data mining lectures lecture 19: pattern discovery padhraic smyth, uc irvine project presentations...

Data Mining Lectures Lecture 19: Pattern Discovery Padhraic Smyth, UC Irvine

Project Presentations

• Thursday this week, each student will make a 4-minute presentation on their project in class (with 1 or 2 minutes for questions)

• Email me your Powerpoint or PDF slides, with your name (e.g., joesmith.ppt), before 10am next Thursday

• Suggested content:– Definition of the task/goal – Description of data sets– Description of algorithms– Experimental results and conclusions– Be visual where possible! (i.e., use figures, graphs, etc)


Final Project Reports

• Must be submitted as an email attachment (PDF, Word, etc) by 12 noon Tuesday next week

– Use “ICS 278 final project report” in the subject line of your email

• Report should be self-contained– Like a short technical paper– A reader should be able to repeat your results

• Include details in appendices if necessary

• Approximately 1 page of text per section (see next slide)– graphs/plots don’t count – include as many of these as you like.

• Can re-use material from proposal and from midterm progress report if you wish


Suggested Outline of Final Project Report

• Introduction:– Clear description of task/goals of the project– Motivation: why is this problem interesting and/or important?

• Discussion of relevant literature – Summarize relevant aspects of prior published/related work

• Technical approach– Data used in your project

• Exploratory data analysis relevant to your task• Include as many of plots/graphs as you think are useful/relevant

– Algorithms used in your project• Clear description of all algorithms used• Credit appropriate sources if you used other implementations

• Experimental Results– Clear description of your experimental methodology– Detailed description of your results (graphs, tables, etc)

• Discussion and Conclusions– What you learned from this project

• Also: References and Appendices (if needed)


ICS 278: Data Mining

Lecture 19: Pattern Discovery Algorithms

Padhraic SmythDepartment of Information and Computer Science

University of California, Irvine


Pattern-Based Algorithms

• “Global” predictive and descriptive modeling– “global” models in the sense that they “cover” all of the data

space

• “Patterns”– More local structure, only describe certain aspects of the data– Examples:

• A single small very dense cluster in input space– e.g., a new type of galaxy in astronomy data

• An unusual set of outliers– e.g., indications of an anomalous event in time-series climate

data• Associations or “rules”

– If bread is purchased and wine is purchased then cheese is purchased with probability p

• Motif-finding in sequences, e.g., – motifs in DNA sequences ~ noisy words in random background


General Ideas for Patterns

• Many patterns can be described in the general form:– if condition 1 then condition 2 (with some certainty)

• Probabilistic rules: If Age > 40 and education > college then income > $50k with probability p

• “Bumps” If Age > 40 and education > college then mean income = $73k

– if antecedent then consequent – if then

• where is generally some “box” in the input space• where is a statement about a variable of interest, e.g., p(y | ) or E [ y |

]

• Pattern support– “Support” = p( ) or p( ) – Fraction of points in input space where the condition applies– Often interested in patterns with larger support


How Interesting is a Pattern?

• Note: “interestingness” is inherently subjective– Depends on what the data analyst already knows

• Difficult to quantify prior knowledge

– How interesting a pattern is, can be a function of• How surprising it is relative to prior knowledge?• How useful (actionable) it is?

– This is a somewhat open research problem

– In general pattern “interestingness” is difficult to quantify• => Use simple “surrogate” measures in practice


How Interesting is a Pattern?

• Interestingness of a pattern– Measures how “interesting” the pattern -> is

• Typical measures of interest– Conditional probability: p( ) – Change in probability: | p( ) - p( ) |

– “Lift” = p( ) / p( ) (also log of this)

– Change in mean target response, e.g., E [y| ]/E[y]


Pattern-Finding Algorithms• Typically… search a data set for the set of patterns that maximize some

score function– Usually a function of both support and “interestingness”– E.g.,

• Association rules• Bump-hunting

• Issues:– Huge combinatorial search space– How many patterns to return to the user– How to avoid problems with redundant patterns

• Statistical issues– Even in random noise, if we search over a very large number of patterns, we are

likely to find something that looks significant– This is known as “multiple hypothesis testing” in statistics– One approach that can help is to conduct randomization tests

• e.g., for matrix data randomly permute the values in each column• Run pattern-discovery algorithm – resulting scores provide a “null distribution”

