Slide helps in generating an understand about the intuition and mathematics / stats behind association rule mining. This presentation starts by highlighting the difference between causal and correlation. This is followed Apriori algorithm and the metrics which are used with it. Each metric is discussed in detail. Then a formulation has been generated in classification setting which can be used to generate rules i.e. rule mining. Other Reference: https://www.slideshare.net/JustinCletus/mining-frequent-patterns-association-and-correlations

1. Association
Rule Mining

2. Understanding
Association
Rules Mining
Concepts

3. Association Rule Mining
Association rule mining is a
procedure which is meant to find
frequent patterns, correlations,
associations, or causal structures
from datasets found in various
kinds of databases such as
relational databases, transactional
databases, and other forms of data
repositories.
Simply; when this, then also this

4. Association Rule Mining
Used to identify -
● Frequent Patterns
● Correlations
● Associations
● Causal Structures
where these are applied → movie recommendations, grocery item placements, product recommendations, etc.

5. Algorithm - Apriori - Metrics
Following three metrics are generally used -
Support: The percentage of transactions that contain all of the items in an item set.
● The higher the support the more frequently the item set occurs.
● Rules with a high support are preferred since they are likely to be applicable to a large number of future transactions.
Confidence: The probability that a transaction that contains the items on the left hand side of the rule also
contains the item on the right hand side.
● The higher the confidence, the greater the likelihood that the item on the right hand side will be purchased or, in other
words, the greater the return rate we can expect for a given rule.
Lift: The probability of all of the items in a rule occurring together divided by the product of the probabilities
of the items on the left and right hand side occurring as if there was no association between them.
● Overall, lift summarizes the strength of association between the products on the left and right hand
side of the rule; the larger the lift the greater the link between the two products.

6. Apriori - Support

7. Apriori - Support

8. Apriori - Confidence

9. Apriori - Confidence

10. Apriori - Confidence

11. Apriori - Confidence

12. Apriori - Lift

13. Apriori - Lift

14. Apriori - Lift

15. Algorithm
Step 1 Set a minimum & maximum Support and Confidence.
Step 2 Take all the subsets in transactions having higher support than
minimum support.
Step 3 Take all the rules of these subsets having higher confidence than
minimum confidence.
Step 4 Generate other rule assessment measures for the rules.
Step 5 Sort the rules by using an appropriate filter.
Cons → Slow Algorithm as it’s a bottom up approach and makes pair from all
available factors and compute related statistics

16. Another Example

17. Other Rule Assessment Measures
● Added Value
● All-confidence
● Casual Confidence
● Casual Support
● Certainty Factor
● Chi-Squared
● Cross-Support Ratio
● Collective Strength
● Confidence
● Conviction
● Cosine
● Coverage
● Descriptive Confirmed Confidence
● Difference of Confidence
● Example & Counter-Example Rate
● Fisher's Exact Test
● Gini Index
● Hyper-Confidence
● Hyper-Lift
● Imbalance Ratio
● Improvement
● Jaccard Coefficient
● J-Measure
● Kappa
● Klosgen
● Kulczynski
● Goodman-Kruskal Lambda
● Laplace Corrected Confidence
● Least Contradiction
● Lerman Similarity
● Leverage
● Lift
● MaxConf
● Mutual Information
● Odds Ratio
● Phi Correlation Coefficient
● Ralambrodrainy Measure
● Relative Linkage Disequilibrium
● Relative Support
● Rule Power Factor
● Sebag-Schoenauer Measure
● Support
● Varying Rates Liaison
● Yule's Q
● Yule's Y

18. Support, Relative Support
Support:
● Support of a rule is defined as the number of transactions that contain both X and Y.
● Used as a measure of significance of a rule.
Symmetric Measure
Range: [0, INF)
Formula:
Relative Support:
● Relative Support is the fraction of transactions that contain both X and Y.
● ⇒ Empirical Joint Probability of the items comprising the rule.
● Used as a measure of significance of a rule.
Symmetric Measure
Range: [0, 1]
Formula:

19. Support, Relative Support

20. Confidence (a.k.a. Strength)
Confidence:
● Confidence of a rule is the conditional probability that a transaction contains the
consequent Y given that it contains the antecedent X.
● Problem with Confidence is that it is sensitive to the frequency of the consequent Y in the
database.
● Caused by the way the confidence is calculated, consequents with higher support will
automatically produce higher confidence values even if there is no association b/w the
items.
Asymmetric Measure
Range: [0, 1]
Formula:

21. Confidence (a.k.a. Strength)

22. Lift (a.k.a. Interest)
Lift:
● Lift is defined as the ratio of the observed joint probability of X and Y to the expected joint
probability if they were statistically independent.
● Lift is susceptible to noise in small databases.
● Caused by the way the confidence is calculated, rare itemsets with low counts (low
probability) which by chance occur a few times (or only once) together will produce
enormous lift values.
Symmetric Measure
Range: [0, INF) (1 means independence)
Formula:

