1. Carson Kai-Sang Leung, Boyu Hao, Fan Jiang ICDE 2010 1

2.  Motivation  Method (UF-streaming+, UF-streaming*, CUF-streaming)  Experimental results  Conclusion 2

3.  There are many situations in which ones are uncertain about the contents of transactions. Moreover, there are also situations in which users are interested in only some portions of the mined frequent itemsets. 3

4. Minsup=1.2 preMinsup=0.9 First batch: a b c d e 1.8 1.6 1.9 0.9 1.4 例如 : expSup({a, e}) = (1 × 0.9 × 0.6) + (1 × 0.9 × 0.7) = 1.17 ≥ preMinsup expSup({c, e}) = (1 × 0.7 × 0.6)+ (1 × 0.8 × 0.7) = 0.98 ≥ preMinsup expSup({d, e}) =1 × 0.9 × 0.1 = 0.09 < preMinsup expSup({a, c, e}) = (1 × 0.9 × 0.7×0.6) + (1 × 0.9 × 0.8×0.7) ≈ 0.88 < preMinsup.) 4

5. First batch: {a} {a, c} {a, e} {b} {c} {c, e} {d} {e} 1.8,1.35, 1.17,1.6,1.5,0.98, 0.9, 1.4 ----------------------------------- Second batch: {a} {a, c} {b} {b, d} {c} {d} 0.9, 0.9, 1.4, 1.4, 1.8, 2.0 5

6. Second batch: {a} {a, c} {b} {b, d} {c} {d} 0.9, 0.9, 1.4, 1.4, 1.8, 2.0 ----------------------------- third batch: {a} {a, c} {b} {b, d} {c} {d} 1.7, 1.53, 1.0, 1.0, 1.9 1.2 post-processing step: {a}:2.6, {a, c}:2.43, {b}:2.4 and {c}:3.7 satisfying C1. 6

7.  the algorithm first uses the same UF-growth mining technique to find all “frequent” itemsets, and it then checks the mined itemsets against userspecified constraints before storing the constrained itemsets in the UF- stream structure.   7

8. Type1: ANTI-MONOTONE CONSTRAINT min(X.attr) ≥ const  R+ (X i.attr ≤ X i+1.attr) max(X.attr) ≤ const  R- (X i.attr ≥ X i+1.attr) Ex : C1 ≡ min(X.WBC) ≥ 10*10 3 /μL  (e, d, c, b, a ) 9.0 9.5 10.5 11.0 11.5 Type2: MONOTONE CONSTRAINT max(X.attr) ≥ const  R- min(X.attr) ≤ const  R+ Ex: C2 ≡ max(X.RBC) ≥ 6.1 × 10 6 /μL  abcde 8.53.37.56.65.9 8 acdeb 8.57.56.65.93.3

9. Type3: CONVERTIBLE ANTI-MONOTONE CONSTRAINT avg (X.attr) ≥ const or sum(X−.attr) ≥ const  R- avg (X.attr) ≤ const or sum(X+.attr) ≤ const  R+ Ex: C3 ≡ sum(X.Rainfall ) ≤ 200mm  Type4: CONVERTIBLE MONOTONE CONSTRAINT sum(X+.attr) ≥ const  R- sum(X−.attr) ≤ const  R+ Ex: C4 ≡sum(X.Rainfall ) ≥ 200mm  abcde 5033200101120 abcde 2015270300180 9 badec 3350101120200 daecb 3002011807052

10. 10

11. C1 ≡ min(X.WBC) ≥ 10000/μL  R+ (e,d,c,b,a)  (c,b,a) check {a} {a, c} {a, e} {b} {c} {c, e} {d} {e}  {a}, {a, c}, {b},{c} 11

12. 12

13.  we proposed three tree-based algorithms—namely, UF- streaming+, UF-streaming∗ and CUF-streaming— which integrate : (i) mining of uncertain data (ii) constrained mining (iii) mining of data streams. These algorithms effectively mine constrained frequent itemsets from uncertain data streams. 13