1 / 21

Action Rules Discovery Systems: DEAR1, DEAR2, ARED, ….. by Zbigniew W. Ra ś

Action Rules Discovery Systems: DEAR1, DEAR2, ARED, ….. by Zbigniew W. Ra ś. Y = {x 2 , x 4 } Z = {x 1 ,x 2 ,x 3 ,x 4 ,x 5 ,x 7 }. LERS. (a, a 1 ) (a, a 2 ) (b, b 1 ) (b,b 2 ) ……….. (d,d 1 ) (d,d 2 ). atomic terms. Decision System S. r = [[(a, a 2 )*(b, b 1 )] → (d, d 1 )]

dara-conrad
Download Presentation

Action Rules Discovery Systems: DEAR1, DEAR2, ARED, ….. by Zbigniew W. Ra ś

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Action Rules Discovery Systems: DEAR1, DEAR2, ARED, ….. by ZbigniewW. Raś

  2. Y = {x2, x4} Z = {x1,x2,x3,x4,x5,x7} LERS (a, a1) (a, a2) (b, b1) (b,b2) ……….. (d,d1) (d,d2) atomic terms Decision System S r = [[(a, a2)*(b, b1)] → (d, d1)] w  Y → w  Z rule sup(r) = 2 conf(r) = 2/2 = 1 Support: Confidence:

  3. Action Rules Discovery (Preprocessing) Partition decision table S Stable:{ a, b} Flexible: {c, e, f} Reclassification direction: 2 1 or 3 1 Splitting the node using the stable attribute Dom(a) = {1,2,3} & Dom(b) = {1,2,3,4,5} a = 1 a = 3 a = 2 All objects have the same value 8 for attribute f, so it is crossed out from the sub-table ( this condition is used for stable attributes as well) T1 T3 All objects have the same decision value, so this sub-table is not analyzed any further None of the objects contain the desired class “1”, so this sub-table stops splitting any further T2 b = 5 b = 1 T5 T4 All the flexible values are the same for both objects , therefore this sub-table is not analyzed any further

  4. System DEAR1 Stable Attribute: {a, c} Flexible Attribute: b Decision Attribute: d a = ? a = 0 Table: Set of rules R with supporting objects c = ? c = ? c = 1 a = 2 c = 0 a = ? T6 T4 T5 c = ? c = 2 Figure of (d, L)-tree T2 T3 (T3, T1) : (a = 2)  (b, 21) ( d, L  H) (a = 2)  (b, 31) ( d, L  H) T1 T2 Figure of (d, H)-tree T1

  5. System DEAR2 b = 1 b = 2 b = 3 Set of rules R with supporting objects Stable Attribute: b Flexible Attribute: {a, c} Decision Attribute: d d = L d = H (b = 1)  (a, 02) ( d, L  H) (b = 1)  (c, 02) ( d, L  H) (b = 1)  (c, 12) ( d, L  H)

  6. Cost of Action Rule Action rule r: [(b1, v1→ w1)  (b2, v2→ w2)  … ( bp, vp→ wp)](x)  (d, k1→ k2)(x) The cost of r in S: costS(r) = {S(vi , wi) : 1  i  p} Action rule r is feasible in S, if costS(r) < S(k1 , k2). For any feasible action rule r, the cost of the conditional part of r is lower than the cost of its decision part.

  7. Cost of Action Rule Example: r = [(b1, v1 → w1) … (bj, vj → wj) …  ( bp, vp → wp)](x)  (d, k1 → k2)(x) In RS[(bj, vj → wj)] we find r1= [(bj1, vj1 → wj1)  (bj2, vj2 → wj2)  … ( bjq, vjq → wjq)](x) (bj, vj → wj)(x) Then, we can compose r with r1 and the same replace term (bj, vj → wj) by term from the left hand side of r1: [(b1, v1 → w1)  … [(bj1, vj1 → wj1)  (bj2, vj2 → wj2)  …  ( bjq, vjq → wjq)] … ( bp, vp → wp)](x)  (d, k1 → k2)(x)

  8. ARED (a, a1 →a1) (a, a2 → a2) (b, b1 → b1) (b, b2 → b2) ……….. (d, d1 → d1) (d, d2 → d2) Y = {x2, x4} Z = {x1,x2,x3,x4,x5,x7} Decision System S atomic action terms r=[(a, a2→ a2)*(b, b1→ b1)] → (d, d1→ d1) (w, w)  (Y, Y ) → (w,w)  (Z, Z) action rule Support: Confidence: sup(r) = 2 conf(r) = 2/2 = 1

