ACTION RULES & META ACTIONS presented by Zbigniew W. Ras University of North Carolina, Charlotte, NC College of Computing and Informatics University of North Carolina, Charlotte

Introduction : Action Rule An action rule /Ras & Wieczorkowska, PKDD 2000/ is a rule extracted from an information system that describes a possible transition of objects from one state to another with respect to a distinguished attribute called a decision attribute Information System Values of attributes can be changed Assumption: - attributes are partitioned into stable and flexible

Introduction : Action Rule Action rule is defined as a term Information System conjunction of fixed condition features shared by both groups proposed changes in values of flexible features desired effect of the action [(ω) ∧ (α → β)] →(ϕ→ψ)

Rules discovered: r 1 = [ Rules discovered: r 1 = [ (b, P)  (d, L)] r 2 = [(a, 2)  r 2 = [(a, 2)  (b, S)  (d, H)] Decision Table (a, 2)  Action rule: [(a, 2)  (b, P  S)](x)  [(d, L  H)](x) Example Xabcd x1x1 0S0L x2x2 0R1L x3x3 0S1L x4x4 0R1L x5x5 2P2L x6x6 2P2L x7x7 2S2H {a, c} - stable attributes, {b, d} - flexible attributes, d - decision attribute. d - decision attribute.

Application domain: Customer Attrition  On average, most US corporations lose half of their customers every five years (Rombel, 2001).  Longer a customer stays with the organization, the more profitable he or she becomes (Pauline, 2000; Hanseman, 2004).  The cost of attracting new customers is five to ten times more than retaining existing ones.  About 14% to 17% of the accounts are closed for reasons that can be controlled like price or service (Lunt, 1993). Action: Reducing the outflow of the customers by 5% can double a typical company’s profit (Rombel, 2001). Facts:

Methods for Action Rules Extraction: 1] Rule-based Prior extraction of classification rules is needed Example – DEAR /Tsay & Ras, tree-based strategy/ 2] Object-based Action rules are extracted directly from DB Example – ARED /similar to Apriori/ Ref 1: "Action rules discovery: System DEAR2, method and experiments", L.-S. Tsay, Z.W. Ras, Journal of Experimental and Theoretical Artificial Intelligence, Taylor & Francis, Vol. 17, No. 1-2, 2005, Ref 2: "Association Action Rules", Z.W. Ras, A. Dardzinska, L.-S. Tsay, H. Wasyluk, IEEE/ICDM Workshop on Mining Complex Data (MCD 2008), Pisa, Italy, ICDM Workshops Proceedings, IEEE Computer Society, 2008,

abcefd bcefd bcefd Splitting the node using the stable attribute Dom(a) = {1,2,3} & Dom(b) = {1,2,3,4,5} 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 a = 1 a = 2 a = 3 bcefd ced ced b = 1 b = 5 All the flexible values are the same for both objects, therefore this sub-table is not analyzed any further Partition decision table S Stable:{ a, b} Flexible: {c, e, f} Reclassification direction: 2  1 or 3  1 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) T1T1 T2T2 T3T3 T4T4 T5T5 Action Rules Discovery (Preprocessing)

Set of rules R with supporting objects (d, H)-tree T1 (d, L)-tree T2 Objectsabcd x1, x2, x3, x40L x1, x30L x2, x42L 1L x5, x63L x7, x821H 12H Objectsabc x1, x2, x3, x40 x1, x30 x2, x42 1 x5, x63 Objectsbc x1, x3 0 x2, x4 2 1 x5, x6 3 Objectsb x2, x42 x5, x63 c = 1c = ? c = 0 Objectsbc x1, x2, x3, x4 Objectsb x1, x3 a = 0 Objectsb x2, x4 a = ? Objectsabc x7, x Objectsbc x7, x81 a = 2 Objectsbc x7, x812 a = ? Stable Attribute: {a, c} Flexible Attribute: b Decision Attribute: d T1 T2 T3 T4 (T3, T1) : (a = 2)  (b, 2  1)  ( d, L  H) (a = 2)  (b, 3  1)  ( d, L  H) Objectsb x7, x81 c = ? c = 2 Objectsb x7, x81 c = ? Objectsb x1, x2, x3, x4 T5 T6 DEAR1 - Rule-Based Action Rules Discovery

