Clustering is the grouping of objects based on their similarities. It can involve initially separating objects into groups and then further dividing those groups based on additional homogeneous features. The goal of cluster analysis is to maximize intra-cluster similarity (objects within the same cluster are very similar) while minimizing inter-cluster similarity (objects from different clusters are very dissimilar). There are two main types of clustering - hierarchical, which creates nested clusters without predefined numbers, and k-means, which partitions objects into k mutually exclusive clusters through iterative reassignment.

1. CLUSTERING

2. WHAT IS CLUSTERING?
1. Grouping of objects based on homogeneous features.
2. Example: In a class of students, boys and girls are separated into two groups.
3. We can further classify the groups further into another set of groups based on
some homogeneous features.
4. Example: Considering the previous example given in point 2, the boys and girls
separated into groups can be further grouped based on there heights for
seating arrangements in the class.

3. OBJECTIVE OF CLUSTER ANALYSIS
• Intra cluster is the sum distances between objects in the same cluster.
• Inter cluster is the distance between objects in different cluster.

4. • Intra cluster • Inter cluster

5. CLUSTERING A SET OF DATAPOINTS

6. TYPES OF CLUSTERING
1. Hierarchical clustering:
• No need to decide number of clusters for ‘n’
number of observations.
• It will automatically create a set of clusters till
when ‘n’ clusters = n set of observations.
• It will create a family tree of clusters better
known as “dendrogram”.
• Two approaches of hierarchical clustering
• Agglomerative approach (“bottom-up”)
• Divisive (“top-down”)

7. TYPES OF CLUSTERING
2. K-means clustering or
portioning clustering:
• Decide k clusters for n
observations when k < n.
• For example n = 10 and k = 2 , we
will have 2 clusters each having 5
observations.
• Reiterations of clustering is
required till when all the
observations are finally allocated
to the respective cluster.

8. DISTANCE COMPUTATION OF COORDINATE POINTS
• Euclidean distance:
• Manhattan distance:
• Mahalanobis distance: A combination of Euclidean and Manhattan distance.

9. METHODS OF CLUSTERING
1. Single linkage method: Measuring the minimum distance between two data
points

10. METHODS OF CLUSTERING
2. Complete linkage method: Measures the maximum distance between two data
points

11. METHODS OF CLUSTERING
3. Average linkage method: Average of all the distance measured between set of
data points