![Single-Linkage Clustering(hierarchical)
• The N*N proximity matrix is D = [d(i,j)]
• The clusterings are assigned sequence
numbers 0,1,......, (n-1)
• L(k) is the level of the kth clustering
• A cluster with sequence number m is
denoted (m)
• The proximity between clusters (r) and (s)
is denoted d [(r),(s)]](https://image.slidesharecdn.com/12typesofclustering-190206064104/85/12-types-of-clustering-7-320.jpg)
12 types of clustering
- 1. Prof. Neeraj Bhargava Vishal Dutt Department of Computer Science, School of Engineering & System Sciences MDS University, Ajmer
- 2. Hierarchical clustering Agglomerative (bottom up) 1. start with 1 point (singleton) 2. recursively add two or more appropriate clusters 3. Stop when k number of clusters is achieved. Divisive (top down) 1. Start with a big cluster 2. Recursively divide into smaller clusters 3. Stop when k number of clusters is achieved.
- 3. General steps of hierarchical clustering Given a set of N items to be clustered, and an N*N distance (or similarity) matrix, the basic process of hierarchical clustering (defined by S.C. Johnson in 1967) is this: Start by assigning each item to a cluster, so that if you have N items, you now have N clusters, each containing just one item. Let the distances (similarities) between the clusters the same as the distances (similarities) between the items they contain. Find the closest (most similar) pair of clusters and merge them into a single cluster, so that now you have one cluster less. Compute distances (similarities) between the new cluster and each of the old clusters. Repeat steps 2 and 3 until all items are clustered into K number of clusters
- 4. Exclusive vs. non exclusive clustering In the first case data are grouped in an exclusive way, so that if a certain datum belongs to a definite cluster then it could not be included in another cluster. A simple example of that is shown in the figure below, where the separation of points is achieved by a straight line on a bi-dimensional plane. On the contrary the second type, the overlapping clustering, uses fuzzy sets to cluster data, so that each point may belong to two or more clusters with different degrees of membership.
- 5. Partitioning clustering 1. Divide data into proper subset 2. recursively go through each subset and relocate points between clusters (opposite to visit-once approach in Hierarchical approach) This recursive relocation= higher quality cluster
- 6. Probabilistic clustering 1. Data are picked from mixture of probability distribution. 2. Use the mean, variance of each distribution as parameters for cluster 3. Single cluster membership
- 7. Single-Linkage Clustering(hierarchical) • The N*N proximity matrix is D = [d(i,j)] • The clusterings are assigned sequence numbers 0,1,......, (n-1) • L(k) is the level of the kth clustering • A cluster with sequence number m is denoted (m) • The proximity between clusters (r) and (s) is denoted d [(r),(s)]