Lecture 3: Data Mining.

Transcription

1 Lecture 3: Data Mining 1 1

2 Roadmap What is data mining? Data Mining Tasks Classification/Decision Tree Clustering Association Mining Data Mining Algorithms Decision Tree Construction Frequent 2-itemsets Frequent Itemsets (Apriori) Clustering/Collaborative Filtering 2 2

3 What is Data Mining? Discovery of useful, possibly unexpected, patterns in data. Subsidiary issues: Data cleansing: detection of bogus data. E.g., age = 150. Visualization: something better than megabyte files of output. Warehousing of data (for retrieval). 3 3

4 Typical Kinds of Patterns 1. Decision trees: succinct ways to classify by testing properties. 2. Clusters: another succinct classification by similarity of properties. 3. Bayes, hidden-markov, and other statistical models, frequent-itemsets: expose important associations within data. 4 4

5 Example: Clusters x x x x x x x x x x x x x x x x x xx x x x x x x x x x x x x x x x x x x x x x x 5 5

6 Applications (Among Many) Intelligence-gathering. Total Information Awareness. Web Analysis. PageRank. Marketing. Run a sale on diapers; raise the price of beer. Detective? 6 6

7 Cultures Databases: concentrate on large-scale (non-mainmemory) data. AI (machine-learning): concentrate on complex methods, small data. Statistics: concentrate on inferring models. 7 7

8 Models vs. Analytic Processing To a database person, data-mining is a powerful form of analytic processing --- queries that examine large amounts of data. Result is the data that answers the query. To a statistician, data-mining is the inference of models. Result is the parameters of the model. 8 8

9 Meaningfulness of Answers A big risk when data mining is that you will discover patterns that are meaningless. Statisticians call it Bonferroni s principle: (roughly) if you look in more places for interesting patterns than your amount of data will support, you are bound to find crap. 9 9

10 Examples A big objection to TIA was that it was looking for so many vague connections that it was sure to find things that were bogus and thus violate innocents privacy. The Rhine Paradox: a great example of how not to conduct scientific research

11 Rhine Paradox --- (1) David Rhine was a parapsychologist in the 1950 s who hypothesized that some people had Extra-Sensory Perception. He devised an experiment where subjects were asked to guess 10 hidden cards --- red or blue. He discovered that almost 1 in 1000 had ESP --- they were able to get all 10 right! 11 11

12 Rhine Paradox --- (2) He told these people they had ESP and called them in for another test of the same type. Alas, he discovered that almost all of them had lost their ESP. What did he conclude? Answer on next slide

13 Rhine Paradox --- (3) He concluded that you shouldn t tell people they have ESP; it causes them to lose it

14 A Concrete Example This example illustrates a problem with intelligencegathering. Suppose we believe that certain groups of evil-doers are meeting occasionally in hotels to plot doing evil. We want to find people who at least twice have stayed at the same hotel on the same day

15 10 9 people being tracked days. The Details Each person stays in a hotel 1% of the time (10 days out of 1000). Hotels hold 100 people (so 10 5 hotels). If everyone behaves randomly (I.e., no evil-doers) will the data mining detect anything suspicious? 15 15

16 Calculations --- (1) Probability that persons p and q will be at the same hotel on day d : 1/100 * 1/100 * 10-5 = Probability that p and q will be at the same hotel on two given days: 10-9 * 10-9 = Pairs of days: 5*

17 Calculations --- (2) Probability that p and q will be at the same hotel on some two days: 5*10 5 * = 5* Pairs of people: 5* Expected number of suspicious pairs of people: 5*10 17 * 5*10-13 = 250,

18 Conclusion Suppose there are (say) 10 pairs of evil-doers who definitely stayed at the same hotel twice. Analysts have to sift through 250,010 candidates to find the 10 real cases. Not gonna happen. But how can we improve the scheme? 18 18

19 Data Mining Tasks Data mining is the process of semi-automatically analyzing large databases to find useful patterns Prediction based on past history Predict if a credit card applicant poses a good credit risk, based on some attributes (income, job type, age,..) and past history Predict if a pattern of phone calling card usage is likely to be fraudulent Some examples of prediction mechanisms: Classification Given a new item whose class is unknown, predict to which class it belongs Regression formulae Given a set of mappings for an unknown function, predict the function result for a new parameter value 19 19

20 Data Mining (Cont.) Descriptive Patterns Associations Find books that are often bought by similar customers. If a new such customer buys one such book, suggest the others too. Associations may be used as a first step in detecting causation E.g. association between exposure to chemical X and cancer, Clusters E.g. typhoid cases were clustered in an area surrounding a contaminated well Detection of clusters remains important in detecting epidemics 20 20