  9. ARED (a, a1 →a1) (a, a2 → a2) (b, b1 → b1) (b, b2 → b2) ……….. (d, d1 → d1) (d, d2 → d2) Y = {x2, x4} Z = {x1,x2,x3,x4,x5,x7} Decision System S atomic action terms r=[(a, a2→ a1)*(b, b1→ b1)] → (d, d1→ d2) (w1, w2)  (Y1, Y2) → (w1,w2)  (Z1, Z2) Y=(Y1,Y2), Z=(Z1,Z2) w = (w1,w2) action rule Support: Confidence: sup(r) = ? conf(r) = ?

  10. ARED (a, a1 →a1) (a, a1 → a2) (b, b1 → b2) (b, b2 → b2) ……….. (d, d1 → d1) (d, d2 → d2) atomic action terms Decision System S Y1→ Z1, Y2→ Z2 r=[(a, a2→ a1)*(b, b1→ b1)] → (d, d1→ d2) (Y1, Y 2) (Z1, Z2) action rule sup(r) = 2 conf(r) = 2/2 = 1 Support: Confidence: Y1 = {x2, x4} Z1 = {x1,x2,x3,x4,x5,x7} Y2 = {x1, x6} Z2 = { x6}

  11. ARED (a, a1 →a1) (a, a1 → a2) (b, b1 → b2) (b, b2 → b2) ……….. (d, d1 → d1) (d, d2 → d2) atomic terms Decision System S r=[(a, a2→ a1)*(b, b1→ b1)] → (d, d1→ d2) (Y1, Y 2) (Z1, Z2) rule sup(r) = 2 conf(r) = 2/2 = 1 Y1 = {x2, x4} Z1 = {x1,x2,x3,x4,x5,x7} Y2 = {x1, x6} Z2 = { x6}

  12. ARED (a, a1 →a1) (a, a1 → a2) (b, b1 → b2) (b, b2 → b2) ……….. (d, d1 → d1) (d, d2 → d2) atomic terms Decision System S r=[(a, a2→ a1)*(b, b1→ b1)] → (d, d1→ d2) (Y1, Y 2) (Z1, Z2) rule sup(r) = 2 conf(r) = 2/2 = 1 Y1 = {x2, x4} Z1 = {x1,x2,x3,x4,x5,x7} Y2 = {x1, x6} Z2 = { x6}

  13. ARED λ1 - minimum support, λ2 - minimum confidence Object reclassification from class d1 to d2 λ1=2, λ2=1/4 Meaning of (d,d1  d2) in S: NS(d,d1 d2)=[{x1,x2, x3, x4, x5, x7}, {x6}] Atomic classification terms: (b,b1b1), (b,b2b2), (b,b3b3) (a,a1a2), (a,a1a1), (a,a2a2), (a,a2a1) (c,c1c2), (c,c2c1), (c,c1c1), (c,c2c2) stable attribute flexible attributes

  14. ARED λ1 - minimum support, λ2 - minimum confidence Object reclassification from class d1 to d2 λ1=2, λ2=1/4 Notation: t1=(b,b1b1), t2=(b,b2b2), t3=(b,b3b3), t4=(a,a1a2), t5=(a,a1a1), t6=(a,a2a2), t7=(a,a2a1), t8=(c,c1c2), t9=(c,c2c1), t10=(c,c1c1), t11=(c,c2c2), t12 = (d,d1 d2). stable attribute flexible attributes

  15. Object reclassification from class d1 to d2 λ1=2, λ2=1/4 For decision attribute in S: NS(d,d1 d2)=[{x1,x2, x3, x4, x5, x7}, {x6}] For classification attribute in S: Not marked λ1=3 NS(t1) = NS(b,b1b1) = [{x1,x2, x4, x6}, {x1,x2, x4,x6}] Mark “-” λ2=0 NS(t2) = NS(b,b2b2) = [{x3,x7, x8}, {x3,x7, x8}] Mark “-” λ1=1 NS(t3) = NS(b,b3b3) = [{x5}, {x5}] Mark “-” λ2=0 NS(t4) = NS (a,a1a2) = [{x1,x6, x7, x8}, {x2,x3, x4,x5}]

