Lecture 2: Data Mining

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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

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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).

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Typical Kinds of Patterns1. 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.

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Example: Clusters

5

x xx x x xx x x x

x x xx x

xxx x

x x x x x

xx x x

x

x xx x x x x x x

x

x

x

Applications (Among Many)• Intelligence-gathering.

– Total Information Awareness.• Web Analysis.

– PageRank.• Marketing.

– Run a sale on diapers; raise the price of beer.• Detective?

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Cultures

• Databases: concentrate on large-scale (non-main-memory) data.

• AI (machine-learning): concentrate on complex methods, small data.

• Statistics: concentrate on inferring models.

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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.

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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.

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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.

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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!

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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.

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Rhine Paradox --- (3)

• He concluded that you shouldn’t tell people they have ESP; it causes them to lose it.

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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

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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

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Decision Trees

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sale custId car age city newCarc1 taurus 27 sf yesc2 van 35 la yesc3 van 40 sf yesc4 taurus 22 sf yesc5 merc 50 la noc6 taurus 25 la no

Example:• Conducted survey to see what customers were interested in new model car• Want to select customers for advertising campaign

trainingset

One Possibility

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sale custId car age city newCarc1 taurus 27 sf yesc2 van 35 la yesc3 van 40 sf yesc4 taurus 22 sf yesc5 merc 50 la noc6 taurus 25 la no

age<30

city=sf car=van

likely likelyunlikely unlikely

YY

Y

NN

N

Another Possibility

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sale custId car age city newCarc1 taurus 27 sf yesc2 van 35 la yesc3 van 40 sf yesc4 taurus 22 sf yesc5 merc 50 la noc6 taurus 25 la no

car=taurus

city=sf age<45

likely likelyunlikely unlikely

YY

Y

NN

N

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

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Clustering

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age

income

education

Another Example: Text• Each document is a vector

– e.g., <100110...> contains words 1,4,5,...• Clusters contain “similar” documents• Useful for understanding, searching documents

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internationalnews

sports

business

Issues

• Given desired number of clusters?• Finding “best” clusters• Are clusters semantically meaningful?

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Association Rule Mining

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tran1 cust33 p2, p5, p8tran2 cust45 p5, p8, p11tran3 cust12 p1, p9tran4 cust40 p5, p8, p11tran5 cust12 p2, p9tran6 cust12 p9

transactio

n

id custo

mer

id products

bought

salesrecords:

• Trend: Products p5, p8 often bough together• Trend: Customer 12 likes product p9

market-basketdata

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

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Finding High-Support Pairs• Baskets(basket, item)• SELECT I.item, J.item, COUNT(I.basket)

FROM Baskets I, Baskets JWHERE I.basket = J.basket AND I.item < J.itemGROUP BY I.item, J.itemHAVING COUNT(I.basket) >= s;

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Example

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basket itemt1 p2t1 p5t1 p8t2 p5t2 p8t2 p11... ...

basket item1 item2t1 p2 p5t1 p2 p8t1 p5 p8t2 p5 p8t2 p5 p11t2 p8 p11... ... ...

check ifcount s

Issues• Performance for size 2 rules

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basket itemt1 p2t1 p5t1 p8t2 p5t2 p8t2 p11... ...

basket item1 item2t1 p2 p5t1 p2 p8t1 p5 p8t2 p5 p8t2 p5 p11t2 p8 p11... ... ...

bigevenbigger!

Performance for size k rules

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

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Classification Rules

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• 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.

Decision Tree

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Decision Tree ConstructionNAME Balance Employed Age DefaultMatt 23,000 No 30 yesBen 51,100 No 48 yesChris 68,000 Yes 55 noJim 74,000 No 40 noDavid 23,000 No 47 yesJohn 100,000 Yes 49 no

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Balance

>=50K<50K

Age

>=45<45

Employed

Class=NotDefault

NoYes

Class=YesDefault

Root

LeafClass=Yes

Default

Class=NotDefault

Node

Construction of Decision Trees

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• 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.