21 Decision Trees Example: Conducted survey to see what customers were interested in new model car Want to select customers for advertising campaign sale custid car age city newcar c1 taurus 27 sf yes c2 van 35 la yes c3 van 40 sf yes c4 taurus 22 sf yes c5 merc 50 la no c6 taurus 25 la no training set 21 21

22 One Possibility Y age<30 N sale custid car age city newcar c1 taurus 27 sf yes c2 van 35 la yes c3 van 40 sf yes c4 taurus 22 sf yes c5 merc 50 la no c6 taurus 25 la no city=sf Y N likely unlikely car=van Y N likely unlikely 22 22

23 Another Possibility Y car=taurus N sale custid car age city newcar c1 taurus 27 sf yes c2 van 35 la yes c3 van 40 sf yes c4 taurus 22 sf yes c5 merc 50 la no c6 taurus 25 la no city=sf Y N likely unlikely age<45 Y N likely unlikely 23 23

24 Issues Decision tree cannot be too deep would not have statistically significant amounts of data for lower decisions Need to select tree that most reliably predicts outcomes 24 24

25 Clustering income education age 25 25

26 Another Example: Text Each document is a vector e.g., < > contains words 1,4,5,... Clusters contain similar documents Useful for understanding, searching documents international news business sports 26 26

27 Issues Given desired number of clusters? Finding best clusters Are clusters semantically meaningful? 27 27

28 Association Rule Mining sales records: transaction id customer id tran1 cust33 p2, p5, p8 tran2 cust45 p5, p8, p11 tran3 cust12 p1, p9 tran4 cust40 p5, p8, p11 tran5 cust12 p2, p9 tran6 cust12 p9 products bought market-basket data Trend: Products p5, p8 often bough together Trend: Customer 12 likes product p

29 Association Rule Rule: {p 1, p 3, p 8 } Support: number of baskets where these products appear High-support set: support threshold s Problem: find all high support sets 29 29

30 Finding High-Support Pairs Baskets(basket, item) SELECT I.item, J.item, COUNT(I.basket) FROM Baskets I, Baskets J WHERE I.basket = J.basket AND I.item < J.item GROUP BY I.item, J.item HAVING COUNT(I.basket) >= s; 30 30

31 Example basket item t1 p2 t1 p5 t1 p8 t2 p5 t2 p8 t2 p basket item1 item2 t1 p2 p5 t1 p2 p8 t1 p5 p8 t2 p5 p8 t2 p5 p11 t2 p8 p check if count s 31 31

32 Issues Performance for size 2 rules big basket item t1 p2 t1 p5 t1 p8 t2 p5 t2 p8 t2 p basket item1 item2 t1 p2 p5 t1 p2 p8 t1 p5 p8 t2 p5 p8 t2 p5 p11 t2 p8 p even bigger! Performance for size k rules 32 32

33 Roadmap What is data mining? Data Mining Tasks Classification/Decision Tree Clustering Association Mining Data Mining Algorithms Decision Tree Construction Frequent 2-itemsets Frequent Itemsets (Apriori) Clustering/Collaborative Filtering 33 33

34 Classification Rules Classification rules help assign new objects to classes. E.g., given a new automobile insurance applicant, should he or she be classified as low risk, medium risk or high risk? Classification rules for above example could use a variety of data, such as educational level, salary, age, etc. person P, P.degree = masters and P.income > 75,000 P.credit = excellent person P, P.degree = bachelors and (P.income 25,000 and P.income 75,000) P.credit = good Rules are not necessarily exact: there may be some misclassifications Classification rules can be shown compactly as a decision tree

35 Decision Tree 35 35

36 Decision Tree Construction NAME Balance Employed Age Default Matt 23,000 No 30 yes Ben 51,100 No 48 yes Chris 68,000 Yes 55 no Jim 74,000 No 40 no David 23,000 No 47 yes John 100,000 Yes 49 no Employed Yes Class=Not Default <50K No Balance Root >=50K Node Leaf Class=Yes Default <45 Age >=45 Class=Not Default Class=Yes Default 36 36

37 Construction of Decision Trees Training set: a data sample in which the classification is already known. Greedy top down generation of decision trees. Each internal node of the tree partitions the data into groups based on a partitioning attribute, and a partitioning condition for the node Leaf node: all (or most) of the items at the node belong to the same class, or all attributes have been considered, and no further partitioning is possible

38 Finding the Best Split Point for Numerical Attributes Complete Class Histograms Counts class-2 class-1 The data comes from a IBM Quest synthetic dataset for function 0 Age Gain Function Best Split Point gain gain function In-core algorithms, such as C4.5, will just online sort the numerical attributes! Age 38 38

