DATA MINING Association Rule Discovery

AR Definition aka Affinity Grouping Common example: Discovery of which items are frequently sold together at a supermarket. If this is known, decisions can be made about: – Arranging items on shelves – Which items should be promoted together – Which items should not simultanously be discounted 2

AR Definition -2- 3

AR Definition -3- Confidence Factor: the degree to which the rule is true across individual records – Confidence Factor = the number of transactions supporting the rule divided by the number of transactions supporting the rule body only – The Confidence Factor in the above example is 70% Support Factor: the relative occurrence of the detected rules within the overall data set of transactions – Support Factor = the number of transactions supporting the rule divided by the total number of transactions – The Support Factor in the above example is thus 13.5% The minimum thresholds for both factors can be set by users or domain experts 4

AR Usefulness Some rules are useful: – unknown, unexpected and indicative of some action to take. Some rules are trivial: – known by anyone familiar with the business. Some rules are inexplicable: – seem to have no explanation and do not suggest a course of action. 5

AR Example : Co-occurrence Table CustomerItems 1orange juice (OJ), cola 2 milk, orange juice, window cleaner 3 orange juice, detergent 4 orange juice, detergent, cola 5 window cleaner, cola OJCleaner MilkColaDetergent OJ Cleaner12110 Milk11100 Cola21031 Detergent

AR Discovery Process A co-occurrence cube would show associations in 3D – it is hard to visualise more dimensions than that – Worse, the number of cells in a co-occurrence hypercube grows exponentially with the number of items: It rapidly becomes impossible to store the required number of cells – Smart algorithms are thus needed for finding frequent large itemsets We would like to: – Choose the right set of items – Generate rules by deciphering the counts in the co-occurrence matrix (for two-item rules) – Overcome the practical limits imposed by many items in large numbers of transactions 7

Choosing the Right Item Set Choosing the right level of detail (the creation of classes and a taxonomy) – For example, we might look for associations between product categories, rather than at the finest-grain level of product detail, e.g. “Corn Chips” and “Salsa”, rather than “Doritos Nacho Cheese Corn Chips (250g)” and “Masterfoods Mild Salsa (300g)” – Important associations can be missed if we look at the wrong level of detail Virtual items may be added to take advantage of information that goes beyond the taxonomy 8

AR: Rules Note: if (nappies and Thursday) then beer is usually better than (in the sense that it is more actionable) if Thursday then nappies and beer because it has just one item in the result. If a 3-way combination is the most common, then perhaps consider rules with just 1 item in the consequent, e.g. if (A and B) then C if (A and C) then B 9 if condition then result

Discovering Large Itemsets The term “frequent item set S” means “a set S that appears in at least fraction s of the baskets,” where s is some chosen constant, typically 0.01 (i.e. 1%). DM datasets are usually too large to fit in main memory. When evaluating the running time of AR discovery algorithms we: – count the number of passes through the data Since the principal cost is often the time it takes to read data from disk, the number of times we need to read each datum is often the best measure of running time of the algorithm. 10

Discovering Large Itemsets -2- There is a key principle, called monotonicity or the a- priori algorithm that helps us find frequent itemsets [AgS1994]: If a set of items S is frequent (i.e., appears in at least fraction s of the baskets), then every subset of S is also frequent. To find frequent itemsets, we can: – Proceed level-wise, finding first the frequent items (sets of size 1), then the frequent pairs, the frequent triples, etc. ¾ Level-wise algorithms use one pass per level. – Find all maximal frequent itemsets (i.e., sets S such that no proper superset of S is frequent) in one (or few) passes 11

The Apriori Algorithm The A-priori algorithm proceeds level-wise. Given support threshold s, in the first pass we find the items that appear in at least fraction s of the baskets. This set is called L1, the frequent 1-itemsets (Presumably there is enough main memory to count occurrences of each item, since a typical store sells no more than 100,000 different items.) Pairs of items in L1 become the candidate pairs C2 for the second pass. The pairs in C2 whose count reaches s become L2, the frequent 2-itemsets. (We hope that the number of C2 is not so large that there is not enough memory for an integer count per candidate pair) 12

