Databases and Data Mining

Lecture 3: Descriptive Data Mining

Peter van der Putten (putten_at_liacs.nl)

Course Outline

• Objective – Understand the basics of data mining – Gain understanding of the potential for applying it in the bioinformatics domain – Hands on experience • Schedule

Date Time

4-Nov-05 13.45 - 15.30

18-Nov-05 13.45 - 15.30

Room

174 413 Lecture Lecture 15.45 - 17.30 306/308 Practical Assignments 25-Nov-05 13.45 - 15.30

2-Dec-05 13.45 - 15.30

413 413 Lecture Lecture 15.45 - 17.30 306/308 Practical Assignments • Evaluation – Practical assignment (2 nd ) plus take home exercise • Website – http://www.liacs.nl/~putten/edu/dbdm05/

Agenda Today: Descriptive Data Mining • Before Starting to Mine….

• Descriptive Data Mining – Dimension Reduction & Projection – Clustering • Hierarchical clustering • K-means • Self organizing maps – Association rules • Frequent item sets • Association Rules • APRIORI • Bio-informatics case: FSG for frequent subgraph discovery

Before starting to mine….

• Pima Indians Diabetes Data – X = body mass index – Y = age

Before starting to mine….

Before starting to mine….

Before starting to mine….

• Attribute Selection – This example: InfoGain by Attribute – Keep the most important ones Diastolic blood pressure (mm Hg) Diabetes pedigree function Number of times pregnant Triceps skin fold thickness (mm) 2-Hour serum insulin (mu U/ml) Age (years) Body mass index (weight in kg/(height in m)^2) Plasma glucose concentration a 2 hours in an oral glucose tolerance test 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20

Before starting to mine….

• Types of Attribute Selection – Uni-variate versus multivariate (sub set selection) • The fact that attribute x is a strong uni-variate predictor does not necessarily mean it will add predictive power to a set of predictors already used by a model – Filter versus wrapper • Wrapper methods involve the subsequent learner (classifier or other)

Dimension Reduction

• Projecting high dimensional data into a lower dimension – Principal Component Analysis – Independent Component Analysis – Fisher Mapping, Sammon’s Mapping etc.

– Multi Dimensional Scaling • See Pattern Recognition Course (Duin)

f.e. age

Data Mining Tasks: Clustering

Clustering is the discovery of groups in a set of instances Groups are different, instances in a group are similar In 2 to 3 dimensional pattern space you could just visualise the data and leave the recognition to a human end user

f.e. age

Data Mining Tasks: Clustering

Clustering is the discovery of groups in a set of instances Groups are different, instances in a group are similar In 2 to 3 dimensional pattern space you could just visualise the data and leave the recognition to a human end user In >3 dimensions this is not possible

Clustering Techniques

• Hierarchical algorithms – Agglomerative – Divisive • Partition based clustering – K-Means – Self Organizing Maps / Kohonen Networks • Probabilistic Model based – Expectation Maximization / Mixture Models

Hierarchical clustering

• • Agglomerative / Bottom up – – – Start with single-instance clusters At each step, join the two closest clusters Method to compute distance between cluster x and y: single linkage (distance between closest point in cluster x and y), average linkage (average distance between all points), complete linkage (distance between furthest points), centroid – Distance measure: Euclidean, Correlation etc.

Divisive / Top Down – – – Start with all data in one cluster Split into two clusters based on

category utility

Proceed recursively on each subset • Both methods produce a

dendrogram

Levels of Clustering

Agglomerative

Dunham, 2003

Divisive

Hierarchical Clustering Example

• Clustering Microarray Gene Expression Data – Gene expression measured using microarrays studied under variety of conditions – On budding yeast

Saccharomyces cerevisiae

– Groups together efficiently genes of known similar function, • Data taken from: Cluster analysis and display of genome-wide expression patterns. Eisen, M., Spellman, P., Brown, P., and Botstein, D. (1998). PNAS, 95:14863-14868; Picture generated with J-Express Pro

Hierarchical Clustering Example

• Method – Genes are the instances, samples the attributes!