ARED – Object Based Action Rule Discovery Xabcd x1x1x1x1 a1a1a1a1 b1b1b1b1 c1c1c1c1 d1d1d1d1 x2x2x2x2 a2a2a2a2 b1b1b1b1 c2c2c2c2 d1d1d1d1 x3x3x3x3 a2a2a2a2 b2b2b2b2 c2c2c2c2 d1d1d1d1 x4x4x4x4 a2a2a2a2 b1b1b1b1 c1c1c1c1 d1d1d1d1 x5x5x5x5 a2a2a2a2 b3b3b3b3 c2c2c2c2 d1d1d1d1 x6x6x6x6 a1a1a1a1 b1b1b1b1 c2c2c2c2 d2d2d2d2 x7x7x7x7 a1a1a1a1 b2b2b2b2 c2c2c2c2 d1d1d1d1 x8x8x8x8 a1a1a1a1 b2b2b2b2 c1c1c1c1 d3d3d3d3 (a, a 1 → a 1 ) (a,a 1 ) (a, a 2 → a 2 ) (a,a 2 ) (b, b 1 → b 1 ) (b, b 2 → b 2 ) ……….. (d, d 1 → d 1 ) (d, d 2 → d 2 ) Decision System S atomic action terms r=[(a, a 2 → a 2 )*(b, b 1 → b 1 )] → (d, d 1 → d 1 ) (w, w)  (Y, Y ) → (w,w)  (Z, Z) action rule Support: Confidence: Y = {x 2, x 4 } Z = {x 1,x 2,x 3,x 4,x 5,x 7 } sup(r) = 2 conf(r) = 2/2 = 1

Xabcd x1x1x1x1 a1a1a1a1 b1b1b1b1 c1c1c1c1 d1d1d1d1 x2x2x2x2 a2a2a2a2 b1b1b1b1 c2c2c2c2 d1d1d1d1 x3x3x3x3 a2a2a2a2 b2b2b2b2 c2c2c2c2 d1d1d1d1 x4x4x4x4 a2a2a2a2 b1b1b1b1 c1c1c1c1 d1d1d1d1 x5x5x5x5 a2a2a2a2 b3b3b3b3 c2c2c2c2 d1d1d1d1 x6x6x6x6 a1a1a1a1 b1b1b1b1 c2c2c2c2 d2d2d2d2 x7x7x7x7 a1a1a1a1 b2b2b2b2 c2c2c2c2 d1d1d1d1 x8x8x8x8 a1a1a1a1 b2b2b2b2 c1c1c1c1 d3d3d3d3 (a, a 1 → a 1 ) (a, a 1 → a 2 ) (b, b 1 → b 2 ) (b, b 2 → b 2 ) ……….. (d, d 1 → d 1 ) (d, d 2 → d 2 ) Decision System S atomic action terms r=[(a, a 2 → a 1 )*(b, b 1 → b 1 )] → (d, d 1 → d 2 ) (Y 1, Y 2 ) (Z 1, Z 2 ) rule Y 1 = {x 2, x 4 } Z 1 = {x 1,x 2,x 3,x 4,x 5,x 7 } Y 2 = {x 1, x 6 } Z 2 = { x 6 } sup(r) = 2 conf(r) = 1/2

Xabcd x1x1x1x1 a1a1a1a1 b1b1b1b1 c1c1c1c1 d1d1d1d1 x2x2x2x2 a2a2a2a2 b1b1b1b1 c2c2c2c2 d1d1d1d1 x3x3x3x3 a2a2a2a2 b2b2b2b2 c2c2c2c2 d1d1d1d1 x4x4x4x4 a2a2a2a2 b1b1b1b1 c1c1c1c1 d1d1d1d1 x5x5x5x5 a2a2a2a2 b3b3b3b3 c2c2c2c2 d1d1d1d1 x6x6x6x6 a1a1a1a1 b1b1b1b1 c2c2c2c2 d2d2d2d2 x7x7x7x7 a1a1a1a1 b2b2b2b2 c2c2c2c2 d1d1d1d1 x8x8x8x8 a1a1a1a1 b2b2b2b2 c1c1c1c1 d3d3d3d3 (a, a 1 → a 1 ) (a, a 1 → a 2 ) (b, b 1 → b 2 ) (b, b 2 → b 2 ) ……….. (d, d 1 → d 1 ) (d, d 2 → d 2 ) Decision System S atomic terms r=[(a, a 2 → a 1 )*(b, b 1 → b 1 )] → (d, d 1 → d 2 ) (Y 1, Y 2 ) (Z 1, Z 2 ) rule Y 1 = {x 2, x 4 } Z 1 = {x 1,x 2,x 3,x 4,x 5,x 7 } Y 2 = {x 1, x 6 } Z 2 = { x 6 } sup(r) = 1 conf(r) = 1/2

