EECS 800 Research Seminar Mining Biological Data

EECS 800 Research SeminarMining Biological Data Instructor: Luke Huan Fall, 2006

Administrative • Last day to add/change sections without written permission • Send a request to reserve reference books in Spahr library

Outline for today • A road map of frequent item set mining • Efficient and scalable frequent itemset mining methods • Mining various kinds of association rules • Summary

What Is Frequent Pattern Analysis? • Motivation: Finding inherent regularities in data • What products were often purchased together?— Beer and diapers?! • What are the subsequent purchases after buying a PC? • What are the commonly occurring subsequences in a group of genes? • What are the shared substructures in a group of effective drugs?

What Is Frequent Pattern Analysis? • Frequent pattern: a pattern (a set of items, subsequences, substructures, etc.) that occurs frequently in a data set • First proposed by Agrawal, Imielinski, and Swami [AIS93] in the context of frequent itemsets and association rule mining • Applications • Identify motifs in bio-molecules • DNA sequence analysis, protein structure analysis • Identify patterns in micro-arrays • Business applications: • Market basket analysis, cross-marketing, catalog design, sale campaign analysis, etc.

Data • An item is an element (a literal, a variable, a symbol, a descriptor, an attribute, a measurement, etc) • A transaction is a set of items • A data set is a set of transactions • A database is a data set

Where Data are Collected • Retailer stores • On-line shopping record • Genetic profiling • Business records • Entities and attributes

The Nature of the Data • Large volume of data • Gigabytes • Terabytes • Usually very sparse • Most of the items are task-irrelevant

Frequent Patterns • Pattern (Itemset): a set of items • E.g., acm={a, c, m} • Support of patterns • Sup(acm)=3 • Given min_sup=3, acm is a frequent pattern • Frequent pattern mining: find all frequent patterns in a database Transaction database TDB

Customer buys both Customer buys diaper Customer buys beer Association Rules • Itemset X = {x1, …, xk} • Find all the rules X  Ywith minimum support and confidence • support, s, is the probability that a transaction contains X  Y • confidence,c, is the conditional probability that a transaction having X also contains Y • Let supmin = 50%, confmin = 50% • Association rules: • A  C (60%, 100%) • C  A (60%, 75%)

Frequent Pattern Mining: A Road Map • Boolean vs. quantitative associations • occupation(x, “college student”)  buys(x, “laptop”) • age(x, “30..39”) ^ income(x, “42..48K”)  buys(x, “car”) [1%, 75%] • Single dimension vs. multiple dimensional associations • Single level vs. multiple-level analysis • What brands of beers are associated with what brands of diapers?

Extensions • Correlation, causality analysis & mining interesting rules • Maxpatterns and frequent closed itemsets • Constraint-based mining • Sequential patterns • Periodic patterns • Structural Patterns

Frequent Pattern Mining Methods • Apriori and its variations/improvements • Mining frequent-patterns without candidate generation • Mining max-patterns and closed itemsets • Mining multi-dimensional, multi-level frequent patterns with flexible support constraints • Interestingness: correlation and causality

Apriori: Candidate Generation-and-test • Frequency anti-monotone property: • Any subset of a frequent itemset must be also frequent — an anti-monotone property • E.g. a transaction containing {beer, diaper, nuts} also contains {beer, diaper} • {beer, diaper, nuts} is frequent implies that {beer, diaper} must also be frequent • No superset of any infrequent itemset should be generated or tested • Many item combinations can be pruned

Apriori-based Mining • Generate length (k+1) candidate itemsets from length k frequent itemsets, and • Test the candidates against DB

Apriori Algorithm • A level-wise, candidate-generation-and-test approach (Agrawal & Srikant 1994) Data base D 1-candidates Freq 1-itemsets 2-candidates Scan D Min_sup=2 Counting 3-candidates Freq 2-itemsets Scan D Scan D Freq 3-itemsets

The Apriori Algorithm • Ck: Candidate itemset of size k • Lk : frequent itemset of size k • L1 = {frequent items}; • for (k = 1; Lk !=; k++) do • Ck+1 = candidates generated from Lk; • for each transaction t in a database do • increment the count of all candidates in Ck+1 that are contained in t • Lk+1 = candidates in Ck+1 with min_support • return k Lk;