39 Best Splits Pick best attributes and conditions on which to partition The purity of a set S of training instances can be measured quantitatively in several ways. Notation: number of classes = k, number of instances = S, fraction of instances in class i = p i. The Gini measure of purity is defined as [ k Gini (S) = 1 - i- - 1 p 2 i When all instances are in a single class, the Gini value is 0 It reaches its maximum (of 1 1 /k) if each class the same number of instances

40 Best Splits (Cont.) Another measure of purity is the entropy measure, which is defined as entropy (S) = p i- 1 ilog 2 p i k i- When a set S is split into multiple sets Si, I=1, 2,, r, we can measure the purity of the resultant set of sets as: purity(s 1, S 2,.., S r ) = r i= = 1 S i S purity (S i ) The information gain due to particular split of S into S i, i = 1, 2,., r Information-gain (S, {S 1, S 2,., S r ) = purity(s ) purity (S 1, S 2, S r ) 40 40

41 Finding Best Splits Categorical attributes (with no meaningful order): Multi-way split, one child for each value Binary split: try all possible breakup of values into two sets, and pick the best Continuous-valued attributes (can be sorted in a meaningful order) Binary split: Sort values, try each as a split point E.g. if values are 1, 10, 15, 25, split at 1, 10, 15 Pick the value that gives best split Multi-way split: A series of binary splits on the same attribute has roughly equivalent effect 41 41

42 Decision-Tree Construction Algorithm Procedure GrowTree (S ) Partition (S ); Procedure Partition (S) if ( purity (S ) > δ p or S < δ s ) then return; for each attribute A evaluate splits on attribute A; Use best split found (across all attributes) to partition S into S 1, S 2,., S r, for i = 1, 2,.., r Partition (S i ); 42 42

43 Finding Association Rules We are generally only interested in association rules with reasonably high support (e.g. support of 2% or greater) Naïve algorithm 1. Consider all possible sets of relevant items. 2. For each set find its support (i.e. count how many transactions purchase all items in the set). Large itemsets: sets with sufficiently high support 43 43

44 Example: Association Rules How do we perform rule mining efficiently? Observation: If set X has support t, then each X subset must have at least support t For 2-sets: if we need support s for {i, j} then each i, j must appear in at least s baskets 44 44

45 Algorithm for 2-Sets (1) Find OK products those appearing in s or more baskets (2) Find high-support pairs using only OK products 45 45

46 Algorithm for 2-Sets INSERT INTO okbaskets(basket, item) SELECT basket, item FROM Baskets GROUP BY item HAVING COUNT(basket) >= s; Perform mining on okbaskets SELECT I.item, J.item, COUNT(I.basket) FROM okbaskets I, okbaskets J WHERE I.basket = J.basket AND I.item < J.item GROUP BY I.item, J.item HAVING COUNT(I.basket) >= s; 46 46

47 Counting Efficiently One way: threshold = 3 basket I.item J.item t1 p5 p8 t2 p5 p8 t2 p8 p11 t3 p2 p3 t3 p5 p8 t3 p2 p sort basket I.item J.item t3 p2 p3 t3 p2 p8 t1 p5 p8 t2 p5 p8 t3 p5 p8 t2 p8 p count & remove count I.item J.item 3 p5 p8 5 p12 p

48 Counting Efficiently Another way: threshold = 3 basket I.item J.item t1 p5 p8 t2 p5 p8 t2 p8 p11 t3 p2 p3 t3 p5 p8 t3 p2 p scan & count count I.item J.item 1 p2 p3 2 p2 p8 3 p5 p8 5 p12 p18 1 p21 p22 2 p21 p remove count I.item J.item 3 p5 p8 5 p12 p keep counter array in memory 48 48

49 Yet Another Way basket I.item J.item t1 p5 p8 t2 p5 p8 t2 p8 p11 t3 p2 p3 t3 p5 p8 t3 p2 p (2) scan & remove false positive (1) scan & hash & count count bucket 1 A 5 B 2 C 1 D 8 E 1 F basket I.item J.item t1 p5 p8 t2 p5 p8 t2 p8 p11 t3 p5 p8 t5 p12 p18 t8 p12 p in-memory hash table threshold = 3 in-memory counters count count I.item J.item 3 p5 p8 1 p8 p11 5 p12 p (3) scan& count I.item J.item 3 p5 p8 5 p12 p (4) remove 49

50 Discussion Hashing scheme: 2 (or 3) scans of data Sorting scheme: requires a sort! Hashing works well if few high-support pairs and many lowsupport ones frequency iceberg queries threshold item-pairs ranked by frequency 50 50

51 Review (1) What s classification problem? What s decision tree? How to build it? What frequent itemset mining problem? How to use SQL to express finding frequent pairs problem? What s the alternatives to find such pairs? 51 51