ARED Meaning of (d,d 1  d 2 ) in S: N S (d,d 1  d 2 )=[{x 1,x 2, x 3, x 4, x 5, x 7 }, {x 6 }] Xabcd x1x1x1x1 a1a1a1a1 b1b1b1b1 c1c1c1c1 d1d1d1d1 x2x2x2x2 a2a2a2a2 b1b1b1b1 c2c2c2c2 d1d1d1d1 x3x3x3x3 a2a2a2a2 b2b2b2b2 c2c2c2c2 d1d1d1d1 x4x4x4x4 a2a2a2a2 b1b1b1b1 c1c1c1c1 d1d1d1d1 x5x5x5x5 a2a2a2a2 b3b3b3b3 c2c2c2c2 d1d1d1d1 x6x6x6x6 a1a1a1a1 b1b1b1b1 c2c2c2c2 d2d2d2d2 x7x7x7x7 a1a1a1a1 b2b2b2b2 c2c2c2c2 d1d1d1d1 x8x8x8x8 a1a1a1a1 b2b2b2b2 c1c1c1c1 d3d3d3d3 stable attribute flexible attributes Object reclassification from class d 1 to d 2 λ1=2, λ2=1/4 Atomic classification terms: (b,b 1  b 1 ), (b,b 2  b 2 ), (b,b 3  b 3 ) (a,a 1  a 2 ), (a,a 1  a 1 ), (a,a 2  a 2 ), (a,a 2  a 1 ) (c,c 1  c 2 ), (c,c 2  c 1 ), (c,c 1  c 1 ), (c,c 2  c 2 ) λ1 - minimum support, λ2 - minimum confidence

ARED Xabcd x1x1x1x1 a1a1a1a1 b1b1b1b1 c1c1c1c1 d1d1d1d1 x2x2x2x2 a2a2a2a2 b1b1b1b1 c2c2c2c2 d1d1d1d1 x3x3x3x3 a2a2a2a2 b2b2b2b2 c2c2c2c2 d1d1d1d1 x4x4x4x4 a2a2a2a2 b1b1b1b1 c1c1c1c1 d1d1d1d1 x5x5x5x5 a2a2a2a2 b3b3b3b3 c2c2c2c2 d1d1d1d1 x6x6x6x6 a1a1a1a1 b1b1b1b1 c2c2c2c2 d2d2d2d2 x7x7x7x7 a1a1a1a1 b2b2b2b2 c2c2c2c2 d1d1d1d1 x8x8x8x8 a1a1a1a1 b2b2b2b2 c1c1c1c1 d3d3d3d3 stable attribute flexible attributes Object reclassification from class d 1 to d 2 λ1=2, λ2=1/4 Notation: t 1 =(b,b 1  b 1 ), t 2 =(b,b 2  b 2 ), t 3 =(b,b 3  b 3 ), t 4 =(a,a 1  a 2 ), t 5 =(a,a 1  a 1 ), t 6 =(a,a 2  a 2 ), t 7 =(a,a 2  a 1 ), t 8 =(c,c 1  c 2 ), t 9 =(c,c 2  c 1 ), t 10 =(c,c 1  c 1 ), t 11 =(c,c 2  c 2 ), t 12 = (d,d 1  d 2 ). λ1 - minimum support, λ2 - minimum confidence

For decision attribute in S: N S (d,d 1  d 2 )=[{x 1,x 2, x 3, x 4, x 5, x 7 }, {x 6 }] Object reclassification from class d 1 to d 2 λ1=2, λ2=1/4 For classification attribute in S: N S (t 1 ) = N S (b,b 1  b 1 ) = [{x 1,x 2, x 4, x 6 }, {x 1,x 2, x 4, x 6 }] N S (t 2 ) = N S (b,b 2  b 2 ) = [{x 3,x 7, x 8 }, {x 3,x 7, x 8 }] N S (t 3 ) = N S (b,b 3  b 3 ) = [{x 5 }, {x 5 }] N S (t 4 ) = N S (a,a 1  a 2 ) = [{x 1,x 6, x 7, x 8 }, {x 2,x 3, x 4, x 5 }] Xabcd x1x1x1x1 a1a1a1a1 b1b1b1b1 c1c1c1c1 d1d1d1d1 x2x2x2x2 a2a2a2a2 b1b1b1b1 c2c2c2c2 d1d1d1d1 x3x3x3x3 a2a2a2a2 b2b2b2b2 c2c2c2c2 d1d1d1d1 x4x4x4x4 a2a2a2a2 b1b1b1b1 c1c1c1c1 d1d1d1d1 x5x5x5x5 a2a2a2a2 b3b3b3b3 c2c2c2c2 d1d1d1d1 x6x6x6x6 a1a1a1a1 b1b1b1b1 c2c2c2c2 d2d2d2d2 x7x7x7x7 a1a1a1a1 b2b2b2b2 c2c2c2c2 d1d1d1d1 x8x8x8x8 a1a1a1a1 b2b2b2b2 c1c1c1c1 d3d3d3d3 Not marked λ1=3 Mark “-” λ2=0 Mark “-” λ1=1 Mark “-” λ2=0

