Action Rules Discovery /Lecture I/

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Action Rules Discovery /Lecture I/. by Zbigniew W. Ras UNC-Charlotte, USA. Interestingness measure. E = [Cond 1 => Cond 2 ]. Presumptive. Objective. Rule : two conditions occur together, with some confidence. Data Mining Task : For a given dataset D, interestingness measure I D and

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## Action Rules Discovery /Lecture I/

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### Action Rules Discovery/Lecture I/

by

Zbigniew W. Ras

UNC-Charlotte, USA

Interestingness measure

E = [Cond1 => Cond2]

Presumptive

Objective

Rule: two conditions occur together, with some confidence

For a given dataset D, interestingness measure ID and

threshold c, find association E such that ID(E) > c.

Knowledge Engineer definesc

Interestingness Function

Two types of Interestingness Measure[Silberschatz and Tuzhilin, 1995]: subjective and objective.

Subjective measure: user-driven, domain-dependent.

Include unexpectedness [Silberschatz and Tuzhilin, 1995],

novelty, actionability [Piatesky-Shapiro & Matheus, 1994].

Objective measure: data-driven and domain-independent.

They evaluate rules based on statistics and structures of patterns, e.g., support, confidence, etc.

Objective Interestingness

Basic Measures for :

Domain: card[]

Support or Strength: card[  ]

Confidence or Certainty Factor: card[]/card[]

Coverage Factor: card[]/card[]

Leverage: card[]/n – [card[]/n]*[card[]/n]

Lift: n  card[]/[card[]*card[]]

Subjective Interestingness

• Rule is interesting if it is:
• unexpected, if it contradicts the user belief about the domain and therefore surprises the user
• novel, if to some extent contributes to new knowledge
• actionable, if the user can take an action to his/her advantage based on this rule

Unexpectedness [Suzuki, 1997]

/does not depend on domain knowledge/

If r = [AB1] has a high confidence and r1 = [A*CB2]

has a high confidence, then r1 is unexpected.

A  B is unexpected with respect to the belief

on the dataset D if the following conditions hold:

B   = False [ B and  logically contradict each other]

A   holds on a large subset of D

 A*  B holds which means A*  

Actionable rules

• Action rules: suggest a way to re-classify objects (for instance customers) to a desired state.
• Action rules can be constructed from classification rules.
• To discover action rules it is required that the set of conditions (attributes) is partitioned into stable and flexible.
• For example, date of birth is a stable attribute, and interest rate on any customer account is a flexible attribute (dependable on bank).

The notion of action rules was proposed by

[Ras & Wieczorkowska, PKDD’00]. Slowinski at al [JETAI, 2004] introduced similar notion called intervention.

Action Rules

Decision table

Any information system of the form

S = (U, AFl ASt {d}), where

• d  AFl ASt is a distinguished attribute called decision.
• ASt - stable attributes, AFl {d} - flexible

Action rule [Ras & Wieczorkowska]:

[t(ASt)  (b1, v1 w1)  (b2, v2 w2)  …  (bp, vp wp)](x)

 [(d, k1 k2)](x), where (i)[(1 i  p)  (biAFl)]

E-Action rule [Ras & Tsay]:

[t(ASt)  (b1,  w1)  (b2, v2 w2)  …  (bp, wp)](x)

 [(d, k1 k2)](x), where (i)[(1 i  p)  (biAFl)]

Action Rules Discovery (Tsay & Ras)

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

Application domain: Customer Attrition

Facts:

• 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).

Action Rules Discovery

Decision table S = (U, AFl ASt {d}).

Assumption: {a1,a2,...,ap}  ASt, {b1,b2,...,bq}  AFl,

ai,1 Dom(ai), bi,1 Dom(bi).

Rule:

r = [a1,1 a2,1 ...  ap,1 ]  [b1,1 b2,1 ...  bq,1]  d1

stable part flexible part

Question:

Do we have to consider pairs of classification rules in order to construct action rules?

Action Rules Discovery

Decision table S = (U, AFl ASt {d}).

Assumption: {a1,a2,...,ap}  ASt, {b1,b2,...,bq}  AFl,

ai,1 Dom(ai), bi,1 Dom(bi).