23. Lift (a.k.a. Interest)

24. Coverage (a.k.a. antecedent support or LHS support)
Coverage:
● Coverage is defined as the relative support of the antecedent X i.e. it is is the fraction of
transactions that contain X.
● ⇒ Empirical Probability of the item X.
● Used as a measure of significance of a rule.
Asymmetric Measure
Range: [0, 1]
Formula:

25. Difference of Confidence
Difference of Confidence:
● .
● .
● .
Asymmetric Measure
Range: [-1, 1]
Formula:

26. Certainty Factor (a.k.a. Loevinger)
Certainty Factor:
● It is a measure of variation of the probability that Y is in transaction when only
considering transactions with X.
● An increasing CF means a decrease of the probability that Y is not in a transaction that X
is in. Negative CFs have a similar interpretation.
Asymmetric Measure
Range: [-1, 1] (0 means independence)
Formula:

27. Leverage
Leverage:
● Leverage measures the difference between the observed and expected joint probability of
XY assuming that X and Y are independent.
● Leverage gives an absolute measure of how surprising a rule is and should be used
together with lift.
● Can be interpreted as gap to independence.
Symmetric Measure
Range: [-1, 1] (0 means independence)
Formula:

28. Leverage
Rule A→ E may be preferable over the first two because it is simpler and has higher leverage

29. Jaccard Coefficient (a.k.a. Coherence)
Jaccard Coefficient:
● This coefficient measure the similarity between two sets.
Symmetric Measure
Range: [-1, 1] (0 means independence)
Formula:

30. Jaccard Coefficient (a.k.a. Coherence)

31. Contingency Table for X and Y

32. Conviction
Conviction:
● Conviction measures the expected error of the rule i.e. how often X occurs in a
transaction where Y does not.
● Thus it can be said that it is a measure of the strength of the rule wrt the complement of
the consequent.
● If the joint probability of X!Y is less than that expected under independence of X and !Y,
then conviction is high, and vice versa.
● An alternative to confidence which was found not to capture direction of association s
adequately.
Asymmetric Measure
Range: [0, INF) (1 means independence, rule that always hold have INF)
Formula:

33. Conviction

34. Odds Ratio
Odds Ratio:
● It is defined as the odds of finding X in transactions which contain Y divided by the odds
of finding X in transactions which do not contain Y.
● Lift is susceptible to noise in small databases.
● Odds ratios greater than 1 imply higher odds of Y occurring in the presence of X as
opposed to its complement !X , whereas odds smaller than one imply higher odds of Y
occurring with !X.
Symmetric Measure
Range: [0, INF) (1 means independence)
Formula:

35. Odds Ratio

36. Mining the patterns to
Develop Rules

37. Filter Used
(CASE
WHEN Itemset only present on BOTH Side THEN (FLOAT(CriticalClass_oddsRatio) - 0)
WHEN Itemset present on BOTH Side THEN (FLOAT(CriticalClass_oddsRatio) - FLOAT(Gen_oddsRatio))
WHEN Itemset only present on GENERAL Side THEN (0 - FLOAT(Gen_oddsRatio)) END) AS Diff_CriticalClassGen_OddsRatio,
Diff_CriticalClassGen_Conviction,
Diff_CriticalClassGen_Supp,
Diff_CriticalClassGen_Certainty,
*
FROM {
| #Handling INFINITY value
|FROM
| Table
|WHERE
| #viewing entries ONLY present on GEN side OR viewing entries ONLY present on CriticalClass side
}
ORDER BY
#rule_rhs desc,
#rule_lhs desc,
Diff_CriticalClassGen_OddsRatio DESC,
Diff_CriticalClassGen_Conviction DESC,
Diff_CriticalClassGen_Supp DESC,
#Diff_CriticalClassGen_Certainty desc,

38. Mining Pattern
Step 1: Run the query.
Step 2: Be creative and with some intuition select some item.
Step 3: Modify the query so that it gives pair with selected
item and again be creative and with intuition select some
item.
Using the discovered pair for further increasing the
pattern
Step a: use the discovered pair as lhs part and run the
query on table with increased rule length.
Step b: Be creative and with some intuition select the
next item.
Using the discovered pair for further analyzing
Step a: Use the existing pair to get raw data and
analyze it.
Step b: Use the existing pair to get derived parameter
data and analyze it (also check for existing critical
class signature + location).
Step c: If discovered pair indeed is adequate and is
finding some critical class, use this signature.
- Testing for FP
- If adequate use it for blocking
Rule Developed

39. Mining the patterns to
Develop Rules
Limitation and Further Work

40. Issues and Fine tuning
● Issues b/c of the data inconsistency in streaming data
● Modifying data Preprocessing for the itemset
●
● Version on Derived Parameters