For decision attribute in S: N S (d,d 1  d 2 )=[{x 1,x 2, x 3, x 4, x 5, x 7 }, {x 6 }] Object reclassification from class d 1 to d 2 λ1=2, λ2=1/4 For classification attribute in S: Xabcd x1x1x1x1 a1a1a1a1 b1b1b1b1 c1c1c1c1 d1d1d1d1 x2x2x2x2 a2a2a2a2 b1b1b1b1 c2c2c2c2 d1d1d1d1 x3x3x3x3 a2a2a2a2 b2b2b2b2 c2c2c2c2 d1d1d1d1 x4x4x4x4 a2a2a2a2 b1b1b1b1 c1c1c1c1 d1d1d1d1 x5x5x5x5 a2a2a2a2 b3b3b3b3 c2c2c2c2 d1d1d1d1 x6x6x6x6 a1a1a1a1 b1b1b1b1 c2c2c2c2 d2d2d2d2 x7x7x7x7 a1a1a1a1 b2b2b2b2 c2c2c2c2 d1d1d1d1 x8x8x8x8 a1a1a1a1 b2b2b2b2 c1c1c1c1 d3d3d3d3 Not marked λ1=2 Mark “-” λ2= 0 Mark “+” λ1=4,λ2=1/4 N S (t 5 ) = N S (a,a 1  a 1 ) = [{x 1,x 6, x 7, x 8 }, {x 1,x 6, x 7, x 8 }] N S (t 6 )= N S (a,a 2  a 2 ) = [{x 2,x 3, x 4, x 5 }, {x 2,x 3, x 4, x 5 }] N S (t 7 )= N S (a,a 2  a 1 ) = [{x 2,x 3, x 4, x 5 }, {x 1,x 6, x 7, x 8 }]

For decision attribute in S: N S (t 12 )=[{x 1,x 2, x 3, x 4, x 5, x 7 }, {x 6 }] Object reclassification from class d1 to d2 λ1=2, λ2=1/4 For classification attribute in S: N S (t 1 )=[{x 1,x 2, x 4, x 6 }, {x 1,x 2, x 4, x 6 }] Not marked λ1=3 N S (t 2 )=[{x 3,x 7, x 8 }, {x 3,x 7, x 8 }] Marked “-” λ2=0 N S (t 3 )=[{x 5 }, {x 5 }] Marked “-” λ1=1 N S (t 4 )=[{x 1,x 6, x 7, x 8 }, {x 2,x 3, x 4, x 5 }] Marked “-” λ2=0 N S (t 5 )=[{x 1,x 6, x 7, x 8 }, {x 1,x 6, x 7, x 8 }] Not marked λ1=2 N S (t 6 )=[{x 2,x 3, x 4, x 5 }, {x 2,x 3, x 4, x 5 }] Marked “-” λ2=0 Mark “+” λ1=4, λ2=1/4 N S (t 7 )=[{x 2,x 3, x 4, x 5 }, {x 1,x 6, x 7, x 8 }] r = [t 7  t 1 ] Xabcd x1x1x1x1 a1a1a1a1 b1b1b1b1 c1c1c1c1 d1d1d1d1 x2x2x2x2 a2a2a2a2 b1b1b1b1 c2c2c2c2 d1d1d1d1 x3x3x3x3 a2a2a2a2 b2b2b2b2 c2c2c2c2 d1d1d1d1 x4x4x4x4 a2a2a2a2 b1b1b1b1 c1c1c1c1 d1d1d1d1 x5x5x5x5 a2a2a2a2 b3b3b3b3 c2c2c2c2 d1d1d1d1 x6x6x6x6 a1a1a1a1 b1b1b1b1 c2c2c2c2 d2d2d2d2 x7x7x7x7 a1a1a1a1 b2b2b2b2 c2c2c2c2 d1d1d1d1 x8x8x8x8 a1a1a1a1 b2b2b2b2 c1c1c1c1 d3d3d3d3