– Ideally, also need a 2nd data set to validate patterns


Task

Generic Pattern Finding

Representation

Score Function

Search/Optimization

Data Management

Models, Parameters

Find patterns

f(support, interestingness)

greedy, branch-and-bound

varies

list of K highest scoring patterns

pattern language


Two Pattern Finding Algorithms

1. Bump-hunting: the PRIM algorithmBump Hunting in High Dimensional DataJ. H. Friedman & N. I. FisherStatistics and Computing, 2000

2. Market basket data: association rule algorithms


“Bump-Hunting” (PRIM) algorithm

• Patient Rule Induction Method (PRIM)– Friedman and Fisher, 2000

• Addresses “bump-hunting” problem:– Assume we have a target variable Y

• Y could be real-valued or a binary class variable– And we have p “input” variables – We want to find “boxes” in input space where E[Y| ] >>

E[Y]• or where E[Y| ] << E[Y] , i.e., “data holes”

– A box is a “conjunctive sentence”, e.g., if Age < 22 and occupation = student

Example of a “box pattern” if Age > 30 and education > bachelor then E[income | ] =

$120k


“Bump Hunting”: Extrema Regions for Target f(x)

• let Sj be set of all possible values for input variable xj

– entire input domain is S = S1 S2 … Sd

• goal: find subregion R S for which– mR = avg xR f(x) >> m– where m = f(x) p(x) dx (target mean, over all inputs)

• subregion size as fraction of full space (“support”): R = xR p(x) dx

• tradeoff between mR and R (increase R => reduce mR) ...

• sample-based estimates used in practice: R = (1/n) XiR 1(XiR), yavgR = 1/(nR) XiR yi – note: mR is true quantity of interest, not yavgR


Greedy Covering

• a generic greedy covering algorithm– first box B1 induced from entire data set– second box B2 induced from data not covered by B1

– … BK induced from remaining data {yi,Xi | Xi j=1…K-1 Bj}

• do until either:– estimated target mean f(x) in Bk becomes too small

• yavgK = avg[yi | Xi Bk & Xi j=1…K-1 Bj] < = (1/n) ni=1 yi

– support of Bk becomes too small K = (1/n) i=1…n 1(Xi Bk & Xi j=1…K-1 Bj)

• then select set of boxes R = j Bj for some threshold– for which each yavgj > some yavgthreshold or– yield largest yavgR for which R = i i some threshold


PRIM algorithm

• PRIM uses “patient greedy search” on individual variables

• Start with all training data and maximal box• Repeat until minimal box (e.g., minimal support or n<10)

– Shrink box by compressing one face of the box– For each variable in input space

• “Peel” off a proportion of observations to optimize E[y |new box], • typical =0.05 or =0.1

• Now “expand” the box if E[y|box] can be increased (“pasting”)

• Yields a sequence of boxes– Use cross-validation (on E[y|box]) to select the best box

• Remove box from training data, then repeat process


Comments on PRIM

• Works one variable at a time– So time-complexity is similar to tree algorithms, i.e.,

• Linear in p, and n log n for sorting

• Nominal variables– Can peel/paste on single values, subsets, negations, etc

• Similar in some sense to CART….but– More “patient” in search (removes only small fraction of data at each

step)

• Useful for finding “pockets” in the input space with high-response– e.g., marketing data: small groups of consumers who spend much

more on a given product than the average consumer– Medical data: patients with specific demographics whose response to a

drug is much better than the average patient


Marketing Data Example (n=9409, p=502)

• freq air travel: y=num flights/yr, global mean(y)=1.7

• B1: mean(y1)=4.2, 1=0.08 (8% market seg)– education >= 16 yrs; income > $50K & missing– occupation in {professional/manager, sales, homemaker}– number of children (<18) in home <= 1

• B2: mean(y2)=3.2, 2=0.07 (~2x global mean)– education > 12 yrs & missing– income > $30K & missing; 18 < age < 54– married / dual income in {single, married-one-income}

• these boxes intuitive: nothing really surprising ...


