What does 'iterative relocation' mean in partitioning clustering?

Objects are moved between clusters again and again to improve an objective

Clusters are merged one pair at a time until one remains

The dendrogram is cut at different heights

Each object is copied into several clusters

Why is k-medoids (PAM) more robust to outliers than k-means?

Its centre is an actual object (medoid), not an average pulled by extreme values

It uses the mean of the cluster as the centre

How does hierarchical clustering give a desired number of clusters without k being specified in advance?

By cutting the dendrogram at the desired level

By running k-means several times

By moving objects between clusters

Which statement about undoing steps is correct?

Hierarchical merges/splits cannot be undone, but partitioning can move objects between clusters

Partitioning cannot undo, hierarchical can

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Short note: Partitioning and hierarchical clustering

Short answer

Partitioning methods like k-means divide data into k clusters via iterative relocation; hierarchical builds a dendrogram by agglomeration or division. Partitioning needs k, is faster but may be a local optimum; hierarchical requires no k, O(n²), merges irreversible.

Write a short note on Partitioning and Hierarchical Clustering.

Partitioning clustering

It divides n objects into k non-overlapping groups (k ≤ n), each with at least one object. An initial partition is created, then objects are moved between clusters again and again (iterative relocation) to improve an objective, such as minimum sum of squared distances to the cluster centres.

k-means: the cluster centre is the mean.
k-medoids (PAM): the centre is an actual object (medoid), more robust to outliers.
Needs k in advance; suits spherical clusters; efficient for large data (O(nkt)); may reach a local optimum.

Hierarchical clustering

It builds a hierarchy of clusters, drawn as a dendrogram, with no need to give k in advance (cut the dendrogram at the desired level).

Agglomerative (AGNES): bottom-up; start with each object as a cluster and repeatedly merge the two closest clusters.
Divisive (DIANA): top-down; start with one cluster and repeatedly split.
Cluster distance: single link (minimum), complete link (maximum), average link, centroid.
A merge or split cannot be undone; cost at least O(n²).

 a b c d e          Agglomerative ->
 (a)(b)(c)(d)(e)  -> (ab)(c)(de) -> (abc)(de) -> (abcde)
                          <- Divisive

Basis	Partitioning	Hierarchical
Result	Flat k clusters	Tree of clusters
k	Needed	Not needed
Speed	Faster	Slower
Undo	Possible	Not possible

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