52 Review (2) Decision Tree Construction NAME Balance Employed Age Default Matt 23,000 No 30 yes Ben 51,100 No 48 yes Chris 68,000 Yes 55 no Jim 74,000 No 40 no David 23,000 No 47 yes John 100,000 Yes 49 no Recursively construct the decision tree Best test condition for a node Categorical attributes, best subset test Numerical attributes, best split point Partition the dataset Leaf Employed Yes Class=Not Default <50K No Class=Yes Default Balance <45 >=50K Age Root Node >=45 Class=Not Default Class=Yes Default 52 52

53 Review (3) Finding High-Support Pairs Baskets(basket, item) SELECT I.item, J.item, COUNT(I.basket) FROM Baskets I, Baskets J WHERE I.basket = J.basket AND I.item < J.item GROUP BY I.item, J.item HAVING COUNT(I.basket) >= s; 53 53

54 Frequent Itemsets Mining TID Transactions Desired frequency 50% (support level) { A, B, E } { B, D } { A, B, E } { A, C } { B, C } { A, C } { A, B } { A, B, C, E } { A, B, C } { A, C, E } {A},{B},{C},{A,B}, {A,C} Down-closure (apriori) property If an itemset is frequent, all of its subset must also be frequent 54 54

55 Lattice for Enumerating Frequent Itemsets null A B C D E AB AC AD AE BC BD BE CD CE DE Found to be Infrequent ABC ABD ABE ACD ACE ADE BCD BCE BDE CDE ABCD ABCE ABDE ACDE BCDE Pruned supersets 55 ABCDE 55

56 Apriori L 0 = C 1 = { 1-item subsets of all the transactions } For ( k=1; C k 0; k++ ) { * support counting * } for all transactions t D for all k-subsets s of t if k C k s.count++ { * candidates generation * } L k = { c C k c.count>= min sup } C k+1 = apriori_gen( L k ) Answer = U k L k 56 56

57 Clustering Clustering: Intuitively, finding clusters of points in the given data such that similar points lie in the same cluster Can be formalized using distance metrics in several ways Group points into k sets (for a given k) such that the average distance of points from the centroid of their assigned group is minimized Centroid: point defined by taking average of coordinates in each dimension. Another metric: minimize average distance between every pair of points in a cluster Has been studied extensively in statistics, but on small data sets Data mining systems aim at clustering techniques that can handle very large data sets E.g. the Birch clustering algorithm! 57 57

58 K-Means Clustering 58 58

59 Hierarchical Clustering Example from biological classification (the word classification here does not mean a prediction mechanism) chordata mammalia reptilia leopards humans snakes crocodiles Other examples: Internet directory systems (e.g. Yahoo!) Agglomerative clustering algorithms Build small clusters, then cluster small clusters into bigger clusters, and so on Divisive clustering algorithms Start with all items in a single cluster, repeatedly refine (break) clusters into smaller ones 59 59

60 Collaborative Filtering Goal: predict what movies/books/ a person may be interested in, on the basis of Past preferences of the person Other people with similar past preferences The preferences of such people for a new movie/book/ One approach based on repeated clustering Cluster people on the basis of preferences for movies Then cluster movies on the basis of being liked by the same clusters of people Again cluster people based on their preferences for (the newly created clusters of) movies Repeat above till equilibrium Above problem is an instance of collaborative filtering, where users collaborate in the task of filtering information to find information of interest 60 60

61 Other Types of Mining Text mining: application of data mining to textual documents cluster Web pages to find related pages cluster pages a user has visited to organize their visit history classify Web pages automatically into a Web directory Data visualization systems help users examine large volumes of data and detect patterns visually Can visually encode large amounts of information on a single screen Humans are very good a detecting visual patterns 61 61

62 Data Streams What are Data Streams? Continuous streams Huge, Fast, and Changing Why Data Streams? The arriving speed of streams and the huge amount of data are beyond our capability to store them. Real-time processing Window Models Landscape window (Entire Data Stream) Sliding Window Damped Window Mining Data Stream 62 62

63 A Simple Problem Finding frequent items Given a sequence (x 1, x N ) where x i [1,m], and a real number θbetween zero and one. Looking for x i whose frequency > θ Naïve Algorithm (m counters) The number of frequent items 1/ θ Problem: N>>m>>1/θ P (Nθ) N 63 63

64 KRP algorithm Karp, et. al (TODS 03) m=12 N=30 Θ=0.35 1/θ = 3 N/ ( 1/θ ) Nθ 64 64

65 Enhance the Accuracy m=12 Θ=0.35 1/θ = 3 Deletion/Reducing = 9 N=30 NΘ>10 ε=0.5 Θ(1- ε )= /(θ ε) = 6 (ε*θ)n (Θ-(ε*Θ))N

66 Frequent Items for Transactions with Fixed Length Each transaction has 2 items Θ=0.60 1/θ 2=