1. Lecture 2: Data Mining

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

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).

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

5. Example: Clusters 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

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

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

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.

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.

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!

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. 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

15. 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

16. Decision Trees Example:
Conducted survey to see what customers were interested in new model car
Want to select customers for advertising campaign
training
set

17. One Possibility age<30 city=sf car=van likely unlikely likely

18. Another Possibility car=taurus city=sf age<45 likely unlikely

19. 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

20. Clustering
income
education
age

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

22. Issues Given desired number of clusters? Finding “best” clusters
Are clusters semantically meaningful?

23. Association Rule Mining
transaction id
customer id
products
bought
sales
records:
market-basket
data
Trend: Products p5, p8 often bough together
Trend: Customer 12 likes product p9

24. Association Rule Rule: {p1, p3, p8}
Support: number of baskets where these products appear
High-support set: support  threshold s
Problem: find all high support sets

25. 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;

26. Example
check if
count  s

27. Issues Performance for size 2 rules even bigger! big
Performance for size k rules

28. 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

29. 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.

30. Decision Tree

31. Decision Tree Construction
Employed
Root
Yes No
Class=Not
Default
Node
Balance
<50K
>=50K
Class=Yes
Default
Age
Leaf
<45
>=45
Class=Not
Default
Class=Yes
Default

32. 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.

33. Finding the Best Split Point for Numerical Attributes
The data comes from a IBM Quest synthetic dataset for function 0
Best Split Point
In-core algorithms, such as C4.5, will just online sort the numerical attributes!

34. 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 = pi.
The Gini measure of purity is defined as
Gini (S) = 1 - 
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. k
i- 1
p2i

35. Best Splits (Cont.)
Another measure of purity is the entropy measure, which is defined as
entropy (S) = – 
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(S1, S2, ….., Sr) = 
The information gain due to particular split of S into Si, i = 1, 2, …., r
Information-gain (S, {S1, S2, …., Sr) = purity(S ) – purity (S1, S2, … Sr) k
i- 1
pilog2 pi r
i= 1
|Si|
|S|
purity (Si)

36. 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

37. Decision-Tree Construction Algorithm
Procedure GrowTree (S ) Partition (S ); Procedure Partition (S) if ( purity (S ) > p or |S| < s ) then return; for each attribute A evaluate splits on attribute A; Use best split found (across all attributes) to partition S into S1, S2, …., Sr, for i = 1, 2, ….., r Partition (Si );

38. Finding Association Rules
We are generally only interested in association rules with reasonably high support (e.g. support of 2% or greater)
Naïve algorithm
Consider all possible sets of relevant items.
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

39. 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

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

41. 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;

42. Counting Efficiently
One way:
threshold = 3
sort
count &
remove

43. Counting Efficiently threshold = 3 scan & count remove keep counter
Another way:
threshold = 3
scan &
count
keep counter
array in memory
remove

44. Yet Another Way (1) threshold = 3 scan & hash & count (4) remove
in-memory
hash table
threshold = 3
(4) remove
(2) scan &
remove
(3) scan& count
in-memory
counters
false positive

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

46. Frequent Itemsets Mining
TID
Transactions
100
{ A, B, E }
200
{ B, D }
300
400
{ A, C }
500
{ B, C }
600
700
{ A, B }
800
{ A, B, C, E }
900
{ A, B, C }
1000
{ A, C, E }
Desired frequency 50% (support level)
{A},{B},{C},{A,B}, {A,C}
Down-closure (apriori) property
If an itemset is frequent, all of its subset must also be frequent

47. Lattice for Enumerating Frequent Itemsets
Found to be Infrequent
Pruned supersets

48. Apriori
L0 =  C1 = { 1-item subsets of all the transactions } For ( k=1; Ck  0; k++ ) { * support counting * } for all transactions t  D for all k-subsets s of t if k  Ck s.count++ { * candidates generation * } Lk = { c  Ck | c.count>= min sup } Ck+1 = apriori_gen( Lk ) Answer = UkLk

49. 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!

50. K-Means Clustering

51. K-means Clustering Partitional clustering approach
Each cluster is associated with a centroid (center point)
Each point is assigned to the cluster with the closest centroid
Number of clusters, K, must be specified
The basic algorithm is very simple

52. 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

53. 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

54. 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

55. 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

56. A Simple Problem P×(Nθ) ≤ N Finding frequent items
Given a sequence (x1,…xN) where xi ∈[1,m], and a real number θ between zero and one.
Looking for xi whose frequency > θ
Naïve Algorithm (m counters)
The number of frequent items ≤ 1/θ
Problem: N>>m>>1/θ
P×(Nθ) ≤ N

57. KRP algorithm ─ Karp, et. al (TODS’ 03)
N=30
Θ=0.35
⌈1/θ⌉ = 3
N/ (⌈1/θ⌉) ≤ Nθ

58. Enhance the Accuracy ⌈1/θ⌉ = 3 ε=0.5 Θ(1- ε )=0.175 ⌈1/(θ×ε)⌉ = 6
m=12
N=30
Deletion/Reducing = 9
NΘ>10
Θ=0.35
⌈1/θ⌉ = 3
ε=0.5 Θ(1- ε )=0.175
⌈1/(θ×ε)⌉ = 6
(ε*Θ)N
(Θ-(ε*Θ))N

59. Frequent Items for Transactions with Fixed Length
Each transaction has 2 items
Θ=0.60
⌈1/θ⌉×2= 4