The Apriori Algorithm -2- The candidate triples, C3 are those sets {X, Y, Z} such that all of {X, Y}, {X, Z} and {Y, Z} are in L2. On the third pass, count the occurrences of triples in C3; those with a count of at least s are the frequent triples, L3. Proceed as far as you like (or until the sets become empty). Li is the frequent sets of size i; C(i+1) is the set of sets of size i + 1 such that each subset of size i is in Li. The pruning using the Apriori property: – All nonempty subsets of a frequent itemset must also be frequent. – This helps because it means that the number of sets which must be considered at each level is much smaller than it otherwise would be. 13

Generating Association Rules from Frequent Itemsets Once the frequent itemsets from transactions in a database D have been found, it is straightforward to generate strong associations rules from them – Where strong association rules satisfy both minimum support and minimum confidence Step 1: For each frequent itemset L, generate all nonempty subsets of L Step 2: For each nonempty subset U of L, output the rule: 14

Generating Association Rules from Frequent Itemsets –Example 1- Suppose we have the following transactional data from a store= Suppose that the data contain the frequent itemset L = {I1, I2, I5}. What are the association rules that can be generated from L? 15

Generating Association Rules from Frequent Itemsets –Example 2- The nonempty subsets of L are {I1,I2}, {I1,I5}, {I2,I5}, {I1}, {I2}, {I5}. The resulting association rules are thus: Suppose the minimum confidence threshold is 70%. Hence, only the second, third and last rules above are output – Since these are the only ones generated that are strong 16

Limitation of Minimum Support Discontinuity in ‘interestingness’ function Feast or famine – minimum support is a crude control mechanism – often results in too few or too many associations Cannot handle dense data Cannot prune search space using constraints on relationship between antecedent and consequent – egconfidence Minimum support may not be relevant – cannot be sufficiently low to capture all valid rules – cannot be sufficiently high to exclude all spurious rules 17

Roles of Constraint Select most relevant patterns – patterns that are likely to be interesting Control the number of patterns that the user must consider Make computation feasible 18

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AR: Is the Rule a Useful Predictor? Confidence Factor is the ratio of the number of transactions with all the items in the rule to the number of transactions with just the items in the condition (rule body). Consider: if B and C then A If this rule has a confidence of 0.33, it means that when B and C occur in a transaction, there is a 33% chance that A also occurs. 20

AR: Is the Rule a Useful Predictor?-2- Consider the following table of probabilities of items and their combinations: 21

AR: Is the Rule a Useful Predictor?-3- Now consider the following rules: It is tempting to choose “If B and C then A”, because it is most confident(33%) – but there is a problem 22

AR: Is the Rule a Useful Predictor? A measure called lift indicates whether the rule predicts the result better than just assuming the result in the first place

AR: Is the Rule a Useful Predictor?-5- When lift > 1, the rule is better at predicting the result than random chance The lift measure is based on whether or not the probability P(condition& result) is higher than it would be if condition and result were statistically independent If there is no statistical dependence between condition and result, improvement = 1. – Because in this case: P(condition & result) = P(condition) × P(result) 24

AR: Is the Rule a Useful Predictor?-6- Consider the lift for our rules: Rulesupportconfidencelift if A and B then C if A and C then B if B and C then A if A then B None of the rules with three items shows any lift - the best rule in the data actually has only two items: “if A then B”. A predicts the occurrence of B 1.31 times better than chance. 25

AR: Is the Rule a Useful Predictor? When lift < 1, negating the result produces a better rule. For example if B and C thennot A has a confidence of 0.67 and thus an lift of 0.67/0.55 = 1.22 Negated rules may not be as useful as the original association rules when it comes to acting on the results