1. Association Rule Mining ARM http://www.cs.ndsu.nodak.edu/~rahal/765/lectures/

2. Lecture Outline Data Mining and Knowledge Discovery Market Basket Research Models Association Rule Mining Apriori Rule Generation Methods To Improve Apriori’s Efficiency Vertical Data Representation

3. What is Data Mining Data mining is the exploration and analysis of large quantities of data in order to discover valid, novel, potentially useful, and ultimately understandable patterns and knowledge in data. Valid: The patterns hold in general. Fargo is in Minnesota ! Novel: We did not know the pattern beforehand. (live in Fargo)  (live in ND) Useful: We can devise actions from the patterns (actionable) Understandable: We can interpret and comprehend the patterns.

4. What Motivated Data Mining? As an evolution in the path of IT 1-Data Collection and Database Creation Primitive File Processing 1960s and earlier 2-Database Management Systems: Hierarchical/Network/Relational database system ERDs SQL Recovery and concurrency control in DBMSs OLTP 1970s-early 1980s

5. 3.1-Advanced Database Systems Object-oriented/object-relational databases Application-oriented databases Spatial, multimedia, scientific, etc … Mid-1980s-present 3.2-Web-based Database Systems XML-based databases systems Web analysis and mining Semantic Web (the whole web as a single XML database) Mid-1990s-present

6. 3.3-Data Warehousing and Data Mining Multi-dimensional Data warehouse and OLAP technology Data Mining and Knowledge Discovery tools to assist people in their decision-making processes Late 1980s-present

7. Why Use Data Mining Today? Market Competition Pressure! “The secret of success is to know something that nobody else knows.” Aristotle Wal-Mart VS K-Mart Right products, right place, right time, and right quantities Personalization, CRM Security, homeland defense Analysis of important application data Bioinformatics Stock market data

8. Human analysis skills are inadequate: Volume and dimensionality of the data High data growth rate Storage Computational power Off-the-shelf software Other factors

9. Where Could All Of This Data Be Coming From? Supermarket scanners Preferred customer cards Sunmart’s MoreCards Credit card transactions Call center records ATM machines Demographic data Sensor networks Cameras Web server logs Customer web site trails Biological data (e.g. MicroArray Experiments for expression levels) Image data

10. Types Of Data/Information Repositories For Data Mining By definition, data mining should be applicable to any kind of information repository Flat files Relational databases data warehouses transactional databases Advanced database systems object-oriented Object-relational

11. Application-oriented databases Multimedia Text Image Video Audio Heterogeneous databases Appear as centralized Independent components managing different parts of the data

12. How Could We Describe Data Numerical : Domain is ordered and can be represented on the continuous real line (e.g. age, income) Continuous? Nominal or categorical : Domain is a finite set without any natural ordering (e.g. occupation, marital status, race) Ordinal : Domain is finite and ordered, (e.g.: grade scale, months in a year)

13. The Knowledge Discovery Process Broader than Data Mining Steps: Identify the problem Data mining Action Evaluation and measurement Deployment and integration into real-life processes and/or applications

14. The Data Mining Step in More Detail Cleaning and integration of various data sources Remove noise and outliers Missing Values (e.g. null values) Noisy data (errors) Inconsistent Data (integration) FirstName and F_Name Selection and transformation of relevant data into appropriate forms Focus on fields of interest Education on salary Create common units Height in cm and inches Generate new fields Discovery of interesting patterns from the data Pattern evaluation to identify the interesting patterns based on some predefined measures Knowledge presentation to communicate the mined knowledge and information to the user mostly through visualization techniques to provide a better view

15. This process can be repeated as needed Data mining systems are expected to handle large amounts of data Analysis of small datasets is sometimes called machine learning SDA – Statistical data analysis. In other words, data mining must be scalable to large data sets Scalability and efficiency

16. Data Mining Original Data Target Data Preprocessed Data Patterns Knowledge Cleaning and integration Selection and transformation Discovery Pattern evaluation Knowledge presentation

17. Data Mining Tasks Characterization the process of summarizing the general characteristics and features of a specific class of data (usually referred to as the target class) Characterizing the items in a store whose sales have decreased by 50% over a certain period of time. There maybe some common characteristics to all those items which we would like to uncover. Produced by a no-longer trusted producer

18. Discrimination Discrimination is very similar to characterization in that it reveals the characteristics of a target class in comparison to those characteristics pertaining to one or more other classes. The target and contrasting classes are specified by user and their data is retrieved from the database before the discrimination process starts. As an example, a user might want to discriminate between the characteristics of the items in a store whose sales have increased by 10% over a certain period of time this year sales have increased by 10% over the same period of time last year.

