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1 DEIM Forum 2016 G ,,,,,,.,,,,, 1. 2 [1],,,,, [2] (, SPM),,,,,,,. [3],, [4]. 2 A,B, A B, B A, B, 2,,, Chen SPM [5](, TI-SPM) PrefixSpan [6], 2,, TI-SPM (, TI) 2,,,.,,, 1. 3,,

2 ,,,,,,,., 2,,, 3,, , 3.,, SPM Agrawal SPM (, SDB) [2]., SDB,.,., [4], 1. 2 A = a 1, a 2,..., a n (, a i. i = 1, 2,..., n), B = b 1, b 2,..., b m (, b i. i = 1, 2,..., m),, A B, A = B. 1 a 1 = b j1, a 2 = b j2,..., a n = b jt 2 n < = t < = m 3 1 < = j 1 j 2... j t < = m 2. A = a 1, a 2,..., a n (, a i. i = 1, 2,..., n) A = B B, A, A =. 3. MinSup(0 < = MinSup < = 1), SDB D, A = a 1, a 2,..., a n (, a i. i = 1, 2,..., n), {Seq A = Seq, (sid, Seq) D, sid Seq } > = Size(D) MinSup, A D MinSup, Sup(a i) a i D, Size(D) D 4. SDB D A, B \A, A. 1 A = B 2 Sup(A) = Sup(B) Sup(A) Sup(A) {s s = Seq, Seq D} TI-SPM Agrawal [2], 2., ,, , 1. Chen 2 TI-SPM [5]., TI-SPM, SDB D, MinSup(0 < = MinSup < = 1), TI- TI- TI-., TI, TI-, TI-, TI-, TI- 5. TI r 1 T 1, T 2,..., T r 1, TI I k (k = 0, 1,..., r 1, r) {0} (k = 0) {t 0 t < I k = T 1 } (k = 1) {t T k 1 t < = T k } (k = 2, 3,..., r 1) {t T r 1 t} (k = r)

3 6. TI- r 1 T 1, T 2,..., T r 1 r + 1 TI TI- V. TI-SPM,, 7. TI- I, TI- V, B TI { b 1 (k = 1) B = b 1, & 1, b 2, & 2,..., b k 1, & k 1, b k (k > = 2), i = 1, 2,..., k b i I, v = 1, 2,..., k 1 & v V. 8. TI- A = (a 1, t 1 ), (a 2, t 2 ),..., (a n, t n ) TI- B = b 1, & 1, b 2, & 2,..., b m 1, & m, b m, 1 < = j 1 j 2... j m < = n {j m }, B A TI-, B = A. 1 b 1 = a j1, b 2 = a j2,..., b m = a jm 2 t ji t ji 1 & i 1 (i = 2, 3,..., s) 9. TI- SDB D, MinSup (0 < = MinSup < = 1), TI- α {(sid, s) (sid, s) D, α = s} > = Size(D) MinSup, α TI-, Chen PrefixSpan [6], TI, I-PrefixSpan [5]., I-PrefixSpan, I-PrefixSPan 10. TI- A = (a 1, t 1 ), (a 2, t 2 ),..., (a n, t n ), TI- B = b 1, & 1, b 2,..., b m 1, & m 1, b m, B A TI- 1 m < = n 2 a i = b i (1 < = i < = m) 3 t i t i 1 & i 1 (1 i < = m 1) 11. A = (a 1, t 1), (a 2, t 2),..., (a n, t n), A TI- TI- B = b 1, & 1, b 2,..., b m 1, & m 1, b m m < = n a ik = b k (1 < = k < = m), A A = (a 1, t 1), (a 2, t 2),..., (a n, t n ), A A B 1 n = n + m i m i m. (0 < = i m < = n) 2 B A TI- 3 A n i m A n i m 12. TI- A = (a 1, t 1 ), (a 2, t 2 ),..., (a n, t n ) TI- B = b 1, & 1, b 2,..., b m 1, & m 1, b m A = (a 1, t 1), (a 2, t 2),..., (a n, t n )., A B = (a m+1, t m+1), (a m+2, t m+2),..., (a n, t n ) B A TI- 13. SDB SDB D, D α TI- SDB D α. I-PrefixSpan SDB D, MinSup TI- I D, SDB., α SDB, β, I TI, TI & Size(D) MinSup, α & β TI-, α & β, TI ( Type, Explain, Code, Name) 4 Code Name null,, 613, (,, 613, ) (,,null,null)., 613, Type, Code Name null., Type Code Name Explain, null. Explain,, [3],.

