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## Action Rules Discovery /Lecture I/

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E = [Cond1 => Cond2]

Presumptive

Objective

Rule: two conditions occur together, with some confidence

Data Mining Task:

For a given dataset D, interestingness measure ID and

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

Knowledge Engineer definesc

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.

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[]]

- 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 = [AB1] has a high confidence and r1 = [A*CB2]

has a high confidence, then r1 is unexpected.

[Padmanabhan & Tuzhilin]

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*

- 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.

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) (biAFl)]

E-Action rule [Ras & Tsay]:

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

[(d, k1 k2)](x), where (i)[(1 i p) (biAFl)]

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, 21) ( d, L H)

(a = 2) (b, 31) ( 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).

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?

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

re-classification task (d, d2 d1):

[a1,1 a2,1 ... ap,1]

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

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 rule r[d2 d1]:

[a1,1 a2,1 ... ap,1]

[(b1, b’1,1 b1,1 ) (b2, b’2,1b2,1) ... (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/

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 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]).

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).

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.

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)

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): iNj+}

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, ij}, 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

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