19. Association Rule Mining The process of discovering association rules among attribute values that exist in a given set of data. Market basket research (MBR) where users are usually interested in mining associations between items in a store by using daily transactions. An example of a rule might be diapers  beer meaning that customers buying diapers are very likely to buy beer. This will give us a good pointer to place diapers next to beer so as to increase sales sometimes people wonder about the strange placement of products in large stores Maternity to infant

20. Classification The process of using a set of training data with known class labels to come up with a model (or function) that predicts the unknown class label of new samples. An example of classification can be found in the banking industry customer characteristics like age, annual income, marital status, etc are used to predict the possibility of approving loan applications (the loan status is the class label). In an initial step, a dataset containing a certain number of customers with known class labels is used to create a classifier which can then be used to predict the class label of a new application ANN Classification is very similar to regression except that the later is applicable to numerical data while the former is applicable to categorical and numerical data.

21. Clustering The is process of grouping data objects into clusters such that intra-cluster similarity is maximized inter-cluster similarity is minimized. In other words, objects within the same clusters are very similar and objects in different clusters are not. E.g. studying collective properties of people at different income levels Cluster people based on incomes Study common properties within clusters Lower income related to lower education

23. Outlier detection Through clustering, we can find groups of objects that behave similarly sometimes, we are only interested in those objects that lie scattered around without behaving similarly to any pattern existing in the data. Those objects are known as outliers as they do not adhere to the patterns defined by the rest of the objects in the dataset. Outlier detection is usually desired in applications where abnormal behavior is of interest such as intrusion detection in networks or terrorist detection in ports of entry not of interest, such as when we clean a dataset from noise

25. Similarity searches given a database of objects, and a “query” object, find all similar objects (neighbours) Google search Given a query which a small document Find all similar documents Ranked order them

26. Final Notes on Data Mining Forms the center of a set of research fields and applications dealing with data analysis: databases, statistics, machine learning, artificial intelligence, information sciences/technology and the like at the same time introduces a lot of new features rendering itself as a separate science. scalability to large datasets

27. Not all types of patterns mined by data mining systems are interesting. Subjective and objective interesting measures.

28. Market Basket Research We will mainly use the Market Basket Research (MBR) application in our ARM description A large set of items, e.g. products sold in a supermarket. A large set of transactions or baskets, each of which contains a small set of the items (called an itemset) bought by a customer during a single visit to a store.

29. The Set Model Data is organized as a "TRANSACTION TABLE" with 2 attributes: TT(Tid, Itemset) A transaction is a customer transaction at a cash register. Each customer is given an identifier, Tid, for every transaction made Itemset is the set of items in the customer's "basket". Note that tuples in TT are not "flat" (each itemset is a "set") i.e. not relational (why?) a transformation can be made to equivalent but normalized models 10c d e 9b d e 8b c e 7b c d 6a d e 5a c e 4a c d 3a b e 2a b d 1a b c TIDAtts

30. The Normalized Set Model Data is organized as a “NORMALIZED TRANSACTION TABLE" with 2 attributes: NTT(Tid,Iid) An itemset is the group of items belonging to the same transaction The TT(Tid, ItemSet) can be "transformed" to NTT(Tid, Iid) and vice versa Could be stored in a database Very deep (10 to 30 tuples) TIDIID 1a 1b 1c 2a 2b 2d 3a 3b 3e 4a 4c 4d 5a 5c 5e 6a 6d 6e 7b 7c 7d 8b 8c 8e 9b 9d 9e 10c d e

31. The Boolean Model: "Boolean Transaction Table“: BTT(Tid, Item-1, Item-2,... Item-n) Tid is a transaction identifier Each column is a particular Item (1 column for each item) a 1  if item is in the basket a 0  if item is not in the basket TT, NTT and BTT are equivalent This is the model mostly chosen for ARM TIDabcde 1 11100 2 11010 3 11001 4 10110 5 10101 6 10011 7 01110 8 01101 9 01011 10 00111

32. Association Rule Mining Association Rule Mining (ARM) finds interesting associations and/or correlation relationships among large sets of data items. Association rules provide information in the form of "if-then" statements. These rules are computed from the data unlike the if-then rules of logic, association rules are probabilistic in nature strength could be measured

33. An association rule defines a relationship of the form: A  C (if A then C) Read as A implies C, where A and C are sets of items in a data set. A called antecedent and C the consequent Given DB, ARM finds all the ARs

34. D = A data set comprising n records (transactions) and m Boolean valued attributes (BTT model) I = The set of m attributes, {i 1,i 2, …,i m }, represented in D. Itemset = Some subset of I. Each record in D is an itemset For all rules A  C: A  I, C  I, and A  C=  (A and C are disjoint).

