---
title: "Short note: Likelihood and distance"
subject: "Data Mining"
chapter: 3
key: "semester_7/data_mining:likelihood-distance-note"
source: https://www.bctengineer.com/q/semester_7/data_mining/likelihood-distance-note
site: BCT Engineering
---

# Short note: Likelihood and distance

Data Mining · Chapter 3: Classification

- Asked in: 2065 Baisakh; year not given, 3 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_7/data_mining/likelihood-distance-note
- Whole chapter: https://www.bctengineer.com/md/semester_7/data_mining/chapter-3

## Question

Write a short note on Likelihood and Distance (technique/principle).

## Short answer

The likelihood-distance principle states that objects with high likelihood (class probability) or small distance are similar. Likelihood is used in Naive Bayes, distance in KNN, clustering, and outlier detection. Normalization is needed so one attribute does not dominate.

## Answer

**Likelihood and Distance** is a principle of data mining for finding patterns by asking how probable a pattern is and how close the data objects are. It is used by mining techniques to decide membership of an object in a group.

#### Likelihood
Likelihood is the probability (chance) that an object belongs to a class or model, given the data. In classification, we pick the class with the highest likelihood. *Example*: Naive Bayes compares P(X | class)·P(class) for each class. Techniques that follow the "most likely" outcome include Bayesian classification and statistical methods.

#### Distance
Distance is a numeric measure of how far apart two objects are in attribute space, e.g. Euclidean distance d(x, y) = √Σ(xᵢ − yᵢ)². The principle is: **data that are close to each other are alike** and probably belong to the same class or cluster.

#### Use
- **Classification**: K-nearest neighbour gives a new object the class of its closest known objects.
- **Clustering**: objects are grouped so that distance within a cluster is small and distance between clusters is large (k-means, hierarchical).
- **Outlier detection**: objects far from all others, or with very low likelihood, are anomalies.

Attributes should be normalised so that a large-valued attribute does not dominate the distance.

## Check yourself

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

1. In classification, which class does the likelihood principle choose?
   A. The class with the highest likelihood (probability) for the object
   B. The class with the most training records
   C. The class whose centre is farthest away
   D. The class chosen at random
   Answer: A. We pick the class with highest likelihood, e.g. Naive Bayes compares P(X|class)P(class). (Key point: Likelihood)

2. What does the distance principle state?
   A. Data that are far apart are alike
   B. Data that are close to each other are alike and probably in the same class or cluster
   C. Distance has no relation to class
   D. Only categorical data can be compared
   Answer: B. Closeness in attribute space implies similarity. (Key point: Distance principle)

3. Why should attributes be normalised before computing distance?
   A. So that likelihood becomes zero
   B. To make all classes equal in size
   C. So a large-valued attribute does not dominate the distance
   D. To convert distance into probability
   Answer: C. Unscaled large-range attributes would dominate the Euclidean distance. (Key point: Normalisation)

## Related in Data Mining

- [DM techniques; likelihood and distance principle](https://www.bctengineer.com/question.md?key=semester_7%2Fdata_mining%3Adm-techniques-close-data-alike) — Data Mining, chapter 3
- [Likelihood and distance; K-means drawbacks](https://www.bctengineer.com/question.md?key=semester_7%2Fdata_mining%3Alikelihood-distance-clustering-kmeans-drawbacks) — Data Mining, chapter 3
- ["Do as your Neighbor Do" principle](https://www.bctengineer.com/question.md?key=semester_7%2Fdata_mining%3Aneighbor-do-likelihood-distance) — Data Mining, chapter 3

## Related in other subjects

- [Principle of optical distance measurement](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Aoptical-distance-measurement-principle) — Surveying II, chapter 2
- [Tacheometry principle, stadia distance and RL](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Atacheometry-principle-stadia-formula) — Surveying II, chapter 2
- [Optical distance principle, tangential horizontal distance](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Aoptical-principle-tangential-horizontal-distance) — Surveying II, chapter 2