b6ea5c495cd38b91e28311b4de1ddd54.ppt

- Количество слайдов: 15

Sisteme de programe pentru timp real Universitatea “Politehnica” din Bucuresti 2004 -2005 Adina Magda Florea http: //turing. cs. pub. ro/sptr_05

Curs Nr. 11 Learning decision rules by evolutionary algorithms 1. 2. 3. 4. Decision rules Representation Genetic operators Fitness function 2

1. Decision rules • Both discrete and continuous values attributes • Rules of the form: if A 1=v 1 and x 1

Decision rules A class ck C Positive examples E+(ck) = {e E: C(e)=ck} Negative examples – E-(ck) = E – E+(ck) A decision rule R if t 1 and t 2. . and tr then ck LHS RHS – class membership of an example Rule set RS – disjunctive set of decision rules with the asme RHS • CRS C – denotes the class on the RHS of an RS • • 4

Decision rules • The EA is called for each class ck C to find the RS separating E+(ck) from E-(ck) • Search criteria – fitness function -> prefers rules consisting of fewer conditions, which cover many ex+ and very few ex- 5

2. Representation • One chromosome encodes an RS • Use variable length chromosomes (as the no. of rules in RS is not knwon) + provide operators which change the no. Of rules • 1 chromosome = concatenation of strings • Each fixed-length string = the LHS of one decision rule (no need for RHS) • 1 string is composed of N sub-strings (LHS) – a condition for each attribute 6

Representation • • Discrete value attributes – binary flags Continous value attributes – li, ui, li

Representation Example • 2 cont val attr: Salary, Amount • 1 disc val attr – Purpose (car, house, school) • Class - Accept Salary - + 100 250 Amount - 250 - 500 750 + - + Purpose 1 1 1 if Amount<250 then ACCEPT 1 1 1 if 100

3. Genetic operators 4 operators applied to a single sule set: • Changing condition • Positive example insertion • Negative example removal • Rule drop 2 operators applied with 2 arguments to RS 1 and RS 2: • Crossover • Rule copy 9

Genetic operators Changing condition • A mutation like operator – alters a single condition related to an attribute Ai • If Ai disc – randomly chooses a flag and flip • If Ai cont – randomly replaces a threshold (li or ui) by a boundary threshold Pos ex insertion • Modifies a single dec rule R in RS to allow to cover a new random e+ E+(CRS) currently uncovered by R • All conditions in the rule, which conflict with e+ have to be altered. • Ai disc – flag set • Ai cont – li

Genetic operators Negative ex removal • The negative example removal operator alters a single rule R from the ruleset RS. • It selects at random a negative example e- from the set of all the negative examples covered by R. • Then it alters a random condition in R in such a way, that the modied rule does not cover e-. • If the chosen condition concerns a discrete attribute Ai the flag which corresponds to Ai(e-) is cleared. • If Ai is a continuous-valued attribute then the condition li < Ai ui is narrowed down either to li’ < Ai <= ui or to li < Ai <= ui’, where li is the smallest boundary threshold such that Ai(e-) >= li’ and ui’ is the largest boundary threshold such that ui’ < Ai(e-). 11

Genetic operators Rule drop and rule copy operators are the only ones capable of changing the number of rules in a ruleset. Rule drop • The single argument rule drop removes a random rule from a ruleset RS. Rule copy • Rule copy adds to one of its arguments RS 1, a copy of a rule selected at random from RS 2, provided that the number of rules in RS 1 is lower than max. R. • max. R is an user-supplied parameter, which limits 12

Genetic operators Crossover • The crossover operator selects at random two rules R 1 and R 2 from the respective arguments RS 1 and RS 2. Then it applies an uniform crossover to the strings representing R 1 and R 2. • Uses rank-based fitness asignment 13

4. Fitness • • • Goal = reduction of the no. of errors ERS – the set of ex covered by the RS (class of RHS – CRS) E+RS = ERS E+(CRS) – set of ex+ correctly classified by RS E-RS = ERS E-(CRS) – set of ex- covered by RS The total no. of ex+ and ex. POS = |E+(CRS)| NEG=|E-(CRS)| = M – POS • The RS correctly classifies: - pos = |E+RS| ex+ and - NEG-neg ex- where neg=|E-RS| 14

Fitness • • • Ferror = Pr(RS) / Compl(RS) Pr(RS) = the probability of classifying correctly an example from the learning set by RS Compl(RS) = the complexity of RS Pr(RS) = (pos + NEG – neg) / (POS+NEG) Compl(RS) = (L/N+1) L – total no. of conditions in RS N – no. of attributes - user supplied in [0. 001. . 0. 1] We are interested in maximizing the probability and minimizing the complexity – to obtain a compact rule set and acorrect classification 15