---
title: "Symmetric and asymmetric data"
subject: "Data Mining"
chapter: 1
key: "semester_7/data_mining:symmetric-asymmetric-data"
source: https://www.bctengineer.com/q/semester_7/data_mining/symmetric-asymmetric-data
site: BCT Engineering
---

# Symmetric and asymmetric data

Data Mining · Chapter 1: Introduction

- Asked in: year not given
- Video: [5.8 Proximity measure for binary Attributes](https://www.youtube.com/watch?v=ug1FrhwG5-s) — OU Education
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_7/data_mining/symmetric-asymmetric-data
- Whole chapter: https://www.bctengineer.com/md/semester_7/data_mining/chapter-1

## Question

Explain symmetric and asymmetric data with example.

## Short answer

Symmetric binary data treats both values equally (e.g., gender), using simple matching coefficient. Asymmetric binary data codes the rare/important outcome as 1 (e.g., disease positive), ignoring 0-0 matches, using Jaccard coefficient.

## Answer

In data mining, the terms symmetric and asymmetric usually describe whether the two values of a binary attribute are equally important.

#### Symmetric binary data
Both values (states) of the attribute are **equally important**, so it does not matter which one is coded 1 and which 0. When comparing objects, a match on either value counts the same.
Example: gender (male/female), or yes/no for "has a bank account". Similarity measure: simple matching coefficient = (q + t) / (q + r + s + t).

#### Asymmetric binary data
The two values are **not equally important**: the rarer or more important outcome is coded 1 (positive), and a match on 0 (negative) carries no information. Only 1-1 matches count.
Example: medical test results, positive (1) vs negative (0) for a disease; or presence of an item in a market basket (1 = bought, 0 = not bought). Similarity measure: Jaccard coefficient = q / (q + r + s), which ignores the 0-0 matches (t).

Here q = number of attributes where both objects are 1, r and s = numbers where they differ (1-0 and 0-1), and t = number where both are 0.

| Point | Symmetric | Asymmetric |
|---|---|---|
| Value importance | Equal | Unequal |
| 0-0 match | Counted | Ignored |
| Measure | Simple matching | Jaccard |

## Check yourself

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

1. In a symmetric binary attribute:
   A. Both values are equally important
   B. Only 1 matters
   C. 0 matters more
   D. Values cannot be coded
   Answer: A. Example: gender; either match counts the same. (Key point: Symmetric binary)

2. Which measure is used for asymmetric binary data?
   A. Simple matching coefficient
   B. Jaccard coefficient q/(q+r+s)
   C. (q+t)/(q+r+s+t)
   D. Euclidean distance
   Answer: B. Jaccard ignores 0-0 matches. (Key point: Asymmetric measure)

3. How are 0-0 matches treated in asymmetric data?
   A. Counted fully
   B. Ignored
   C. Doubled
   D. Treated as 1-1
   Answer: B. Only 1-1 matches carry information. (Key point: 0-0 matches)

## Related in other subjects

- [Symmetric vs asymmetric key encryption](https://www.bctengineer.com/question.md?key=semester_7%2Fcomputer_networks_and_security%3Asymmetric-vs-asymmetric) — Computer Networks and Security, chapter 8, asked 3×
- [Asymmetric vs symmetric DSL; ADSL modems](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Aasync-sync-dsl-adsl-modems) — Telecommunications, chapter 8