4 ,,,,, Type Type, Code Name 3. 2,, Type, Explain, Code, Name 4,, Wright [8].,,, SDB.,,,,,, Name Type,Explain,Code, TI-SPM,, TI-SPM I-PrefixSpan [5], TI-, TI-,, T-PrefixSpan, TI-SPM, Huang [7] T-PrefixSpan. Huang,,, 3, T-PrefixSpan, T-PrefixSpan,,,, SDB. 14. (i, t) I, i I t, i t (i, t) 15. s s,. s = (i 1, t 1), (i 2, t 2),..., (i n, t n)., s length(s) length(s) n, O s = i 1, i 2,..., i n s 16. T I k s = (i 1, t 1), (i 2, t 2),..., (i n, t n), T I k T I k t k+1 t k (k = 1, 2,..., n 2, n 1) 17. SDB D S, SDB D D {(sid, s) sid, s S}, D 2 sid. SDB SDB SDB, SDB, 18. P MinSup (0 < = MinSup < = 1), SDB D, P = i 1, X 1, i 2, X 2,..., i n 1, X n 1, i n ( j i j, k X k 5 (min k, mod k, ave k, med k, max k ), O P = i 1, i 2,..., i n 1, i n, O P D SDB MinSup,, min k, mod k, ave k, med k, max k., O P D S = i 1, t 1, i 2, t 2,..., i m 1, t m 1, i m, i k = i j k, i k+1 = i j k+1 k = 1, 2,..., n 1, 1 < = j 1 j 2... j n 1 j n < = m, T I k = t j k+1 t j k Set T Ik., X k = (min k, mod k, ave k, med k, max k ),min k = min Set T Ik, mod k Set T Ik, ave k Set T Ik, med k Set T Ik, max k = max Set T Ik.,

5 X j = (min j, mod j, ave j, med j, max j) (1 < = j n), min j = max j, i j i j+1, min j = max j = 0, O P P 19. SDB D A, B \A, A 1 A.B A, B, A = B. 2 (1), A = a 1, T 1, a 2, T 2,..., a n 1, T n 1, a n, B = b 1, T 1, b 2, T 2,..., b m 1, T m 1, b m, a k = b jk, a k+1 = b jk+1 k = 1, 2,..., n 1, 1 < = j 1 j 2... j n < = m., T k = (min k, mod k, ave k, med k, max k ), T j k = (min j k, mod j k, ave j k, med j k, max j k ), min k > = min j k max k < = max j k. 3 Sup(A) < = Sup(B) Sup(A) Sup(A) {s s = S, (sid, S) D, sid S }., 1 SDB D, MinSup = SDB D sid 10 (A, 1), (B, 3), (C, 7), (E, 10) 20 (A, 1), (B, 4), (E, 7) 30 (A, 2), (B, 6), (B, 9) 40 (A, 2), (B, 5) 50 (A, 2), (B, 7), SDB SDB O D 2, O D MinSup = 0.4, A, B, E, A, B, B, E, A, B, E. 2 D SDB O D sid 10 A, B, C, E 20 A, B, E 30 A, B, B 40 A, B 50 A, B O D, D, A, B, E D, A, B A B, D {2, 3, 3, 4, 5},,,,,, A, (2, 3, 3, 3, 5), B, B, E, A, B, E, B, (3, 5, 5, 5, 7), E, A, (2, 2, 2, 2, 3), B, (3, 5, 5, 5, 7), E., D MinSup = 0.4 A, B, E, A, (2, 3, 3, 3, 5), B, B, (3, 5, 5, 5, 7), E, A, (2, 2, 2, 2, 3), B, (3, 5, 5, 5, 7), E., A, B, A, (2, 3, 3, 3, 5), B, A, (2, 2, 2, 2, 3), B, (3, 5, 5, 5, 7), E. PrefixSpan [6] SDB T-PrefixSpan. T-PrefixSpan Algorithm 1., SDB D SDB Original(D), S Original(S), A B AB. X n X n, S n S n, A n T (A n)., Smirnov-Grubbs [9] α = ( Type, Explain, Code, Name) 4, t.,,,, Type, Explain, Code, Name SDB, T-PrefixSpan, 4..,,,, ,

