Centroid clustering algorithms aim to partition objects into clusters to minimize distances between objects and cluster centroids. K-means clustering assigns objects to the nearest centroid and recalculates centroids until clusters stabilize. Agglomerative hierarchical clustering starts with each object in its own cluster and recursively merges the closest pairs of clusters until all objects are in one cluster, shown as a dendrogram. Distances between clusters can be calculated as single, complete, or average linkages based on distances between members.

1. CLUSTERING

2. IntroductionCentroid - Center of a clusterCentroid could be either a real point or an imaginary one.Objective function –Measures the quality of clustering (small value is desirable)Calculated by summing the squares of distances of each point from the centroid of the clusterTwo types of Clustering are:k-means ClusteringHierarchical Clustering

3. k-means ClusteringIt is an exclusive clustering algorithmAlgorithm:Select a value for ‘k’Select ‘k’ objects in an arbitrary fashion. Use it as an initial set of k centroidsAssign each object to the cluster for which it is nearest to the centroidRecalculate the centroidsRepeat steps 3 & 4 until centroids don’t move.It may not find the best set of clusters but will always terminate.

4. Agglomerative Hierarchical ClusteringAlgorithm:Assign each object to its own single-object cluster. Calculate the distance between each pair (distance matrix)Select and merge the closest pairsCalculate the distance between this new cluster and other clusters.Repeat steps 2 & 3 until all objects are in single cluster

5. ExampleBefore clusteringAfter two passes

6. ExampleIt gives the entire hierarchy of clustersDendrogram (A Binary tree) – End result of hierarchical clustering

7. Distance MeasureThree ways of calculating distances:Single-link clustering Shortest distance from any member of one cluster to any member of another clusterComplete-link clustering Longest distance from any member of one cluster to any member of another clusterAverage-link clustering Average distance from any member of one cluster to any member of another cluster

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