Rule:

r = [a1,1 a2,1 ...  ap,1 ]  [b1,1 b2,1 ...  bq,1]  d1

stable part flexible part

Action rule r[d2  d1] associated with r and

[a1,1 a2,1 ...  ap,1] 

[(b1,  b1,1 ) (b2, b2,1) ...  (bq, bq,1)]  (d, d2 d1)

Action Rules Discovery

Action rule r[d2  d1]:

[a1,1 a2,1 ...  ap,1] 

[(b1,  b1,1 ) (b2, b2,1) ...  (bq, bq,1)]  (d, d2 d1)

Support

Sup(r[d2  d1]) =

{x  U: (a1(x)=a1,1)  (a2(x)=a2,1)...(ap(x)=ap,1)  (d(x)=d2)}.

/d2-objects which potentially can be reclassified by r[d2  d1] to d1/

Sup(R[d2  d1]) = {Sup(r[d2  d1]): r  R},

where R- classification rules extracted from S.

/d2-objects which potentially can be reclassified by r[d2  d1] to d1/

Action Rules Discovery

Action rule r[d2  d1]:

[a1,1 a2,1 ...  ap,1] 

[(b1, b’1,1 b1,1 ) (b2, b’2,1b2,1) ...  (bq, bq,1)] 

(d, d2 d1)

Support

Sup(r[d2  d1]) =

{x  U: (b1(x)=b’1,1)  (b2(x)=b’2,1) 

(a1(x)=a1,1)  (a2(x)=a2,1) ... (ap(x)=ap,1)  (d(x)=d2)}.

/d2-objects which potentially can be reclassified by

r[d2  d1] to d1/

Action Rules Discovery

Let Ud2 = {x  U: d(x)=d2}. Then

Bd2  d1 = Ud2 - Sup(R[d2  d1])

is a set of d2-objects in S which are d1-resistant.

Let Sup(R[  d1]) = {Sup(R[d2  d1]) : d2 d1}. Then

B d1 = U - Sup(R[  d1])

is a set of objects in S which are d1-resistant

(can not be re-classified to class d1).

Action Rules Discovery

Action rules r[d2  d1], r‘[d2  d3] are p-equivalent (), if

r/bi = r'/bi always holds when r/bi, r'/bi are both defined,

for every bi ASt AFl.

Let x  Sup(r[d2  d1]). We say that

x positively supports r[d2  d1]

if there is no action rule r‘[d2  d3] extracted from S, d3 d1,

which is p-equivalent to r[d2  d1] and x  Sup( r‘[d2  d3]).

Action Rules Discovery

Let Sup+(R[d2  d1]) =

{x  Sup(r[d2  d1]): x positively supports r[d2  d1]}.

Confidence

Conf(r[d2  d1]) =

{card[Sup+(r[d2  d1])]/card[Sup(r[d2  d1])]}  Conf(r).

Conf(r[  d1]) =

{card[Sup+(r[  d1])]/card[Sup(r[  d1])]}  Conf(r).

Cost of Action Rule [Tzacheva & Ras]

Assumption: S= (X, A, V) is information system, Y  X.

Attribute b  A is flexible in S and b1, b2 Vb.

By S(Y, b1, b2) we mean a number from (0, +] which describes the average predicted cost of approved action associated with a possible re-classification of qualifying objects in Y from class b1 to b2. Object

x  Y qualifies for re-classification from b1 to b2, if b(x) = b1.

S(Y, b1, b2) = +, if there is no action approved which is

required for a possible re-classification of qualifying objects

in Y from class b1 to b2

If Y is uniquely defined, we often write S(b1, b2)instead of S(Y, b1, b2).

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.

Cost of Action Rule

Assumption: Cost of r is too high!

r = [(b1, v1 → w1) … (bj, vj → wj) …  ( bp, vp → wp)](x) 

(d, k1 → k2)(x)

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)

Class movability-index

FS - decision attribute ranking – positive integer associated

with a decision value

/objects of higher decision attribute ranking are seen as

objects more preferably movable between decision classes

than objects of lower rank/.

Nj+ = {i  N: FS(dj) – FS(di)  0}.

Class movability-index assigned to Nj,

ind(Nj) = {FS(dj)– FS(di): iNj+}

Class movability-index

Let Pj(i) = Sup+(r[dj di])

/Pj(i) – all objects in U which can be reclassified from

the decision class dj to the decision class di

Pj(N) = {Pj(i): i  N, ij}, for any N {1,2,…,k}

where {d1,d2,…,dk} are all decision classes.

Class movability-index (m-index) assigned to dj-object x:

indS(x) = max{ind(Nj): Nj{1,2,…,k}  x Pj(N)}

Questions?

Thank You