Important Details of Apriori • How to generate candidates? • Step 1: self-joining Lk • Step 2: pruning • Example of Candidate-generation • L3={abc, abd, acd, ace, bcd} • Self-joining: L3*L3 • abcd from abc and abd • acde from acd and ace • Pruning: • acde is removed because ade is not in L3 • C4={abcd}

How to Generate Candidates? • Suppose the items in Lk-1 are listed in an order • Step 1: self-joining Lk-1 insert into Ck select p.item1, p.item2, …, p.itemk-1, q.itemk-1 from Lk-1 p, Lk-1 q where p.item1=q.item1, …, p.itemk-2=q.itemk-2, p.itemk-1 < q.itemk-1 • Step 2: pruning For each itemsets c in Ck do For each (k-1)-subsets s of c do if (s is not in Lk-1) then delete c from Ck

How to Count Supports of Candidates? • Why counting supports of candidates a problem? • The total number of candidates can be very huge • One transaction may contain many candidates • Method: • Candidate itemsets are stored in a hash-tree • Leaf node of hash-tree contains a list of itemsets and counts • Interior node contains a hash table • Subset function: finds all the candidates contained in a transaction

Revisit the Apriori Algorithm • Ck: Candidate itemset of size k • Lk : frequent itemset of size k • L1 = {frequent items}; • for (k = 1; Lk !=; k++) do • Ck+1 = candidates generated from Lk; • for each transaction t in a database do • increment the count of all candidates in Ck+1 that are contained in t • Lk+1 = candidates in Ck+1 with min_support • return k Lk;

Challenges of Frequent Pattern Mining • Challenges • Multiple scans of transaction database • Huge number of candidates • Tedious workload of support counting for candidates • Improving Apriori: general ideas • Reduce passes of transaction database scans • Shrink number of candidates • Facilitate support counting of candidates

Once both A and D are determined frequent, the counting of AD can begin Once all length-2 subsets of BCD are determined frequent, the counting of BCD can begin 1-itemsets 2-itemsets 1-itemsets … DIC: Reduce Number of Scans ABCD ABC ABD ACD BCD AB AC BC AD BD CD Transactions B C D A Apriori {} Itemset lattice 2-items S. Brin R. Motwani, J. Ullman, and S. Tsur, 1997. DIC 3-items

Partition: Scan Database Only Twice • Any itemset that is potentially frequent in DB must be frequent in at least one of the partitions of DB • Scan 1: partition database and find local frequent patterns • Scan 2: consolidate global frequent patterns • A. Savasere, E. Omiecinski, and S. Navathe. An efficient algorithm for mining association in large databases. In VLDB’95

DHP: Reduce the Number of Candidates • Observation: the first a few iterations take a large portion of the total CPU consumption • Intuition: give Apriori a jump strart! • Identify all frequent k-patterns where k is a small number > 1 in the first scan of a DB • Use a hash table to keep track of frequent k-patterns For each transaction t in DB do For each triplet (k-patterns) s of t do H[s] ← H[s] +1

DHP: Reduce the Number of Candidates • Technique: a hashing bucket count <min_sup  every candidate in the buck is infrequent • Candidates: a, b, c, d, e • Hash entries: {ab, ad, ae} {bd, be, de} … • Large 1-itemset: a, b, d, e • The sum of counts of {ab, ad, ae} < min_sup  ab should not be a candidate 2-itemset • J. Park, M. Chen, and P. Yu, 1995, An effective hash-based algorithm for mining association rules. ICMD’95.

 a b c d ab ac ad bc bd cd abc abd acd bcd abcd An New Algebraic Frame: Set Enumeration Tree • Subsets of I can be enumerated systematically • I={a, b, c, d}

 a b c d ab ac ad bc bd cd abc abd acd bcd abcd Borders of Frequent Itemsets • Connected • X and Y are frequent and X is an ancestor of Y implies that all patterns between X and Y are frequent

 a b c d ab ac ad bc bd cd abc abd acd bcd abcd Projected Databases • To find a child Xy of X, only X-projected database is needed • The sub-database of transactions containing X • Item y is frequent in X-projected database

