation Let: n the number of objects to classify; C k L and C k R the two classes merged at level k (k=1,...,n-1) “ ” C 2 L ∪ C 2 h “ ” C k L ∪ C k R h the height necessary to merge R C k L and C k R C 2 C 2 L R D. Bruzzese, U. Giani, D. Vistocco ( ————————————————————- Stairstep-like dendrogram cut —————————— Sismec 2009 6 / 21