Finding the Best Split Point for Numerical Attributes

Gain Function

00.020.040.060.080.1

20 27 34 41 48 55 62 69 76

Age

gai

n

gain function

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Complete Class Histograms

02040

Age

Cou

nts

class-2

class-1

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!

Best Splits

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• 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.

kk

ii- 1- 1pp22

ii

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)

rr

ii= 1= 1

||SSii||

||SS||

purity purity ((SSii))

kk

i- i- 11ppiiloglog2 2 ppii

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

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Decision-Tree Construction Algorithm

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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 );

Finding Association Rules

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• We are generally only interested in association rules with reasonably high support (e.g. support of 2% or greater)

• Naïve algorithm1. 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

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

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Algorithm for 2-Sets

(1) Find OK products– those appearing in s or more baskets

(2) Find high-support pairs using only OK products

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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;

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Counting Efficiently• One way:

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basket I.item J.itemt1 p5 p8t2 p5 p8t2 p8 p11t3 p2 p3t3 p5 p8t3 p2 p8... ... ...

sort

basket I.item J.itemt3 p2 p3t3 p2 p8t1 p5 p8t2 p5 p8t3 p5 p8t2 p8 p11... ... ...

count &remove count I.item J.item

3 p5 p85 p12 p18... ... ...

threshold = 3

Counting Efficiently• Another way:

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basket I.item J.itemt1 p5 p8t2 p5 p8t2 p8 p11t3 p2 p3t3 p5 p8t3 p2 p8... ... ...

remove count I.item J.item3 p5 p85 p12 p18... ... ...

scan &count

count I.item J.item1 p2 p32 p2 p83 p5 p85 p12 p181 p21 p222 p21 p23... ... ...

keep counterarray in memory

threshold = 3

Yet Another Way

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basket I.item J.itemt1 p5 p8t2 p5 p8t2 p8 p11t3 p2 p3t3 p5 p8t3 p2 p8... ... ...

(1)scan &hash &count

count bucket1 A5 B2 C1 D8 E1 F... ...

in-memoryhash table threshold = 3

basket I.item J.itemt1 p5 p8t2 p5 p8t2 p8 p11t3 p5 p8t5 p12 p18t8 p12 p18... ... ...

(2) scan &remove

count I.item J.item3 p5 p85 p12 p18... ... ...

(4) removecount I.item J.item

3 p5 p81 p8 p115 p12 p18... ... ...

(3) scan& count

in-memorycounters

false positive

Discussion• 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

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item-pairs ranked by frequency

fre

que

ncy

threshold

iceberg queries

Frequent Itemsets MiningTID Transactions

100 { A, B, E }

200 { B, D }

300 { A, B, E }

400 { A, C }

500 { B, C }

600 { A, C }

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

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Lattice for Enumerating Frequent Itemsets

Found to be Infrequent

null

AB AC AD AE BC BD BE CD CE DE

A B C D E

ABC ABD ABE ACD ACE ADE BCD BCE BDE CDE

ABCD ABCE ABDE ACDE BCDE

ABCDE

null

AB AC AD AE BC BD BE CD CE DE

A B C D E

ABC ABD ABE ACD ACE ADE BCD BCE BDE CDE

ABCD ABCE ABDE ACDE BCDE

ABCDEPruned supersets

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

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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!

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K-Means Clustering

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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

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

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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

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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

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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

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A Simple Problem

• 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

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P×(Nθ) ≤ N

KRP algorithm ─ Karp, et. al (TODS’ 03)

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Θ=0.35

⌈1/θ⌉ = 3

N=30 m=12

N/ (⌈1/θ⌉) ≤ Nθ

Enhance the Accuracy

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Θ=0.35

⌈1/θ⌉ = 3

ε=0.5 Θ(1- ε )=0.175

⌈1/(θ×ε)⌉ = 6

N=30 m=12

NΘ>10

(ε*Θ)N

(Θ-(ε*Θ))N

Deletion/Reducing = 9

Frequent Items for Transactions with Fixed Length

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Each transaction has 2 items

Θ=0.60

⌈1/θ⌉×2= 4