– Agglomerative – Distance measure = correlation • Data taken from: Cluster analysis and display of genome-wide expression patterns. Eisen, M., Spellman, P., Brown, P., and Botstein, D. (1998). PNAS, 95:14863-14868; Picture generated with J-Express Pro

Simple Clustering: K-means

• • • • • Pick a number (k) of cluster centers (at random) Cluster centers are sometimes called codes, and the k codes a codebook • Assign every item to its nearest cluster center F.i. Euclidean distance Move each cluster center to the mean of its assigned items • Repeat until convergence change in cluster assignments less than a threshold KDnuggets

K-means example, step 1

Initially distribute codes randomly in pattern space Y KDnuggets k 2 k 1 X k 3

K-means example, step 2

Y Assign each point to the closest code KDnuggets k 2 k 1 X k 3

K-means example, step 3

Move each code to the mean of all its assigned points Y KDnuggets k 1

k 1 k 2

k 2 X k 3

k 3

K-means example, step 2

Repeat the process – Y reassign the data points to the codes

Q: Which points are reassigned?

KDnuggets k 2 X k 1 k 3

K-means example

Repeat the process – Y reassign the data points to the codes

Q: Which points are reassigned?

KDnuggets k 2 X k 1 k 3

K-means

example Y re-compute cluster means k 2 KDnuggets X k 1 k 3

K-means

example move cluster centers to cluster means KDnuggets Y k 2 X k 3 k 1

K-means clustering summary

Advantages • Simple, understandable • items automatically assigned to clusters Disadvantages • Must pick number of clusters before hand • All items forced into a cluster • Sensitive to outliers Extensions • Adaptive k-means • K-mediods (based on median instead of mean) – 1,2,3,4,100  average 22, median 3

Biological Example

• Clustering of yeast cell images – Two clusters are found – Left cluster primarily cells with thick capsule, right cluster thin capsule • caused by media, proxy for sick vs healthy

Self Organizing Maps (Kohonen Maps) • Claim to fame – Simplified models of cortical maps in the brain – Things that are near in the outside world link to areas near in the cortex – For a variety of modalities: touch, motor, …. up to echolocation – Nice visualization • From a data mining perspective: – SOMs are simple extensions of k-means clustering – Codes are connected in a lattice – In each iteration codes neighboring winning code in the lattice are also allowed to move

SOM

10x10 SOM Gaussian Distribution

SOM

SOM

SOM

SOM example

Famous example: Phonetic Typewriter • SOM lattice below left is trained on spoken letters, after convergence codes are labeled • Creates a ‘phonotopic’ map • Spoken word creates a sequence of labels

Famous example: Phonetic Typewriter • Criticism – Topology preserving property is not used so why use SOMs and not adaptive k-means for instance?

• K-means could also create a sequence • This is true for most SOM applications!

– Is using clustering for classification optimal?

Bioinformatics Example Clustering GPCRs • Clustering G Protein Coupled Receptors (GPCRs) [Samsanova et al, 2003, 2004] • Important drug target, function often unknown

Bioinformatics Example Clustering GPCRs

Association Rules Outline

• What are frequent item sets & association rules?

• Quality measures – support, confidence, lift • How to find item sets efficiently?

– APRIORI • How to generate association rules from an item set?

• Biological examples KDnuggets

Market Basket Example Gene Expression Example

TID Produce 1 2 3 4 5 6 7 8 9

MILK, BREAD, EGGS BREAD, SUGAR BREAD, CEREAL MILK, BREAD, SUGAR MILK, CEREAL BREAD, CEREAL MILK, CEREAL MILK, BREAD, CEREAL, EGGS MILK, BREAD, CEREAL • Frequent item set • {MILK, BREAD} = 4 • Association rule • {MILK, BREAD}  {EGGS} • Frequency / importance = 2 (‘ Support ’) • Quality = 50% (‘ Confidence ’) • What genes are expressed (‘active’) together?