Tree-Projection Method • Find frequent 2-itemsets • For each frequent 2-itemset xy, form a projected database • The sub-database containing xy • Recursive mining • If x’y’ is frequent in xy-proj db, then xyx’y’ is a frequent pattern

Why Is Tree-projection Fast? • A bi-level unfolding of set enumeration tree • Major operations • Finding frequent 2-itemsets: faster than matching candidates • Form projected databases • AAP’01

Reduce Pattern Number by Sampling • Select a sample of original database, mine frequent patterns within sample using Apriori • Scan database once to verify frequent itemsets found in sample, only bordersof closure of frequent patterns are checked • Example: check abcd instead of ab, ac, …, etc. • Scan database again to find missed frequent patterns • H. Toivonen. Sampling large databases for association rules. In VLDB’96

Bottleneck of Frequent-pattern Mining • Multiple database scans are costly • Mining long patterns needs many passes of scanning and generates lots of candidates • To find frequent itemset i1i2…i100 • # of scans: 100 • # of Candidates: (1001) + (1002) + … + (110000) = 2100-1 = 1.27*1030 ! • Bottleneck: candidate-generation-and-test • Can we avoid candidate generation?

Mining Frequent Patterns Without Candidate Generation • Grow long patterns from short ones using local frequent items • “abc” is a frequent pattern • Get all transactions having “abc”: DB|abc • “d” is a local frequent item in DB|abc  abcd is a frequent pattern

{} Header Table Item frequency head f 4 c 4 a 3 b 3 m 3 p 3 f:4 c:1 c:3 b:1 b:1 a:3 p:1 m:2 b:1 p:2 m:1 Construct FP-tree from a Transaction Database TID Items bought (ordered) frequent items 100 {f, a, c, d, g, i, m, p}{f, c, a, m, p} 200 {a, b, c, f, l, m, o}{f, c, a, b, m} 300 {b, f, h, j, o, w}{f, b} 400 {b, c, k, s, p}{c, b, p} 500{a, f, c, e, l, p, m, n}{f, c, a, m, p} min_support = 3 • Scan DB once, find frequent 1-itemset (single item pattern) • Sort frequent items in frequency descending order, f-list • Scan DB again, construct FP-tree F-list=f-c-a-b-m-p

Benefits of the FP-tree Structure • Completeness • Preserve complete information for frequent pattern mining • Never break a long pattern of any transaction • Compactness • Reduce irrelevant info—infrequent items are gone • Items in frequency descending order: the more frequently occurring, the more likely to be shared • Never be larger than the original database (not count node-links and the count field) • For Connect-4 DB, compression ratio could be over 100

Partition Patterns and Databases • Frequent patterns can be partitioned into subsets according to f-list • F-list=f-c-a-b-m-p • Patterns containing p • Patterns having m but no p • … • Patterns having c but no a nor b, m, p • Pattern f • Completeness and non-redundency

{} Header Table Item frequency head f 4 c 4 a 3 b 3 m 3 p 3 f:4 c:1 c:3 b:1 b:1 a:3 p:1 m:2 b:1 p:2 m:1 Find Patterns Having P • Starting at the frequent item header table in the FP-tree • Traverse the FP-tree by following the link of each frequent item p • Accumulate all of transformed prefix paths of item p to form p’s conditional pattern base Conditional pattern bases item cond. pattern base c f:3 a fc:3 b fca:1, f:1, c:1 m fca:2, fcab:1 p fcam:2, cb:1

{} f:3 c:3 a:3 m-conditional FP-tree Find Patterns Having Item m But No p • For each pattern-base • Accumulate the count for each item in the base • Construct the FP-tree for the frequent items of the pattern base • m-conditional pattern base: • fca:2, fcab:1 {} Header Table Item frequency head f 4 c 4 a 3 b 3 m 3 p 3 All frequent patterns relate to m m, fm, cm, am, fcm, fam, cam, fcam f:4 c:1 c:3 b:1 b:1   a:3 p:1 m:2 b:1 p:2 m:1