For decision attribute in S: N S (t 12 )=[{x 1,x 2, x 3, x 4, x 5, x 7 }, {x 6 }] Object reclassification from class d1 to d2 λ1=2, λ2=1/4 For classification attribute in S: N S (t 8 )= N S (c,c 1  c 2 ) = [{x 1,x 4, x 8 }, {x 2, x 3, x 5, x 6, x 7 }] Not marked Marked “-” N S (t 10 ) = N S (c,c 1  c 1 ) = [{x 1, x 4, x 8 }, {x 1, x 4, x 8 }] Marked “-” N S (t 11 ) = N S (c,c 2  c 2 )= [{x 2, x 3, x 5, x 6, x 7 }, {x 2, x 3, x 5, x 6, x 7 }] Not marked conf = 2/3 *1/5 <λ 2 N S (t 9 ) = N S (c,c 2  c 1 ) = [{x 2, x 3, x 5, x 6, x 7 }, {x 1, x 4, x 8 }] Xabcd x1x1x1x1 a1a1a1a1 b1b1b1b1 c1c1c1c1 d1d1d1d1 x2x2x2x2 a2a2a2a2 b1b1b1b1 c2c2c2c2 d1d1d1d1 x3x3x3x3 a2a2a2a2 b2b2b2b2 c2c2c2c2 d1d1d1d1 x4x4x4x4 a2a2a2a2 b1b1b1b1 c1c1c1c1 d1d1d1d1 x5x5x5x5 a2a2a2a2 b3b3b3b3 c2c2c2c2 d1d1d1d1 x6x6x6x6 a1a1a1a1 b1b1b1b1 c2c2c2c2 d2d2d2d2 x7x7x7x7 a1a1a1a1 b2b2b2b2 c2c2c2c2 d1d1d1d1 x8x8x8x8 a1a1a1a1 b2b2b2b2 c1c1c1c1 d3d3d3d3

For decision attribute in S: N S (t 12 )=[{x 1,x 2, x 3, x 4, x 5, x 7 }, {x 6 }] Object reclassification from class d1 to d2λ1=2, λ2=1/4 For classification attribute in S: Marked “+” N S (t 1 *t 11 )=[{x 2, x 6 }, {x 2, x 6 }] Marked “-”, λ1=1 N S (t 5 *t 8 )=[{x 1, x 8 }, {x 6, x 7 }] Marked “-”, λ1=1 Rule r = [t 1 *t 8 →t 12 ], conf = 1/2 ≥ λ 2, sup=2 ≥ λ 1 Now action terms of length 2 from unmarked action terms of length 1 N S (t 1 *t 5 )=[{x 1, x 6 }, {x 1, x 6 }] Marked “-”, λ1=1 N S (t 1 *t 8 )=[{x 1, x 4 }, {x 2, x 6 }] N S (t 5 *t 11 )=[{x 6, x 7 }, {x 6, x 7 }] Marked “-”, λ1=1 N S (t 8 *t 11 )=[ Ø, {x 2, x 3, x 5, x 6, x 7 }] Marked “-” N S (t 1 )=[{x 1,x 2, x 4, x 6 }, {x 1,x 2, x 4, x 6 }], N S (t 5 )=[{x 1,x 6, x 7, x 8 }, {x 1,x 6, x 7, x 8 }], N S (t 8 )=[{x 1,x 4, x 8 }, {x 2, x 3, x 5, x 6, x 7 }], N S (t 11 )= [{x 2, x 3, x 5, x 6, x 7 }, {x 2, x 3, x 5, x 6, x 7 }].

ARED For decision attribute in S: N S (t 12 )=[{x 1,x 2, x 3, x 4, x 5, x 7 }, {x 6 }] Object reclassification from class d1 to d2λ1=2, λ2=1/4 For classification attribute in S: Action rules: [[(b,b1 →b1 )*(c,c1 → c2)] → (d, d1→d2) ] [[(a,a2 →a1 ] → (d, d1→d2) ] Xabcd x1x1x1x1 a1a1a1a1 b1b1b1b1 c1c1c1c1 d1d1d1d1 x2x2x2x2 a2a2a2a2 b1b1b1b1 c2c2c2c2 d1d1d1d1 x3x3x3x3 a2a2a2a2 b2b2b2b2 c2c2c2c2 d1d1d1d1 x4x4x4x4 a2a2a2a2 b1b1b1b1 c1c1c1c1 d1d1d1d1 x5x5x5x5 a2a2a2a2 b3b3b3b3 c2c2c2c2 d1d1d1d1 x6x6x6x6 a1a1a1a1 b1b1b1b1 c2c2c2c2 d2d2d2d2 x7x7x7x7 a1a1a1a1 b2b2b2b2 c2c2c2c2 d1d1d1d1 x8x8x8x8 a1a1a1a1 b2b2b2b2 c1c1c1c1 d3d3d3d3