  16. Object reclassification from class d1 to d2 λ1=2, λ2=1/4 For decision attribute in S: NS(d,d1 d2)=[{x1,x2, x3, x4, x5, x7}, {x6}] For classification attribute in S: Not marked λ1=2 NS(t5) = NS(a,a1a1) = [{x1,x6, x7, x8}, {x1,x6, x7,x8}] Mark “-” λ2= 0 NS(t6)= NS(a,a2a2) = [{x2,x3, x4, x5}, {x2,x3, x4,x5}] Mark “+” λ1=4,λ2=1/4 NS(t7)= NS(a,a2a1) = [{x2,x3, x4, x5}, {x1,x6, x7,x8}]

  17. Object reclassification from class d1 to d2 λ1=2, λ2=1/4 For decision attribute in S: NS(t12)=[{x1,x2, x3, x4, x5, x7}, {x6}] For classification attribute in S: Not marked λ1=3 NS(t1)=[{x1,x2, x4, x6}, {x1,x2, x4,x6}] Marked “-” λ2=0 NS(t2)=[{x3,x7, x8}, {x3,x7, x8}] Marked “-” λ1=1 NS(t3)=[{x5}, {x5}] Marked “-” λ2=0 NS(t4)=[{x1,x6, x7, x8}, {x2,x3, x4,x5}] Not marked λ1=2 NS(t5)=[{x1,x6, x7, x8}, {x1,x6, x7,x8}] Marked “-” λ2=0 NS(t6)=[{x2,x3, x4, x5}, {x2,x3, x4,x5}] NS(t7)=[{x2,x3, x4, x5}, {x1,x6, x7,x8}] Mark “+” λ1=4, λ2=1/4 r = [t7 t1]

  18. Object reclassification from class d1 to d2 λ1=2, λ2=1/4 For decision attribute in S: NS(t12)=[{x1,x2, x3, x4, x5, x7}, {x6}] For classification attribute in S: conf = 2/3 *1/5 <λ2 Not marked NS(t8)= NS(c,c1c2) = [{x1,x4, x8}, {x2, x3, x5,x6, x7}] Marked “-” NS(t9) = NS(c,c2c1) = [{x2, x3, x5, x6, x7}, {x1, x4, x8}] Marked “-” NS(t10) = NS(c,c1c1) = [{x1, x4, x8}, {x1, x4,x8}] Not marked NS(t11) = NS (c,c2c2)= [{x2, x3, x5, x6, x7}, {x2, x3, x5,x6, x7}]

  19. Object reclassification from class d1 to d2 λ1=2, λ2=1/4 Now action terms of length 2 from unmarked action terms of length 1 For decision attribute in S: NS(t12)=[{x1,x2, x3, x4, x5, x7}, {x6}] For classification attribute in S: NS(t1)=[{x1,x2, x4, x6}, {x1,x2, x4,x6}] , NS(t5)=[{x1,x6, x7, x8}, {x1,x6, x7,x8}], NS(t8)=[{x1,x4, x8}, {x2, x3, x5,x6, x7}], NS(t11)= [{x2, x3, x5, x6, x7}, {x2, x3, x5,x6, x7}]. Marked “-”,λ1=1 NS(t1*t5)=[{x1, x6}, {x1, x6}] Marked “+” NS(t1*t8)=[{x1, x4}, {x2, x6}] Rule r = [t1*t8→t12], conf = 1/2 ≥ λ2, sup=2 ≥ λ1 Marked “-”,λ1=1 NS(t1*t11)=[{x2, x6}, {x2, x6}] Marked “-”,λ1=1 NS(t5*t8)=[{x1, x8}, {x6, x7}] Marked “-”,λ1=1 NS(t5*t11)=[{x6, x7}, {x6, x7}] Marked “-” NS(t8*t11)=[Ø, {x2, x3, x5, x6, x7}]

  20. ARED Algorithm Object reclassification from class d1 to d2 λ1=2, λ2=1/4 For decision attribute in S: NS(t12)=[{x1,x2, x3, x4, x5, x7}, {x6}] For classification attribute in S: Action rules: [[(b,b1→b1)*(c,c1→c2)] → (d, d1→d2)] [[(a,a2→a1] → (d, d1→d2)]

  21. Questions? Thank You

More Related