Pattern Finding Algorithms

1. Bump-hunting: the PRIM algorithm

2. Market basket data: association rule algorithms


Transaction Data and Market Baskets

• Supermarket example: (Srikant and Agrawal, 1997)

– #items = 50,000, #transactions = 1.5 million

• Data sets are typically very sparse

ItemsTransa

ctions x x

xx

x x xx

x x xxx x

xx

x

xx

x

x


Market Basket Analysis

• given: a (huge) “transactions” database– each transaction representing basket for 1 customer visit– each transaction containing set of items (“itemset”)

• finite set of (boolean) items (e.g. wine, cheese, diaper, beer, …)

• Association rules– classically used on supermarket transaction databases– associations: Trader Joe’s customers frequently buy wine &

cheese• rule: “people who buy wine also buy cheese 60% of time”

– infamous “beer & diapers” example:• “in evening hours, beer and diapers often purchased together”

– generalize to many other problems, e.g.:• baskets = documents, items = words• baskets = WWW pages, items = links


Market Basket Analysis: Complexity

• usually transaction DB too huge to fit in RAM– common sizes:

• number of transactions: 105 to 108 (hundreds of millions)• number of items: 102 to 106 (hundreds to millions)

• entire DB needs to be examined– usually very sparse

• e.g. ~ 0.1% chance of buying random item

– subsampling often a useful trick in DM, but• here, subsampling could easily miss the (rare) interesting patterns

• thus, runtime dominated by disk read times– motivates focus on minimizing number of disk scans


Association Rules: Problem Definition

• given: set I of items, set T transactions, t T, t I– Itemset Z = a set of items (any subset of I)

• support count (Z) = num transactions containing Z – given any itemset Z I, (Z) = | { t | t T, Z t } |

• association rule: – R=“X Y [s,c]”, X,Y I, XY=

• support: – s(R) = s(XY) = (XY)/|T| = p(XY)

• confidence: – c(R) = s(XY) / s(X) = (XY) / (X) = = p(X | Y)

• goal: find all R such that– s(R) given minsup– c(R) given minconf


Comments on Association Rules

• association rule: R=“X Y [s,c]”– Strictly speaking these are not “rules”

• i.e., we could have “wine => cheese” and “cheese => wine”• correlation is not causation

• The space of all possible rules is enormous– O( 2p ) where p = the number of different items– Will need some form of combinatorial search algorithm

• How are thresholds minsup and minconf selected?– Not that easy to know ahead of time how to select these


Example

• simple example transaction database (|T|=4): – Transaction1 = {A,B,C}– Transaction2 = {A,C}– Transaction3 = {A,D} – Transaction4 = {B,E,F}

• with minsup=50%, minconf=50%:– R1: A --> C [s=50%, c=66.6%]

• s(R1) = s({A,C}) , c(R1) = s({A,C})/s({A}) = 2/3

– R2: C --> A [s=50%, c=100%]• s(R2) = s({A,C}), c(R2) = s({A,C})/s({C}) = 2/2

s({A}) = 3/4 = 75%s({B}) = 2/4 = 50%s({C}) = 2/4 = 50%s({A,C}) = 2/4 = 50%


Finding Association Rules

• two steps:– step 1: find all “frequent” itemsets (F)

• F = {Z | s(Z) minsup} (e.g. Z={a,b,c,d,e})

– step 2: find all rules R: X --> Y such that:• X Y F and X Y= (e.g. R: {a,b,c} --> {d,e})• s(R) minsup and c(R) minconf

• step 1’s time-complexity typically >> step 2’s• step 2 need not scan the data (s(X),s(Y) all cached in step 1)• search space is exponential in |I|, filters choices for step 2• so, most work focuses on fast frequent itemset generation

• step 1 never filters viable candidates for step 2


Finding Frequent Itemsets

• frequent itemsets: {Z | s(Z)>minsup}• “Apriori (monotonicity) Principle”: s(X) s(XY)

– any subset of a frequent itemset must be frequent

• finding frequent itemsets:– bottom-up approach:

• do level-wise, for k=1 … |I|– k=1: find frequent singletons– k=2: find frequent pairs (often most costly)– step k.1: find size-k itemset candidates from the freq size-(k-

1)’s of prev level– step k.2 prune candidates Z for which s(Z)<minsup

• each level requires a single scan over all the transaction data– computes support counts (Z) = | { t | t T, Z t } for all size-

k Z candidates

s({A}) = 3/4 = 75%s({B}) = 2/4 = 50%s({C}) = 2/4 = 50%s({A,C}) = 2/4 = 50%


Apriori Example (minsup=2)

