FPMax

Finds only maximal frequent itemsets - excludes any itemset that is a subset of another frequent itemset.

When to Use FPMax

• Need compact representation
• Only care about longest patterns
• Want to reduce output size
• Don't need all frequent itemsets

Strengths

• Compact output (fewer itemsets)
• Faster than finding all itemsets
• Reduces redundancy significantly
• Easier to review results
• Lower memory for storing results

Weaknesses

• Loses subset information
• May miss useful smaller patterns
• Cannot derive all rules from maximal itemsets alone
• Less comprehensive than other algorithms

How it Works

FPMax extends the FP-Growth algorithm to find only maximal itemsets:

1. Use FP-tree structure like FP-Growth
2. During mining, check if itemset is maximal
3. Skip itemsets that are subsets of known frequent itemsets
4. Only output itemsets that are not contained in any larger frequent itemset

Key Principle: A maximal frequent itemset is one that is frequent, but none of its immediate supersets are frequent.

What are Maximal Itemsets?

Definition: An itemset is maximal if it is frequent AND no superset of it is frequent.

Example:

All Frequent Itemsets:

[A]: support 0.5
[B]: support 0.4
[C]: support 0.3
[A, B]: support 0.3
[A, C]: support 0.25
[B, C]: support 0.2
[A, B, C]: support 0.15

Maximal Itemsets Only:

[A, B, C]: support 0.15

The maximal itemset [A, B, C] implies that [A], [B], [C], [A, B], [A, C], and [B, C] are also frequent (by the Apriori property). FPMax only returns the longest pattern.

Trade-off: You lose the individual support values for subsets. You know they're frequent, but not how frequent.

When to Choose FPMax

Best for:

• Exploratory analysis with many items
• Need to identify "full patterns" only
• Want manageable number of results
• Don't need support for every subset
• Storage or output size is a concern

Don't use FPMax when:

• Need support values for subsets
• Want to generate all possible rules
• Need comprehensive pattern analysis
• Smaller patterns are important for your use case

Parameters

All association algorithms share these common parameters:

Data Format

Input Format: 'long' or 'wide'

How your transaction data is structured:

Wide Format:

• Each column represents one item
• Each row is a transaction
• Values are 1 (item present) or 0 (item absent)
• Example:

  TransactionID | Bread | Milk | Eggs | Butter
  1             | 1     | 1    | 0    | 1
  2             | 0     | 1    | 1    | 0

Long Format:

• Each row is one item in a transaction
• Requires Transaction ID column to group items
• More natural for real-world data
• Example:

  TransactionID | Item
  1             | Bread
  1             | Milk
  1             | Butter
  2             | Milk
  2             | Eggs

Feature Configuration

Feature Columns (required)

• Wide format: List all item columns
• Long format: Select the single column containing item names

Transaction ID Column (required for long format) Column that identifies which transaction each item belongs to.

Contains Multiple Items (long format only) Check if a single row can contain multiple items (e.g., "Bread, Milk, Eggs").

Item Separator (if multiset) Character separating multiple items (default: comma).

• Example: "Bread, Milk, Eggs" uses "," as separator

Segmentation (Optional)

Segmentation Column Analyze different customer segments separately:

• Store locations (downtown vs. suburban)
• Customer types (premium vs. regular)
• Time periods (weekday vs. weekend)

Target Segment Value Filter to analyze only specific segment.

Model Parameters

Minimum Support (default: 0.02, required) Threshold for how frequently an itemset must appear.

• 0.02 = 2% of transactions
• Lower values: Find rare patterns, but slower and more results
• Higher values: Only common patterns, faster
• Recommendations:
  • Large stores (>10k transactions): 0.001-0.01 (0.1%-1%)
  • Medium stores: 0.01-0.05 (1%-5%)
  • Small datasets: 0.05-0.1 (5%-10%)

Maximum Itemset Length (default: 3, required) Maximum number of items in a pattern.

• 2: Pairs only (A -> B)
• 3: Triples (A, B -> C)
• 4+: Complex patterns (slower, harder to interpret)
• Recommendations:
  • Start with 2-3 for interpretability
  • Increase only if needed

Rule Evaluation Metric (default: "lift", required) How to measure rule strength:

• lift: Strength of association (recommended)
• confidence: Reliability of rule
• leverage: Lift adjusted by item frequencies
• conviction: Dependency strength

Metric Threshold (default: 1.2, required) Minimum value for the selected metric to keep a rule.

• For lift: >1.0 (1.2 = 20% more likely)
• For confidence: 0.5-0.9 (50%-90% probability)

Advanced Filtering (Optional)

Enable Advanced Filtering Set both confidence and lift thresholds simultaneously for stricter rules.

Minimum Confidence (default: 0.6) Probability that Y is purchased given X is purchased.

• 0.6 = 60% of transactions with X also have Y
• Range: 0.1-1.0

Minimum Lift (default: 1.1) How much more likely Y is with X versus without X.

• 1.0 = No association (independent)
• 1.1 = 10% increase in likelihood
• 2.0 = 2x more likely
• Range: >0.0 (typically >1.0 for meaningful rules)

Understanding Association Metrics

Support

Definition: How frequently an itemset appears in the database.