6 Algorithm 1 T-PrefixSpan Input : SDB D, MinSup Output : P Call : T-PrefixSpan(,D) Procedure : T-PrefixSpan(α,D α) 1: D α = Original(D α ) 2: if α! = null then 3: P GetProperTime(α, D α, D α) 4: end if 5: B {β (s = D α, β s) (Sup(β) > = Size(D) Minsup)} 6: for β B do 7: D αβ { sid, s D α αβ = Original(s)} 8: Call T-PrefixSpan(αβ, D αβ ) 9: end for Subroutine : GetProperTime(α, D α, D α) 1: if length(α) == 1 then 2: return α 3: end if 4: K {k sid, s D α,original(s) D α, k = s,original(k) == α} 5: T = {{}, {},..., {}}( T = length(α) 1) 6: for k K do 7: for i = 0,..., length(k 1) do 8: T i T (k i+1 ) T (k i ) 9: end for 10: end for 11: W = α 0, α 1,..., α length(α) 1 12: for i = 0,..., length(α) 2 do 13: T i 14: min i = min T i 15: mod i = (T i ) 16: ave i = (T i ) 17: med i = (T i ) 18: max i = max T i 19: X i = (min i, mod i, ave i, med [ i], max [ i]) 20: W = α 0,..., α i, X i, α i+1..., α length(α) 1 21: end for 22: return W, ,, T-PrefixSpan,,,, OS : Windows7 Professional 64bit CPU : Intel(R) Xeon(R) CPU E GHz(8CPUs) Memory : 16GB Java (1), (2)TUR-Bt,,,, 3 3 TUR-Bt WATATUMI [10],, ID., HP [11], (1), (2)TUR-Bt 2, 3. (1), (2)TUR-Bt , 2, 3, 4, 5, 6. 1,.,

7 2 TUR-Bt 6 TUR-Bt 3 4 TUR-Bt 5 TUR-Bt,, T-PrefixSpan,,,., , 0 7,, 2, 2. 7, 8..,. 7 8,,,., MinSup = 0.02, 8, 7,., SDB,

,, TUR-Bt,,,,, 7, (A) (#25240014), HP [11], 8.,,,,,, 5,,,,. 5. 2 PrefixSpan [6], T-PrefixSpan,, CloSpan [4],Clasp [12],CSpan [13],, 2,,, T-PrefixSpan TI-SPM, [1],,,,,. DEIM Forum 2014, F6-2, 2014.

487-499, 1994. [3],,,,. DEIM Forum 2015, G5-1, 2015. [4] X. Yan, J. Han and R.Afshar. CloSpan: Mining closed sequential patterns in large databases. Proc.SIAM Int 1 Conf. Data Mining (SDM 03), pp.

8 ,, TUR-Bt,,,,, 7, (A) (# ), HP [11], 8.,,,,,, 5,,,, PrefixSpan [6], T-PrefixSpan,, CloSpan [4],Clasp [12],CSpan [13],, 2,,, T-PrefixSpan TI-SPM, [1],,,,,. DEIM Forum 2014, F6-2, [2] Rakesh Agrawal and Ramakrishnan Srikant. Fast algorithms for mining association rules in large databases. Proceeding of the 20th International Conference on Very Large Data Bases, pp , [3],,,,. DEIM Forum 2015, G5-1, [4] X. Yan, J. Han and R.Afshar. CloSpan: Mining closed sequential patterns in large databases. Proc.SIAM Int 1 Conf. Data Mining (SDM 03), pp , May [5] Yen-Liang Chen, Mei-Ching Chiang and Ming-Tat Ko. Discovering time-interval sequential patterns in sequence databases. Expert Systems with Applications 25, pp , [6] Jian Pei, Jiawei Han, Behzad Mortazavi-Asl, Helen Pinto, Qiming Chen, Umeshwar Dayal, Mei-Chun Hsu. PrefixSpan: Mining Sequential Patterns Efficiently by Prefix- Projected Pattern Growth. Proceeding of 2001 International Conference on Data Engineering, pp , [7] Zhengxing Huang, Xudong Lu and Huilong Duan. On mining clinical pathway patterns from medical behaviors. Artificial Intelligence in Medicine 56 (2012) 35-65, [8] Aileen P. Wright, Adam T. Wright, Allison B. McCoy and Dean F.Sittig. The use of sequential pattern mining to predict next prescribed medications. Journal of Biomedical Informatics 53(2015) 73-80, [9] [10] WATATUMI izanami.html [11] [12] Antonio Gomariz, Manuel Campos, Roque Marin and Bart Goethals. Clasp: An efficient algorithm for mining frequent closed sequences. PAKDD 2013, LNAI7818, Part I, pp , [13] V.Purushothama Raju and G.P. Saradhi Varma. MIN- ING CLOSED SEQUENTIAL PATTERNS IN LARGE SE- QUENCE DATABASES. International Journal of Database Management Systems ( IJDMS ) Vol.7, No.1, February 2015.

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