transactions T{1,3,4}{2,3,5}

{1,2,3,5}{2,5}

itemset sup{1} 2{2} 3{3} 3{4} 1{5} 3

itemset sup{1} 2{2} 3{3} 3{5} 3

F1 C2itemset{1,2}{1,3} {1,5} {2,3}{2,5}{3,5}

C1

itemset sup{1,2} 1{1,3} 2 {1,5} 1 {2,3} 2 {2,5} 3 {3,5} 2

C2

itemset sup{1,3} 2{2,3} 2{2,5} 3 {3,5} 2

F2

itemset {2,3,5}

C3 itemset sup{2,3,5} 2

F3

count(scan T)

count(scan T)

count(scan T)

filter

gen

gen

filter

bottleneck:

itemset sup{2,3,5} 2

C3filter

notice how |C3| << |C2|

C3 knows can avoid gen{1,2,3} (and {1,3,5}) apriori,without counting, because

{1,2} ({1,5}) not freq


Problems with Association Rules

• Consider 4 highly correlated items A, B, C, D– Say p(subset i|subset j) > minconf for all possible pairs of

disjoint subsets– And p(subset i subset j) > minsup

– How many possible rules?• E.g., A->B, [A,B]=>C, [A,C]=>B, [B,C]=>A• All possible combinations: 4 x 23 • In general for K such items, K x 2K-1 rules• For highly correlated items there is a combinatorial explosion of

redundant rules• In practice this makes interpretation of association rule results

difficult


References on Association Rules

• Chapter 13 in text (Sections 13.1 to 13.5)

• Early papers:– R. Agrawal and R. Srikant, Fast algorithms for mining association rules,

in Proceedings of VLDB 1994, pp.487-499, 1994.– R. Agrawal et al. Fast discovery of association rules, in Advances in

Knowledge Discovery and Data Mining, AAAI/MIT Press, 1996.

• More recent:– Good review in Chapter 6 of Data Mining: Concepts and Techniques, J.

Han and M. Kamber, Morgan Kaufmann, 2001.– J. Han, J. Pei, and Y. Yin, Mining frequent patterns without candidate

generation, Proceedings of SIGMOD 2000, pages 1-12.– Z. Zheng, R. Kohavi, and L. Mason, Real World Performance of

Association Rule Algorithms, Proceedings of KDD 2001


Study on Association Rule Algorithms

• Z. Zheng, R. Kohavi, and L. Mason, Real World Performance of Association Rule Algorithms, Proceedings of KDD 2001

• Evaluated a variety of association rule algorithms– Used both real and simulated transaction data sets

• Typical real data set from Web commerce:– Number of transactions = 500k– Number of items = 3k– Maximum transaction size = 200– Average transaction size = 5.0


Study on Association Rule Algorithms

• Conclusions:– Very narrow range of minsup yields interesting rules

• Minsup too small => too many rules• Minsup too large => misses potentially interesting patterns

– Superexponential growth of rules on real-world data

– Real-world data is different to simulated transaction data used in research papers, e.g.,

• Simulated transaction sizes have a mode away from 1• Real transaction sizes have a mode at 1 and are highly skewed

– Speed-up improvements demonstrated on artificial data did not generalize to real transaction data


Beyond Binary Market Baskets

• counts (vs yes/no)– e.g. “3 wines” vs “wine”

• quantitative (non-binary) item variables– popular: discretize real variable into k binary variables– e.g. {age=[30:39],incomeK=[42:48]} buys_PC

• Item hierachies– Common in practice, e.g., clothing -> shirts -> men’s shirts, etc– Can learn rules that generalize across the hierarchy

• mining sequential associations/patterns and rules– e.g. {1@0,2@5} 4@15


Task

Association Rule Finding

Representation

Score Function

Search/Optimization

Data Management

Models, Parameters

Find association rules

P(A,B,C) > minsup,

P(C|A, B) > minconf

Breadth-first candidate generation

Linear scans

list of all rules satisfying thresholds

[A and B] => C


Task

Bump Hunting (PRIM)

Representation

Score Function

Search/Optimization

Data Management

Models, Parameters

Find high score bumps

E[y|A,B] and p(A,B)

Greedy search

None

Set of “boxes”

[A,B] => E[y|A,B] > E[y]


Summary

• Pattern finding– An interesting and challenging problem– How to search for interesting/unusual “regions” of a high-

dimensional space

– Two main problems• Combinatorial search• How to define “interesting” (this is the harder problem)

– Two examples of algorithms• PRIM for bump-hunting• Apriori for association rule mining

– Many open problems in this research area (room for new ideas!)

data mining lectures lecture 19: pattern discovery padhraic smyth, uc irvine project presentations...

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