Interface / CSNA Meeting St. Louis

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Interface / CSNA Meeting St. Louis Estimating the Cluster Tree of a Density Werner Stuetzle Rebecca Nugent Department of Statistics University of Washington June 11, 2005 Interface / CSNA Meeting St. Louis

Interface / CSNA Meeting St. Louis June 11, 2005 Interface / CSNA Meeting St. Louis

Interface / CSNA Meeting St. Louis June 11, 2005 Interface / CSNA Meeting St. Louis

Interface / CSNA Meeting St. Louis Groups K-means with k = 2 June 11, 2005 Interface / CSNA Meeting St. Louis

Interface / CSNA Meeting St. Louis June 11, 2005 Interface / CSNA Meeting St. Louis

Interface / CSNA Meeting St. Louis Detect that there are 5 or 6 distinct groups. Assign group labels to observations. June 11, 2005 Interface / CSNA Meeting St. Louis

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Interface / CSNA Meeting St. Louis rs = 1 rs = 5 rs = 2 June 11, 2005 Interface / CSNA Meeting St. Louis

Interface / CSNA Meeting St. Louis June 11, 2005 Interface / CSNA Meeting St. Louis

Interface / CSNA Meeting St. Louis Note large tree fragments in bottom left panel June 11, 2005 Interface / CSNA Meeting St. Louis

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Interface / CSNA Meeting St. Louis June 11, 2005 Interface / CSNA Meeting St. Louis

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Interface / CSNA Meeting St. Louis rs = 1 rs = 5 rs = 2 June 11, 2005 Interface / CSNA Meeting St. Louis

Interface / CSNA Meeting St. Louis Runt Pruning algorithm: generate_cluster_tree_node (mst, runt_size_threshold) { node = new_cluster_tree_node node.leftson = node.rightson = NULL node.obs = leaves (mst) cut_edge = longest_edge_with_large_runt_size (mst, runt_size_threshold) if (cut_edge) { node.leftson = generate_cluster_tree_node (left_subtree (cut_edge), runt_size_threshold) node.rightson = generate_cluster_tree_node (right_subtree (cut_edge), runt_size_threshold) } return (node) } rs = 1 rs = 5 rs = 2 June 11, 2005 Interface / CSNA Meeting St. Louis

Interface / CSNA Meeting St. Louis June 11, 2005 Interface / CSNA Meeting St. Louis

Interface / CSNA Meeting St. Louis Note large tree fragments in bottom left panel June 11, 2005 Interface / CSNA Meeting St. Louis

Interface / CSNA Meeting St. Louis June 11, 2005 Interface / CSNA Meeting St. Louis

Interface / CSNA Meeting St. Louis June 11, 2005 Interface / CSNA Meeting St. Louis

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Interface / CSNA Meeting St. Louis June 11, 2005 Interface / CSNA Meeting St. Louis

Interface / CSNA Meeting St. Louis June 11, 2005 Interface / CSNA Meeting St. Louis

Interface / CSNA Meeting St. Louis June 11, 2005 Interface / CSNA Meeting St. Louis

Interface / CSNA Meeting St. Louis June 11, 2005 Interface / CSNA Meeting St. Louis

Interface / CSNA Meeting St. Louis Runt Pruning algorithm: generate_cluster_tree_node (mst, runt_size_threshold) { node = new_cluster_tree_node node.leftson = node.rightson = NULL node.obs = leaves (mst) cut_edge = longest_edge_with_large_runt_size (mst, runt_size_threshold) if (cut_edge) { node.leftson = generate_cluster_tree_node (left_subtree (cut_edge), runt_size_threshold) node.rightson = generate_cluster_tree_node (right_subtree (cut_edge), runt_size_threshold) } return (node) } rs = 1 rs = 5 rs = 2 June 11, 2005 Interface / CSNA Meeting St. Louis

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