• Interaction / regulation • Similar function

ID Expressed Genes in Sample 1 2 3 4 5 6 7 8 9

GENE1, GENE2, GENE 5 GENE1, GENE3, GENE 5 GENE2 GENE8, GENE9 GENE8, GENE9, GENE10 GENE2, GENE8 GENE9, GENE10 GENE2 GENE11

Association Rule Definitions

• • • • •

Set of items: Transactions:

I={I 1 ,I 2 ,…,I m } D={t 1 ,t 2 , …, t n }, t j 

Itemset:

{I i1 ,I i2 , …, I ik }  I I

Support of an itemset:

Percentage of transactions which contain that itemset.

Large (Frequent) itemset:

Itemset whose number of occurrences is above a threshold.

Dunham, 2003

Frequent Item Set Example

Dunham, 2003 I = { Beer, Bread, Jelly, Milk, PeanutButter} Support of {Bread,PeanutButter} is 60%

Association Rule Definitions

• • •

Association Rule (AR):

implication X  where X,Y  I and X,Y disjunct; Y

Support of AR (s) X



Y

: Percentage of transactions that contain X  Y

Confidence of AR (

a

) X



Y:

Ratio of number of transactions that contain X  Y to the number that contain X Dunham, 2003

Dunham, 2003

Association Rules Ex (cont’d)

Association Rule Problem

• • Given a set of items I={I 1 ,I 2 ,…,I m } and a database of transactions D={t 1 ,t 2 , …, t n } where t i ={I i1 ,I i2 , …, I ik } and I ij

Association Rule Problem

 I, the is to identify all association rules X  Y with a minimum support and confidence.

NOTE:

of X  Support of X Y.

 Y is same as support Dunham, 2003

Association Rules Example

•

Q: Given frequent set {A,B,E}, what association rules have minsup = 2 and minconf= 50% ?

A, B => E : conf=2/4 = 50% A, E => B : conf=2/2 = 100% B, E => A : conf=2/2 = 100% E => A, B : conf=2/2 = 100% Don’t qualify A =>B, E : conf=2/6 =33%< 50% B => A, E : conf=2/7 = 28% < 50% __ => A,B,E : conf: 2/9 = 22% < 50%

TID List of items 1 2 3 4 5 6 7 8 9 A, B, E

B, D B, C A, B, D A, C B, C A, C

A, B, C, E

A, B, C KDnuggets

Solution Association Rule Problem • First, find all frequent itemsets with sup >=minsup – Exhaustive search won’t work • Assume we have a set of

m

items  2 m subsets!

– Exploit the subset property (APRIORI algorithm) • For every frequent item set, derive rules with confidence >= minconf KDnuggets

Finding itemsets: next level

• Apriori algorithm (Agrawal & Srikant) • Idea: use one-item sets to generate two-item sets, two-item sets to generate three-item sets, ..

– Subset Property: If (A B) is a frequent item set, then (A) and (B) have to be frequent item sets as well!

– In general: if X is frequent

k

-item set, then all (

k

-1)  item subsets of X are also frequent Compute

k

-item set by merging (

k

-1)-item sets KDnuggets

An example

• Given: five three-item sets (A B C), (A B D), (A C D), (A C E), (B C D) • Candidate four-item sets: (A B C D)

Q: OK?

A: yes, because all 3-item subsets are frequent (A C D E)

Q: OK?

A: No, because (C D E) is not frequent KDnuggets

From Frequent Itemsets to Association Rules • Q: Given frequent set {A,B,E}, what are possible association rules? – A => B, E – A, B => E – A, E => B – B => A, E – B, E => A – E => A, B – __ => A,B,E (empty rule), or true => A,B,E KDnuggets

Example: ‘Generating Rules from an Itemset • Frequent itemset from golf data:

Humidity = Normal, Windy = False, Play = Yes (4)

• Seven potential rules: If Humidity = Normal and Windy = False then Play = Yes If Humidity = Normal and Play = Yes then Windy = False If Windy = False and Play = Yes then Humidity = Normal If Humidity = Normal then Windy = False and Play = Yes If Windy = False then Humidity = Normal and Play = Yes If Play = Yes then Humidity = Normal and Windy = False If True then Humidity = Normal and Windy = False and Play = Yes KDnuggets 4/4 4/6 4/6 4/7 4/8 4/9 4/12

Example: Generating Rules • Rules with support > 1 and confidence = 100%: 1 2 3 4 ...