35. An Example DB Items = 5 I = {a,b,c,d,e} Transactions = 10 D = {{a,b,c}, {a,b,d}, {a,b,e}, {a,c,d}, {a,c,e}, {a,d,e}, {b,c,d}, {b,c,e}, {b,d,e}, {c,d,e}} 10c d e 9b d e 8b c e 7b c d 6a d e 5a c e 4a c d 3a b e 2a b d 1a b c TIDAtts

36. Support of an Itemset Support of an itemset IS is the number of transactions in D containing all items in IS (support of IS={ab} is 3?) Given a support threshold s, sets of items that appear in > s transactions are called frequent itemsets The process is called frequent itemset mining

37. Items={m=milk, c=cheese, p=pepsi, b=bread, j=juice}. Support threshold = 3 transactions. T1 = {m, c, b}T2 = {m, p, j} T3 = {m, b}T4 = {c, j} T5 = {m, p, b}T6 = {m, c, b, j} T7 = {c, b, j}T8 = {b, c} Frequent itemsets: {m}, {c}, {b}, {j}, {m, b}, {c, b}, {j, c}.

38. Support and Confidence of a Rule A  C Support of an itemset IS is the number of transactions containing all items in IS Itemsets are used to derive rules Support of a rule R: A  C is the number of transactions in D containing all items in A U C. Frequent rule Significance of a rule Confidence of a rule is Support(R)/ Support(A) Confident rule Strength of a rule Out of those containing A, how many also contain C Frequent + Confident  Strong

39. Example B1 = {m, c, b}B2 = {m, p, j} B3 = {m, b}B4 = {c, j} B5 = {m, p, b}B6 = {m, c, b, j} B7 = {c, b, j}B8 = {b, c} An association rule: {m, b}  c. What is the confidence? support(m, b, c) = 2 Support(m, b) = 4 Confidence = 2/4 = 50%. And so what does that mean? 50% that contain {m, b} also contain c

40. More On The Problem Definition ARM is a two-step process: Find all frequent itemsets: By definition, each of these itemsets will occur at least as frequently as a pre-determined minimum support threshold Generate strong association rules from the frequent itemsets: By definition, these rules must satisfy the minimum support and minimum confidence thresholds A typical question: “find all strong association rules with support > s and confidence > c.” Given a database D Find all frequent itemsets (F) using s Produce all strong association rules using c

41. Finding F is the most computationally expensive part, once we have the frequent sets generating ARs is straight forward

42. The Anti-Monotonicity (downward- closure) of Support Naïve: generate all subset itemsets of I and test each The number of potential subset itemsets 2 m If m=5, #potential itemsets = 32 If m=20, #potential itemsets 1,048,576 Imagine what would supermarkets have? m = 10,000? Conclusion? Naïve approach is infeasible Breakthrough: If an itemset A has support greater than s then all its subsets must also be have support greater than s example Alternatively if an itemset A is not frequent then none of its supersets will be supported. Proposed by Agrawal 1993 from IBM Almaden Research Center…its started ARM and the field of data mining

43. Apriori Proposed by Agrawal Apriori Uses the downward-closure of support to reduce the number of itemsets that need to be counted (called candidate frequent itemsets C) Works on a level-by-level basis (i.e. uses frequent itemsets L from the previous to generate frequent itemsets at this level) C k and L k At every level k generates C k from L k-1 and counts their frequency in the database

44. Two steps are performed to generate C k Join Step: C k is generated by joining L k-1 with itself Prune Step: all itemsets in C k whose k-1 subsets are not ALL frequent (i.e. present in L k-1 ) are removed How many subsets does an itemset of size k have? 2 k E.g. k=3 How many subsets of size k-1 does an itemset of size k have? k

45. The Apriori Algorithm Pseudo-code: C k : Candidate frequent itemset of size k L k : frequent itemset of size k L 1 = {frequent items}; for (k = 1; L k !=  ; k++) do begin C k+1 = candidates generated from L k ; Remove any itemset from C k+1 that has at least one infrequent k subset for each transaction t in database do increment the counts of all candidates in C k+1 that are contained in t (count the frequency of each itemset in C k+1 ) L k+1 = candidates in C k+1 with min_support end return  k L k ;

46. Example of Generating Candidates Suppose the items in all itemsets are listed in some order L 3 ={abc, abd, acd, ace, bcd} Self-joining: L 3 *L 3 Combine any two itemsets in L k if they only differ by the last item abcd from abc and abd acde from acd and ace C 4 = {abcd, acde} Pruning: abcd: abc, abd, acd, bcd acde: acd, ace, ade, cde C 4 ={abcd}