Association Action Rules 1. (a, a 1 → a 2 ), where a is symbolic attribute attribute a 1, a 2 ∈ V a if a 1 = a 2 then a – stable on a 1 Atomic Action Terms: 2. (a, [a 1, a 2 ]  [a 3, a 4 ]), where a is numerical, a 1  a 2 < a 3  a 4, and a i  V a 3. (a, [a 1, a 2 ]  [a 3, a 4 ]), where a is numerical, a 1  a 2 < a 3  a 4, and a i  V a  - value is increased ;  - value is decreased

Association Action Rules Candidate action set - any collection of atomic actions Action set - candidate action set which does not contain two atomic actions referring to the same attribute Example: {(b, b 2 ), (b, [b 1, b 2 ]  [b 3, b 4 ])} – candidate action set but not action set. Action term - conjunction of atomic actions forming an action set. Example: (a, a 2 )  (c, c 1  c 2 )  (b, [b 1, b 2 ]  [b 3, b 4 ])

Association Action Rules Interpretation N S of action terms in S=(X,A,V): N S ((a, a 1  a 2 )) = [{x  X : a(x) = a 1 }, {x  X : a(x) = a 2 }]. N S ((a, [a 1, a 2 ]  [a 3, a 4 ])) = [{x  X : a 1  a(x)  a 2 }, {x  X : a 3  a(x)  a 4 }] N S ((a, [a 1, a 2 ]  [a 3, a 4 ])) = [{x  X : a 1  a(x)  a 2 }, {x  X : a 3  a(x)  a 4 }] N S ((a,  [a 3, a 4 ])) = [{x  X : a(x)  a 3 }, {x  X : a 3  a(x)  a 4 }] N S ((a, [a 3, a 4 ]  )) = [{x  X : a 3  a(x)  a 4 }, {x  X : a 4  a(x)}]

Association Action Rules Information System S=(X, A, V) N S (t)=[Y 1, Y 2 ]N S (t’)=[Z 1, Z 2 ] Action Rule: r = [t → t’] Support: Confidence: t = t 1  t 2  …  t k Atomic actions

Meta-actions /A. Tuzhilin (2006)/ Actions which trigger changes of flexible attributes either directly or indirectly because of correlations among certain attributes in the system. Example 1: Taking a drug / Lamivudine is used for treatment of chronic hepatitis B. It improves the seroconversion of e-antigen positive hepatitis B and also improves histology staging of the liver but at the same time it can cause a number of other symptoms. This is why doctors have to order certain lab tests to check patient’s response to that drug. Example 2: Classification attributes are: Explain difficult concepts effectively, Stimulate student interest in the course, Provide sufficient feedback. Meta-actions : Change the content of the course, Change the textbook of the course, …

Action Rules - continuation Influence Matrix A1A1 A2A2 A3A3 A4A4 …..AmAm M1M1 E 11 E 12 E 13 E 14 E 1m M2M2 E 21 E 22 E 23 E 24 E 2m M3M3 E 31 E 32 E 33 E 34 E 3m M4M4 E 41 E 42 E 43 E 44 E 4m ….. MnMn E m1 E m2 E m3 E m4 E mn A 1, A 2, A 3, …, A m – attributes M 1, M 2, M 3, …, M n – meta actions E ij – atomic action or NULL, i  m, j  n Atomic actions triggered by M 3 Action rule: r = [t  (d, d 1  d 2 )], where t – action term

Action Rules - continuation Meta-actions based decision system S(d)=(X,A  {d}, V ), with A= {A 1,A 2,…,A m } A1A1 A2A2 A3A3 A4A4 …..AmAm M1M1 E 11 E 12 E 13 NullE 1m M2M2 NullE 22 E 23 E 24 E 2m M3M3 E 31 E 32 Null M4M4 E 41 NullE 43 E 44 E 4m ….. MnMn E m1 NullE m3 E m4 E mn Influence Matrix r = [(A 1, a 1  a 1 ’)  (A 2, a 2  a 2 ’)  (A 4, a 4  a 4 ’)])  (d, d 1  d 1 ’) Candidate action rule - Meta-action M 3 triggers two atomic actions: {E 32 = [a 2  a 2 ’], E 31 = [a 1  a 1 ’]} We say that r is valid in S with respect to meta-action M 3 if the atomic actions triggered by M 3 do not contradict with atomic actions in r.