Recursive Mining • Patterns having m but no p can be mined recursively • Optimization: enumerate patterns from single-branch FP-tree • Enumerate all combination • Support = that of the last item • m, fm, cm, am • fcm, fam, cam • fcam root f:3 c:3 a:3 m-projected FP-tree

a1:n1 a1:n1 {} {} a2:n2 a2:n2 a3:n3 a3:n3 r1 C1:k1 C1:k1 r1 = b1:m1 b1:m1 C2:k2 C2:k2 C3:k3 C3:k3 A Special Case: Single Prefix Path in FP-tree • Suppose a (conditional) FP-tree T has a shared single prefix-path P • Mining can be decomposed into two parts • Reduction of the single prefix path into one node • Concatenation of the mining results of the two parts + 

Mining Frequent Patterns With FP-trees • Idea: Frequent pattern growth • Recursively grow frequent patterns by pattern and database partition • Method • For each frequent item, construct its conditional pattern-base, and then its conditional FP-tree • Repeat the process on each newly created conditional FP-tree • Until the resulting FP-tree is empty, or it contains only one path—single path will generate all the combinations of its sub-paths, each of which is a frequent pattern

Why Is FP-Growth the Winner? • Divide-and-conquer: • decompose both the mining task and DB according to the frequent patterns obtained so far • leads to focused search of smaller databases • Other factors • no candidate generation, no candidate test • compressed database: FP-tree structure • no repeated scan of entire database • basic ops—counting local freq items and building sub FP-tree, no pattern search and matching

Implications of the Methodology • Mining closed frequent itemsets and max-patterns • CLOSET (DMKD’00) • Mining sequential patterns • FreeSpan (KDD’00), PrefixSpan (ICDE’01) • Constraint-based mining of frequent patterns • Convertible constraints (KDD’00, ICDE’01) • Computing iceberg data cubes with complex measures • H-tree and H-cubing algorithm (SIGMOD’01)

 a b c d ab ac ad bc bd cd abc abd acd bcd abcd Borders and Max-patterns • Max-patterns: borders of frequent patterns • A subset of max-pattern is frequent • A superset of max-pattern is infrequent

Closed Patterns • A long pattern contains a combinatorial number of sub-patterns, e.g., {a1, …, a100} contains (1001) + (1002) + … + (110000) = 2100 – 1 = 1.27*1030 sub-patterns! • Solution: Mine closed patterns and max-patterns instead • An itemset Xis closed if X is frequent and there exists no super-pattern Y  X, with the same support as X (proposed by Pasquier, et al. @ ICDT’99) • Closed pattern is a lossless compression of freq. patterns • Reducing the # of patterns and rules

Closed Patterns and Max-Patterns • Exercise. DB = {<a1, …, a100>, < a1, …, a50>} • Min_sup = 1. • What is the set of closed itemset? • <a1, …, a100>: 1 • < a1, …, a50>: 2 • What is the set of max-pattern? • <a1, …, a100>: 1 • What is the set of all patterns? • !!

MaxMiner: Mining Max-patterns • 1st scan: find frequent items • A, B, C, D, E • 2nd scan: find support for • AB, AC, AD, AE, ABCDE • BC, BD, BE, BCDE • CD, CE, CDE, DE, • Since BCDE is a max-pattern, no need to check BCD, BDE, CDE in later scan • R. Bayardo. Efficiently mining long patterns from databases. In SIGMOD’98 Potential max-patterns Min_sup=2

Mining Frequent Closed Patterns: CLOSET • Flist: list of all frequent items in support ascending order • Flist: d-a-f-e-c • Divide search space • Patterns having d • Patterns having d but no a, etc. • Find frequent closed pattern recursively • Every transaction having d also has cfa  cfad is a frequent closed pattern • J. Pei, J. Han & R. Mao. CLOSET: An Efficient Algorithm for Mining Frequent Closed Itemsets", DMKD'00. Min_sup=2

CLOSET+: Mining Closed Itemsets by Pattern-Growth • Itemset merging: if Y appears in every occurrence of X, then Y is merged with X • Sub-itemset pruning: if Y כ X, and sup(X) = sup(Y), X and all of X’s descendants in the set enumeration tree can be pruned • Hybrid tree projection • Bottom-up physical tree-projection • Top-down pseudo tree-projection • Item skipping: if a local frequent item has the same support in several header tables at different levels, one can prune it from the header table at higher levels • Efficient subset checking

EECS 800 Research Seminar Mining Biological Data