58 Association rule Humidity=Normal Windy=False Temperature=Cool Outlook=Overcast Temperature=Cold Play=Yes ...

Outlook=Sunny Temperature=Hot  Play=Yes  Humidity=Normal  Play=Yes  Humidity=Normal ...

 Humidity=High Sup.

4 4 4 3 ...

2 Conf.

100% 100% 100% 100% ...

100% • In total: 3 rules with support four, 5 with support three, and 50 with support two KDnuggets

KDnuggets

Weka associations: output

Extensions and Challenges

• Extra quality measure: Lift – The

lift

of an association rule

I => J

is defined as: • lift = P(J|I) / P(J) • Note, P(I) = (support of I) / (no. of transactions) • ratio of confidence to expected confidence – Interpretation: • if lift > 1, then I and J are positively correlated lift < 1, then I are J are negatively correlated.

lift = 1, then I and J are independent • Other measures for interestingness – A  B, B  C, but not A  C • Efficient algorithms • Known Problem – What to do with all these rules? How to exploit / make useful / actionable?

KDnuggets

Biomedical Application Head and Neck Cancer Example 1. ace27=0 fiveyr=alive 381  2. gender=M ace27=0 467  tumorbefore=0 372 tumorbefore=0 455 conf:(0.98) conf:(0.97) 3. ace27=0 588  tumorbefore=0 572 4. tnm=T0N0M0 ace27=0 405  conf:(0.97) tumorbefore=0 391 conf:(0.97) 5. loc=LOC7 tumorbefore=0 409  6. loc=LOC7 442  tnm=T0N0M0 391 conf:(0.96) tnm=T0N0M0 422 conf:(0.95) 7. loc=LOC7 gender=M tumorbefore=0 374  tnm=T0N0M0 357 conf:(0.95) 8. loc=LOC7 gender=M 406  9. gender=M fiveyr=alive 633  tnm=T0N0M0 387 tumorbefore=0 595 10. fiveyr=alive 778  tumorbefore=0 726 conf:(0.95) conf:(0.94) conf:(0.93)

Bioinformatics Application

• The idea of association rules have been customized for bioinformatics applications • In biology it is often interesting to find frequent structures rather than items – For instance protein or other chemical structures • Solution: Mining Frequent Patterns – FSG (Kuramochi and Karypis, ICDM 2001) – gSpan (Yan and Han, ICDM 2002) – CloseGraph (Yan and Han, KDD 2002)

FSG: Mining Frequent Patterns

FSG: Mining Frequent Patterns

FSG Algorithm for finding frequent subgraphs

Frequent Subgraph Examples AIDS Data • Compounds are active, inactive or moderately active (CA, CI, CM)

Predictive Subgraphs

• The three most discriminating sub-structures for the PTC, AIDS, and Anthrax datasets

FSG References

• • • • •

Frequent Sub-structure Based Approaches for Classifying Chemical Compounds

Mukund Deshpande, Michihiro Kuramochi, and George Karypis ICDM 2003

An Efficient Algorithm for Discovering Frequent Subgraphs

Michihiro Kuramochi and George Karypis IEEE TKDE

Automated Approaches for Classifying Structures

Mukund Deshpande, Michihiro Kuramochi, and George Karypis BIOKDD 2002

Discovering Frequent Geometric Subgraphs

Michihiro Kuramochi and George Karypis ICDM 2002

Frequent Subgraph Discovery

Michihiro Kuramochi and George Karypis 1st IEEE Conference on Data Mining 2001

Recap

• Before Starting to Mine….

• Descriptive Data Mining – Dimension Reduction & Projection – Clustering • Hierarchical clustering • K-means • Self organizing maps – Association rules • Frequent item sets • Association Rules • APRIORI • Bio-informatics case: FSG for frequent subgraph discovery • Next week – Bioinformatics Data Mining Cases / Lab Session / Take Home Exercise