Action Rules - continuation Meta-actions based decision system S(d)=(X,A  {d}, V ), with A= {A 1,A 2,…,A m } A1A1 A2A2 A3A3 A4A4 …..AmAm M1M1 E 11 E 12 E 13 E 14 E 1m M2M2 E 21 E 22 E 23 E 24 E 2m M3M3 E 31 E 32 E 33 E 34 E 3m M4M4 E 41 E 42 E 43 E 44 E 4m ….. MnMn E m1 E m2 E m3 E m4 E mn Influence Matrix We say that action rule r extracted from S(d) is supported by meta-actions in M={M i1, M i2, …, M in }, if r is valid in S with respect to each meta-action in M and each atomic action at the left-hand side of r is triggered by minimum one meta-action in M.

Action Rules Discovery - Example abc M1M1 b1b1 c 2  c 1 M2M2 a 2  a 1 b2b2 M3M3 a 1  a 2 c 2  c 1 M4M4 b1b1 c 1  c 2 M5M5 b1b1 M6M6 a 1  a 2 c 1  c 2 Influence Matrix for S(d) Candidate action rules: r 1 = [[(b, b 1 )  (c, c 1  c 2 )] )  (d, d 1  d 2 )], valid with respect to M 4, M 5, M 6 r 2 = [(a, a 2  a 1 ) )  (d, d 1  d 2 )], valid with respect to M 2, M 4, M 5 but not valid with respect to M 2

Application Domain Database HEPAR (Medical Center of Postgraduate Education, Warsaw, Poland) prepared by Dr. med. Hanna Wasyluk  758 patients described by 106 attributes (including 31 laboratory tests with values discretized to: “below normal”, “normal”, “above normal”). 14 attributes are stable. Two tests are invasive tests:  758 patients described by 106 attributes (including 31 laboratory tests with values discretized to: “below normal”, “normal”, “above normal”). 14 attributes are stable. Two tests are invasive tests: HBsAg [in tissue], HBcAg [in tissue]. There are 7 decision values (attribute d): I. Acute hepatitis IIa. IIa. Subacute hepatitis (types BC) IIb. IIb. Subacute hepatitis (alcohol-abuse) IIIa. IIIa.Chronic hepatitis (curable) IIIb. IIIb.Chronic hepatitis (non-curable) IV. IV.Cirrhosis hepatitis V. V.Liver cancer We ask for re-classifications: IIb  I, IIIa  I

Application Domain Chosen d-reduct has no invasive tests, 11% incomplete data {m, n, q, u, y, aa, ah, ai, am, an, aw, bb, bg, by, cj, cm} m Bleeding nSubjaundice symptoms qEructation uObstruction yWeight loss aaSmoking ahHistory of viral hepatitis (stable) aiSurgeries in the past (stable) amHistory of hospitalization (stable) anJaundice in pregnancy awErythematous dermatitis bbCysts bgSharp liver edge (stable) bmBlood cell plaque byAlkaline phosphatase cjProthrombin index cmTotal cholesterol dDecision attribute

Application Domain: Database HEPAR but with history of s, s  No history of viral hepatitis but with history of surgery and hospitalization, sharp, no s, t,  liver edge normal, no subjaundice symptoms, total cholesterol normal,  ew  erythematous dermatitis normal, weight normal, no cysts, patient does not smoke  [(ah=1)  (ai=2)  (am=2)  (bg=1)]  (cm=1)  (aw=1)  (u,  1)  (bb=1)  (aa=1)   (q,  1)  (m,  1)  (n=1)  (bm,  up)  (y=1)  (by,  up)   (d, IIIa  I )  [(ah=1)  (ai=2)  (am=2)  (bg=1)]  (cm=1)  (aw=1)  (u,  1)  (bb=1)  (aa=1)   (q,  1)  (m,  1)  (n=1)  (bm,  up)  (y=1)  (by,  down)  (d, IIIa  I )  Two quite similar action rules have been constructed: By getting rid of obstruction, eructation, bleeding, by decreasing the b By getting rid of obstruction, eructation, bleeding, by decreasing the blood cell and by changing the level of a we should be able plaque and by changing the level of alkaline phosphatase we should be able reclassify the patient from IIIa group to I. reclassify the patient from IIIa group to I. Attribute values of twhave to stay unchanged. Attribute values of total cholesterol, weight, and smoking have to stay unchanged.

