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unit 3/02_Apriori_Algorithm.md

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+# The Apriori Algorithm
+
+**Apriori** is a classic algorithm to find frequent itemsets.
+
+## Key Principle (Apriori Property)
+> "All non-empty subsets of a frequent itemset must also be frequent."
+- *Meaning*: If `{Beer, Diapers}` is frequent, then `{Beer}` must be frequent and `{Diapers}` must be frequent.
+- **Reverse**: If `{Beer}` is NOT frequent, then `{Beer, Diapers}` cannot be frequent. (This helps us ignore/prune many combinations).
+
+## How it Works
+1. **Scan 1**: Count all single items. Remove those below minimum support.
+2. **Join**: Combine remaining items to make pairs (Size 2).
+3. **Prune**: Remove pairs that contain infrequent items.
+4. **Scan 2**: Count the pairs. Remove those below support.
+5. **Repeat**: Make Size 3 itemsets, Size 4, etc., until no more can be found.
+
+## Example
+**Transactions**:
+1. {Bread, Milk}
+2. {Bread, Diapers, Beer, Eggs}
+3. {Milk, Diapers, Beer, Cola}
+4. {Bread, Milk, Diapers, Beer}
+5. {Bread, Milk, Diapers, Cola}
+
+**Minimum Support = 3**
+
+1. **Count Items**:
+   - Bread: 4 (Keep)
+   - Milk: 4 (Keep)
+   - Diapers: 4 (Keep)
+   - Beer: 3 (Keep)
+   - Cola: 2 (Drop)
+   - Eggs: 1 (Drop)
+
+2. **Make Pairs**:
+   - {Bread, Milk}, {Bread, Diapers}, {Bread, Beer}...
+
+3. **Count Pairs**:
+   - {Bread, Milk}: 3 (Keep)
+   - {Bread, Diapers}: 3 (Keep)
+   - {Milk, Diapers}: 3 (Keep)
+   - {Diapers, Beer}: 3 (Keep)
+   - ...others dropped...
+
+4. **Result**: We found the frequent groups!