Mining Diverse Patterns

@(Pattern Discovery in Data Mining)

Mining Diverse Patterns
- - Mining Multi-level Association Rules
  - Mining Multi-dimensional Associations
  - Mining Quantitative Associations
  - Mining Negative Correlations
  - Mining Compressed Patterns
  - Mining Colossal Patterns

Mining Multi-level Association Rules

The intuition to set hierarchical min_sup: Level-reduced min-support (Items at the lower level are expected to have lower support)

Efficient mining: Shared multi-level mining (Use the lowest min-support to pass down the set of candidates)

Redundancy Filtering at Mining Multi-Level Associations:

* Multi-level association mining may generate many redundant rules

* Redundancy filtering: Some rules may be redundant due to “ancestor” relationships between items

* (Suppose the 2% milk sold is about 1?4 of milk sold in gallons)

1. milk → wheat bread [support = 8%, confidence = 70%]

2. 2% milk → wheat bread [support = 2%, confidence = 72%]

A rule is redundant if its support is close to the “expected” value, according to its “ancestor” rule, and it has a similar confidence as its “ancestor”
Rule (1) is an ancestor of rule (2), so rule(2) is to prune.

Customized Min-Supports for Different Kinds of Items

* We have used the same min-support threshold for all the items or item sets to be mined in each association mining

* In reality, some items (e.g., diamond, watch, …) are valuable but less frequent

* It is necessary to have customized min-support settings for different kinds of items

* One Method: Use group-based “individualized” min-support

* E.g., {diamond, watch}: 0.05%; {bread, milk}: 5%; …

* How to mine such rules efficiently?

* Existing scalable mining algorithms can be easily extended to cover such cases

Mining Multi-dimensional Associations

Single-dimensional rules (e.g., items are all in “product” dimension)
- buys(X, “milk”) → buys(X, “bread”)
Multi-dimensional rules (i.e., items in ≥ 2 dimensions or predicates)
- Inter-dimension association rules (no repeated predicates)
  - age(X, “18-25”) ∧ occupation(X, “student”) → buys(X, “coke”)
- Hybrid-dimension association rules (repeated predicates)
  - age(X, “18-25”) ∧ buys(X, “popcorn”) → buys(X, “coke”)
Attributes can be categorical or numerical
- Categorical Attributes (e.g., profession, product: no ordering among values): Data cube for inter-dimension association
- Quantitative Attributes: Numeric, implicit ordering among values— discretization, clustering, and gradient approaches

Mining Quantitative Associations

Mining Negative Correlations

Rare Pattern vs. Negative Pattern
Defining Negative Correlated Patterns
Support-based definition
Kulczynski measure-based difinision
Exercise

Mining Compressed Patterns

Given a table of patterns and their supports:

Why mining compressed patterns? Since there are too many scattered patterns but not so meaningful.

We can find that P1 and P2 are similar both in item-sets and support, and so do P1 and P5 with similar item-sets. But how to compressed those similar patterns?

We can also analyze about it that:

* Closed patterns

* P1, P2, P3, P4, P5(all have no identical supports)

* Emphasizes too much on support

* There is no compression

* Max-patterns

* P3: information loss

* Desired output (a good balance):

* P2, P3, P4

So we can define some compressing method

pattern distance measure

Dist(P1,P2)=1?|T(P1)∪T(P2)||T(P1)∩T(P2)|
- δ-clustering: For each pattern P, find all patterns which can be expressed by P and whose distance to P is within δ (δ-cover)
- All patterns in the cluster can be represented by P
- Method for efficient, direct mining of compressed frequent patterns (e.g., Xin et al., VLDB’05)
Redundancy-Aware Top-k Patterns