Meta Actions (drugs) Action Rule II requires getting rid of: - obstruction (u) HEPATILTRIPHALA - eructation (q) HEPATILHEPARGEN - bleeding (m) HEPATILHEPARGEN decreased b (bm) HEPATILHEPARGEN decreased blood cell plaque (bm) HEPATILHEPARGEN increased level of a increased level of alkaline phosphatase (by) HEPATILHEPARGEN Cost of Meta Action Rules [(ah=1)  (ai=2)  (am=2)  (bg=1)]  (cm=1)  (aw=1)  (u,  1)  (bb=1)  (aa=1)  (q,  1)  (m,  1)  (n=1)  (bm,  up)  (y=1)  (by,  down)  (d, IIIa  I ) ========================================================= [(ah=1)  (ai=2)  (am=2)  (bg=1)]  (cm=1)  (aw=1)  (bb=1)  (aa=1)  (n=1)  (y=1)  [obstruction, eructation, bleeding, increased b (aa=1)  (n=1)  (y=1)  [obstruction, eructation, bleeding, increased blood cell, increased level of a ]  [Take HEPATIL]  (d, IIIa  I ) plaque, increased level of alkaline phosphatase ]  [Take HEPATIL]  (d, IIIa  I ) [(ah=1)  (ai=2)  (am=2)  (bg=1)]  (cm=1)  (aw=1)  (bb=1)  (aa=1)  (n=1)  (y=1)  [obstruction, eructation, bleeding, increased b, increased level (y=1)  [obstruction, eructation, bleeding, increased blood cell plaque, increased level of a ]  [Take HEPERGEN & TRIPHALA]  (d, IIIa  I ) of alkaline phosphatase ]  [Take HEPERGEN & TRIPHALA]  (d, IIIa  I )

Simple Association Action Rules (a, a 1 → a 2 ) - atomic action set cost((a, a 1 → a 2 )) - cost of action expecting to change value of attribute a from a 1 to a 2. t 1 = (a, a 1 → a 2 ), t 2 = (b, b 1 → b 2 ) - two atomic action sets t 1, t 2 are positively correlated if changes t 1, t 2 support each other Change t 1 implies change t 2 and t 2 implies change t 1.

Simple Association Action Rules Definition: Let t = t 1  t 2  …  t m is a frequent action set, where each t i - atomic action set. Let T = {t 1, t 2,…, t m } and: t i ~t j iff t i and t j are positively correlated. Equivalence relation, partitions T into equivalence classes (T = T 1  T 2  …  T k )

Simple Association Action Rules Definition: Let t = t 1  t 2  …  t m is a frequent action set, where each t i - atomic action set. Let T = {t 1, t 2,…, t m } and: t i ~t j iff t i and t j are positively correlated. Now: In each equivalence class T i, an atomic action set a(T i ) of the lowest cost is identified. The cost of t is defined as: cost(t) = ∑{cost(a(T i )): 1≤ i ≤ k}

Simple Association Action Rules Definition: Let t = t 1  t 2  …  t m is a frequent action set, where each t i - atomic action set. Let T = {t 1, t 2,…, t m } and: t i ~t j iff t i and t j are positively correlated. Now: The cost of t is defined as: cost(t) = ∑{cost(a(T i )): 1≤ i ≤ k} a(T 1 )  a(T 2 )  …  a(T k ) → [t – {a(T i ): 1  i  k}] - simple association action rule.

Simple Association Action Rules Definition: Let t = t 1  t 2  …  t m is a frequent action set, where each t i - atomic action set. Let T = {t 1, t 2,…, t m } and: t i ~t j iff t i and t j are positively correlated. Now: The cost of t is defined as: cost(t) = ∑{cost(a(T i )): 1≤ i ≤ k} r = [ a(T 1 )  a(T 2 )  …  a(T k ) → [t – {a(T i ): 1  i  k}] ] - simple association action rule. The cost of r is defined as the cost of a(T 1 )  a(T 2 )  …  a(T k )

Action Reducts XBCED x1b2c1e1d2 x2b1c3e2d2 x3b1c1d2 x4b1c3e1d2 x5b1c1e1d1 x6b1c1e1d1 x7b2e2d1 x8b1c2e2d1 X2={x1,x2,x3,x4}, X1={x5,x6,x7,x8} x1x2x3x4 x5b2c3+e20c3 x6b2c3+e20c3 x7c1+e1b1+c3b1+c1b1+c3+e1 x8b2+c1+e1c3c1c3+e1 Discernable Table b2 is needed to discern x1 from x5 Action Reducts: R(x1)=b2[c1+e1][b2+c1+e1]= b2c1 + b2e1 R(x2)=c3, R(x3)=NIL, R(x4)=c3 Action Rules: (B,  b2)(C,  c1)  (D, d1  d2) (B,  b2)(E,  e1)  (D, d1  d2) (C,  c3)  (D, d1  d2)

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