47. How To Generate Candidates? L k  C k+1 Step 1: self-joining L k insert into C k+1 select p.item 1, p.item 2, …, p.item k, q.item k from L k p, L k q where p.item 1 =q.item 1, …, p.item k-1 =q.item k-1, p.item k < q.item k Step 2: pruning forall itemsets c in C k+1 do forall k-subsets s of c do if (s is not in L k ) then delete c from C k+1

48. An Example – Support 2 Database D Scan D C1C1 C2C2 C2C2 L3L3 C3C3 L1L1 L2L2

49. Generation of Association Rules Given all frequent itemsets Every frequent itemset I of size > 2 is divided into a candidate head Y and a body X such that X intersection Y = {}. This process starts with Y = {}, resulting in the rule I  {} always holds with 100% confidence (why?) After that, the algorithm iteratively generates candidate heads of size k + 1, starting with k = 0

50. Is Apriori Fast Enough? Performance Bottlenecks The core of the Apriori algorithm: Uses frequent (k – 1)-itemsets to generate candidate frequent k- itemsets Uses databases scan to collect counts for the candidate itemset – 1 scan per level The bottleneck of Apriori: candidate generation Huge candidate sets: 10 4 frequent 1-itemset will generate 10 7 candidate 2-itemsets To discover a frequent pattern of size 100, e.g., {a 1, a 2, …, a 100 }, one needs to generate 2 100  10 30 candidates. Multiple scans of database: Needs n scans, n is the length of the longest pattern One scan per level

51. Improving Apriori Transaction reduction Reducing the number of transactions scanned in future iterations A transaction that does not contain any frequent k-itemsets cannot contain any frequent (k+1)- itemsets. E.g. Frequent 1 itemsets {1, 3, 5} Trans = {2,4} As a result, we need not consider it further for subsequent scans of D for l-itemsets where l>k. Saves on scanning times

52. Partitioning Using this approach we only need two database scans to generate all frequent itemsets Good when original DB can’t fit in memory First, we divided D, into n non-overlapping partitions such that each can easily fits into memory. The minimum support threshold (referred to local support threshold) for itemsets in each partition is minsuppxN/|D| (where N is the number of transactions in that partition). For each partition, all frequent itemsets within that partition are found. These are called local frequent itemsets.

53. For each itemset, we record tids of the transactions containing the items in the itemset. As a result, we could find the local frequent itemsets in just one database scan. Local frequent itemsets may not be frequent with respect to the entire database, D; however, any frequent itemset in D must occur as a local frequent itemset in at least one partition Therefore we could use the local frequent itemsets as candidates with respect to D.

54. Second, we scan D to get the support of all candidate itemsets (which have already been generated using the partitions). Partition size and number of partitions are set so that each partition can fit into main memory and therefore be read only once in each phase. Good when original DB can’t fit in memory

55. Sampling This is statistical-based approach the principle that since we can not deal with the whole population, we can get a representative sample (usually random) whose size is much smaller than the population and work with that. The accuracy of approaches used this idea depends on how “representative” the chosen sample is. In short, we select a sample S form D and generate all frequent itemsets in S usually using a lower support threshold than minsupp. Some approaches that follow this idea claim that they can mine all rules using samples.

56. Tries Another data structure that is commonly used is a trie (or prefix-tree). The first approach to ever use tries in ARM is Frequent Pattern Growth (FPGrowth) by Han et al. The idea here is to view each transaction as an ordered string of items. The idea is compress by maximizing overlap between transactions Every k-itemset is attached to its k - 1-prefix. Every node stores the last item in the itemset it represents, its support, and its branches

58. Vertical Data Representation Each item, I, is represented by a bit vector, V I The support of an item is the count of 1s in its vector The support of an itemset {a,b} is the count of 1s in V a & V b

59. TT Layout An Example BTT Layout TID1 2 3 4 5 1001 0 1 1 0 2000 1 1 0 1 3001 1 1 0 1 4000 1 0 0 1 Binary Vertical (BV) Layout D TID1 2 3 4 5 1001 0 1 1 0 2000 1 1 0 1 3001 1 1 0 1 4000 1 0 0 1

60. Support(3) = 3 Support (3,5) = 2 Support (1,3,5) = 1 Just ANDing operations Could be optimized by compression through P-trees Saves time Database D TID1 2 3 4 5 1001 0 1 1 0 2000 1 1 0 1 3001 1 1 0 1 4000 1 0 0 1

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66. Questions ? Thank you !!!