In basic partitioning clustering, which statement is correct?

n objects form k clusters (k <= n), each with at least one object and each object in exactly one cluster

Each object may belong to many clusters

What is the working principle?

Create an initial partition, then iteratively relocate objects to improve an objective until no improvement

Merge closest clusters until one remains

Expand dense regions from core points

Which is a limitation of partitioning clustering?

It reaches only a local optimum and is poor for non-convex clusters

Year not given

Short note: Partitioning clustering

Short answer

Partitioning clustering divides n objects into k clusters by iteratively relocating points to minimize an objective like SSE. Main algorithms include K-means (centroid-based), K-medoids (medoid-based, robust to noise), and K-modes (categorical data). It requires k in advance, is efficient O(nkt), but finds spherical clusters and depends on initialization.

Write a short note on Partitioning Clustering.

Partitioning clustering divides a data set of n objects into k clusters (k ≤ n), where each cluster has at least one object and each object belongs to exactly one cluster (in the basic form). Objects in a cluster should be close to each other and far from objects in other clusters.

Working

Choose k and create an initial partition (random or chosen centres).
Use iterative relocation: move objects from one cluster to another to improve the objective function (e.g. minimise SSE = Σ d(x, centre)²).
Stop when no further improvement occurs.

Main algorithms

K-means: each cluster is represented by the mean (centroid). Fast, but sensitive to outliers.
K-medoids (PAM): each cluster is represented by an actual object (medoid), so it is robust to noise; costly for large data (CLARA and CLARANS scale better).
K-modes for categorical data.

Initial centres -> assign objects to nearest centre
      ^                         |
      |                         v
 recompute centres  <-  clusters formed (repeat till stable)

Features

Needs k in advance; efficient on large data (O(nkt)); gives spherical, similar-sized clusters.
Depends on initial choice; reaches a local, not global, optimum.
Not good for non-convex clusters or very different sizes.

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Short note: Partitioning clustering

Working

Main algorithms

Features

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