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Symmetric and asymmetric data
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.
Explain symmetric and asymmetric data with example.
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 |
✓ Answer checked by Claude Opus 5.5 (high effort)
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