Partitional versus hierarchical A partitional clustering is a division of the set of data objects into subsets(clusters) a hierarchical clustering is a set of nested clusters that are organized as a tree Each node (cluster)in the tree except for the leaf nodes)is the union of its children(sub-clusters) The root of the tree is the cluster containing all the objects Often, but not always the leaves of the tree are singleton clusters of individual data objects 8/20/2016 PATTERN RECOGNITION
Partitional versus hierarchical A partitional clustering is a division of the set of data objects into subsets (clusters). A hierarchical clustering is a set of nested clusters that are organized as a tree. Each node (cluster) in the tree (except for the leaf nodes) is the union of its children (sub-clusters). The root of the tree is the cluster containing all the objects. Often, but not always, the leaves of the tree are singleton clusters of individual data objects. 8/20/2016 PATTERN RECOGNITION 6
Partitional versus hierarchical The following figures form a hierarchical (nested clustering with 1, 2, 4 and 6 clusters on each level a hierarchical clustering can be viewed as a sequence of partitional clusterings a partitional clustering can be obtained by taking any member of that sequence, i.e. by cutting the hierarchical tree at a certain level 8/20/2016 PATTERN RECOGNITION
Partitional versus hierarchical The following figures form a hierarchical (nested) clustering with 1, 2, 4 and 6 clusters on each level. A hierarchical clustering can be viewed as a sequence of partitional clusterings. A partitional clustering can be obtained by taking any member of that sequence, i.e. by cutting the hierarchical tree at a certain level. 8/20/2016 PATTERN RECOGNITION 7
Partitional versus hierarchical (a) Original points (b)Two clusters x十+ (c)Four clusters (d)Six clusters 8/20/2016 PATTERN RECOGNITION
Partitional versus hierarchical 8/20/2016 PATTERN RECOGNITION 8
Exclusive versus fuzzy In an exclusive clustering, each object is assigned to a single cluster. However, there are many situations in which a point could reasonably be placed in more than one cluster 8/20/2016 PATTERN RECOGNITION 9
Exclusive versus fuzzy In an exclusive clustering, each object is assigned to a single cluster. However, there are many situations in which a point could reasonably be placed in more than one cluster. 8/20/2016 PATTERN RECOGNITION 9
Exclusive versus fuzzy In a fuzzy clustering, every object belongs to every cluster with a membership weight that is between o(absolutely does not belong) and 1 absolutely belongs This approach is useful for avoiding the arbitrariness of assigning an object to only one cluster when it is close to several a fuzzy clustering can be converted to an exclusive clustering by assigning each object to the cluster in which its membership value is the highest 8/20/2016 PATTERN RECOGNITION
Exclusive versus fuzzy In a fuzzy clustering, every object belongs to every cluster with a membership weight that is between ◦ 0 (absolutely does not belong) and ◦ 1 (absolutely belongs). This approach is useful for avoiding the arbitrariness of assigning an object to only one cluster when it is close to several. A fuzzy clustering can be converted to an exclusive clustering by assigning each object to the cluster in which its membership value is the highest. 8/20/2016 PATTERN RECOGNITION 10