---
title: "Short note: Partitioning clustering"
subject: "Data Mining"
chapter: 5
key: "semester_7/data_mining:partitioning-clustering-note"
source: https://www.bctengineer.com/q/semester_7/data_mining/partitioning-clustering-note
site: BCT Engineering
---

# Short note: Partitioning clustering

Data Mining · Chapter 5: Cluster Analysis

- Asked in: year not given
- Video: [#24 Partitioning Clustering - K Means Algorithm |DM|](https://www.youtube.com/watch?v=190xjQHVdrE) — Trouble- Free
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_7/data_mining/partitioning-clustering-note
- Whole chapter: https://www.bctengineer.com/md/semester_7/data_mining/chapter-5

## Question

Write a short note on 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.

## Answer

**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
1. Choose k and create an initial partition (random or chosen centres).
2. Use **iterative relocation**: move objects from one cluster to another to improve the objective function (e.g. minimise SSE = Σ d(x, centre)²).
3. 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.

```text
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.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. In basic partitioning clustering, which statement is correct?
   A. Each object may belong to many clusters
   B. n objects form k clusters (k <= n), each with at least one object and each object in exactly one cluster
   C. k must be greater than n
   D. Clusters form a tree
   Answer: B. Partitioning divides n objects into k non-overlapping non-empty clusters. (Key point: Definition)

2. What is the working principle?
   A. Create an initial partition, then iteratively relocate objects to improve an objective until no improvement
   B. Merge closest clusters until one remains
   C. Expand dense regions from core points
   D. Build a grid
   Answer: A. Initial partition plus iterative relocation to reduce, for example, SSE. (Key point: Working)

3. Which is a limitation of partitioning clustering?
   A. It is too slow for large data
   B. It does not need k
   C. It reaches only a local optimum and is poor for non-convex clusters
   D. It cannot use means
   Answer: C. It depends on initial choice and suits spherical, similar-sized clusters. (Key point: Limitations)

## Related in Data Mining

- [Need of clustering; hierarchical vs partitioning; K-means](https://www.bctengineer.com/question.md?key=semester_7%2Fdata_mining%3Acluster-need-hier-vs-partition-kmeans) — Data Mining, chapter 5
- [Short note: Partitioning and hierarchical clustering](https://www.bctengineer.com/question.md?key=semester_7%2Fdata_mining%3Apartition-hierarchical-clustering-note) — Data Mining, chapter 5
- [Major clustering approaches](https://www.bctengineer.com/question.md?key=semester_7%2Fdata_mining%3Aclustering-approaches) — Data Mining, chapter 5