Formula: support(X) = (transactions containing X) / (total transactions)

Example:

• 100 transactions total
• [Bread, Milk] appears in 20 transactions
• support([Bread, Milk]) = 20/100 = 0.2 = 20%

Interpretation:

• 0.01 (1%): Rare pattern
• 0.05 (5%): Moderate frequency
• 0.2 (20%): Very common pattern

Use: Filter out rare, potentially spurious patterns

Confidence

Definition: Probability of finding Y in transactions that contain X.

Formula: confidence(X -> Y) = support(X U Y) / support(X)

Example:

• support([Bread]) = 0.5 (50% of transactions)
• support([Bread, Butter]) = 0.3 (30% of transactions)
• confidence(Bread -> Butter) = 0.3 / 0.5 = 0.6 = 60%

Interpretation:

• 0.6 = 60% of customers who buy bread also buy butter
• Higher confidence = more reliable rule

Limitation: Can be misleading if Y is very common

Lift

Definition: How much more likely Y is with X versus without X.

Formula: lift(X -> Y) = confidence(X -> Y) / support(Y)

Example:

• confidence(Bread -> Butter) = 0.6
• support(Butter) = 0.4 (40% buy butter overall)
• lift(Bread -> Butter) = 0.6 / 0.4 = 1.5

Interpretation:

• lift = 1.0: No association (X and Y are independent)
• lift > 1.0: Positive association (Y more likely with X)
  • 1.5 = 50% increase in likelihood
  • 2.0 = 2x more likely (100% increase)
• lift < 1.0: Negative association (Y less likely with X)

Why Lift is Best for Discovery:

• Accounts for item popularity
• Detects true associations vs. coincidence
• Symmetric: lift(X -> Y) = lift(Y -> X)

Leverage

Definition: Difference between observed and expected co-occurrence.

Formula: leverage(X -> Y) = support(X U Y) - support(X) x support(Y)

Example:

• support([Bread, Butter]) = 0.3 (observed)
• support(Bread) x support(Butter) = 0.5 x 0.4 = 0.2 (expected if independent)
• leverage = 0.3 - 0.2 = 0.1

Interpretation:

• 0: No association
• Positive: Items appear together more than expected
• Negative: Items appear together less than expected
• Magnitude matters: Higher absolute value = stronger relationship

Conviction

Definition: Dependency measure - how much more Y depends on X.

Formula: conviction(X -> Y) = (1 - support(Y)) / (1 - confidence(X -> Y))

Example:

• support(Butter) = 0.4
• confidence(Bread -> Butter) = 0.6
• conviction = (1 - 0.4) / (1 - 0.6) = 0.6 / 0.4 = 1.5

Interpretation:

• 1.0: No association (independent)

• 1.0: Y depends on X

• infinity: Perfect dependency (always Y when X)

Use: Measures how much the rule deviates from independence

Configuration Tips

Best Practices for FPMax

When to Use:

• Exploratory data analysis with many items
• Need high-level patterns only
• Output size is a concern
• Want to quickly identify major patterns

Recommended Settings:

• min_support = 0.02-0.05 (find substantial patterns)
• max_length = 3-4 (allow longer maximal patterns)
• Focus on interpretation of longest patterns

Understanding Output:

• Expect significantly fewer itemsets
• Each maximal itemset represents a "family" of subsets
• All subsets of maximal itemsets are also frequent
• You lose individual support values for subsets

Comparing Output Size

Example with 1000 items, min_support = 0.01:

All Frequent Itemsets (FP-Growth):

• 1-itemsets: 500
• 2-itemsets: 5,000
• 3-itemsets: 10,000
• Total: 15,500 itemsets

Maximal Itemsets (FPMax):

• Total: ~200 maximal itemsets

Reduction: 98.7% fewer itemsets to review

Common Issues and Solutions

Missing Useful Smaller Patterns

Symptom: Important 2-itemsets not visible in results

Explanation: FPMax only shows maximal itemsets. Smaller patterns are implied but not reported.

Solutions:

• If you need smaller patterns, use FP-Growth instead
• Manually derive subsets from maximal itemsets
• Use FPMax for overview, then FP-Growth for details
• Consider whether you truly need all subsets

Fewer Rules than Expected

Symptom: Rule generation produces very few rules

Explanation: Rules are only generated from maximal itemsets, losing many potential rules.

Solutions:

• FPMax is not ideal for comprehensive rule mining
• Use FP-Growth or Apriori for full rule generation
• FPMax is best for pattern discovery, not rule mining
• Consider FPMax for exploration, then switch algorithms

Cannot Reconstruct Subset Support

Symptom: Need support values for subsets of maximal itemsets

Explanation: FPMax doesn't report subset supports

Solutions:

• Use FP-Growth instead if you need all support values
• FPMax provides guarantee subsets are frequent, but not how frequent
• Cannot reliably estimate subset support from maximal itemset
• This is a fundamental limitation of maximal mining

Too Few Maximal Itemsets Found

Symptom: FPMax returns very few or no itemsets

Solutions:

• Lower min_support (common cause)
• Increase max_length (maximal itemsets tend to be longer)
• Verify data format and preprocessing
• Check if dataset truly has longer frequent patterns

Unexpected Maximal Itemsets

Symptom: Maximal itemsets seem wrong or surprising

Verification Steps:

• Run FP-Growth to see all frequent itemsets
• Manually verify maximal itemsets have frequent subsets
• Check that no superset of maximal itemset is frequent
• Validate against domain knowledge

Common Cause: Low max_length setting artificially limits maximality. Increase max_length to see truly maximal patterns.