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## Classifier conditions using gene expression programming,” tech (2008)

Citations: | 9 - 0 self |

### Citations

3667 |
Genetic Programming: On the Programming of Computers by Means of Natural Selection
- Koza
- 1992
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Citation Context ...anding of functional conditions by exploring the use of gene expression programming [7, 8] to define LCS conditions. Gene expression programming (GEP) is partially similar to genetic programming (GP) =-=[11]-=- in that their phenotype structures are both trees of functions and terminals. However, in GEP the phenotype results from translation of an underlying genome, a linear chromosome, which is the object ... |

340 | Classifier fitness based on accuracy
- Wilson
- 1995
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Citation Context ...ng traditional hyperrectangular conditions have trouble when the regularities of interest have boundaries that are oblique to the coordinate axes. Because classifier fitness (in current LCSs like XCS =-=[19]-=- and its variants) is based on accuracy, the usual consequence is evolution of a patchwork of classifiers with large and small conditions that cover the regularity, including its oblique boundary, wit... |

259 |
Cognitive systems based on adaptive algorithms
- Holland, Reitman
- 1978
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Citation Context ... part on the course of the evolutionary process. But it also depends on whether the condition syntax actually permits the regularities to be represented. Classifier system environments were initially =-=[10]-=- defined over binary domains. The corresponding condition syntax consisted of strings from {1,0,#}, with # a “don’t care” symbol matching either 1 or 0. This syntax is effective for conjunctive regula... |

148 | An Algorithmic Description of XCS
- Butz, Wilson
- 2002
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Citation Context ... a match threshold of 0.0. In covering and in mutation, the first (root) element of the chromosome was not allowed to be a terminal. Partially following [21] and using the notation of Butz and Wilson =-=[5]-=-, parameter settings for the experiment were: population size N = 100, learning rate β = 0.4, error threshold ǫ0 = 0.01, fitness power ν = 5, GA threshold θGA = 12, crossover probability (one point) χ... |

89 | Get real! XCS with continuous-valued inputs. In: Learning Classifier Systems, From Foundations to Applications
- Wilson
- 2000
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Citation Context ...1 or 0. This syntax is effective for conjunctive regularities—ANDs of variables and their negations—but cannot express, e.g., x1 OR x2. Later, for real-vector environments, conditions were introduced =-=[20]-=- consisting of conjunctions of interval predicates, where each predicate matches if the corresponding input variable is between a pair of values. The same logical limitation also applies—only conjunct... |

52 | MV: Rule-Based Evolutionary Online Learning Systems – A Principled Approach to LCS Analysis and Design
- Butz
- 2006
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Citation Context ...hreshold (which could conceivably be adaptive). Since over-generality leads to error, too low a threshold will increase the time required to evolve accurate classifiers. There is a substantial theory =-=[3]-=- of factors, including generality, that affect the rate of evolution in XCS-like systems; it should be applicable here. On compactness the situation is actually much improved by the fact that regulari... |

51 | SW: Classifiers that approximate functions
- Wilson
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Citation Context ...) 0.8 0.6 0.4 0.2 0 1 0 0.2 0.4 0.6 x 0.8 1 0 1 0.8 0.6 0.4 y 0.2 Figure 1: “Tent” payoff landscape P(x,y). The landscape of Figure 1 can be learned by XCSF [24] in its function approximation version =-=[21, 22]-=-. XCSF approximates non-linear functions by covering the landscape with classifiers that compute local linear approximations to the function’s value. Each such classifier will match in a certain subdo... |

46 |
Extending the representation of classifier conditions part ii: from messy coding to s-expressions
- Lanzi
- 1999
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Citation Context ...l with dimensionality. Further general approaches to condition syntax include neural networks (NNs) [1] and compositions of basis functions—trees of functions and terminals—such as LISP S-expressions =-=[13]-=-. In both cases, matching is defined by the output exceeding a threshold (or equal to 1 (true) in the case of S-expressions of binary operators). NNs and S-expressions are in principle both able to re... |

44 |
Learning Classifier Systems, From Foundations to Applications
- Stolzmann, Butz
- 2000
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Citation Context ...th conventional rectilinear conditions. An initial experiment approximating a nonlinear oblique environment showed excellent fit to the regularities. 1 Introduction A learning classifier system (LCS) =-=[14]-=- is a learning system that seeks to gain reinforcement from its environment via an evolving population of conditionaction rules called classifiers. Broadly, each classifier has a condition, an action,... |

43 | Function approximation with a classifier system
- Wilson
- 2001
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Citation Context ...) 0.8 0.6 0.4 0.2 0 1 0 0.2 0.4 0.6 x 0.8 1 0 1 0.8 0.6 0.4 y 0.2 Figure 1: “Tent” payoff landscape P(x,y). The landscape of Figure 1 can be learned by XCSF [24] in its function approximation version =-=[21, 22]-=-. XCSF approximates non-linear functions by covering the landscape with classifiers that compute local linear approximations to the function’s value. Each such classifier will match in a certain subdo... |

25 | T.: Accuracy-based neuro and neuro-fuzzy classifier systems
- Bull, O’Hara
- 2002
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Citation Context ...ng a particular, if orientable, shape, and the number of points needed by convex hulls is exponential with dimensionality. Further general approaches to condition syntax include neural networks (NNs) =-=[1]-=- and compositions of basis functions—trees of functions and terminals—such as LISP S-expressions [13]. In both cases, matching is defined by the output exceeding a threshold (or equal to 1 (true) in t... |

21 | Compact rulesets from XCSI
- Wilson
- 2002
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Citation Context ...ctually much improved by the fact that regularity-fitting classifiers do evolve, in contrast to the poor fit of rectilinear classifiers for all but rectilinear en8vironments. Considerable work (e.g. =-=[23, 6, 9, 18, 4]-=-) exists on algorithms that reduce evolved populations down to minimal classifier sets that completely and correctly cover the problem environment. If the population consists of poorly fitting classif... |

20 | L.: A comparison of bloat control methods for genetic programming
- Luke, Panait
- 2006
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Citation Context ...ble. For this, GEP would seem to be better than other functional systems such as GP because once a chromosome size is chosen, the expression tree size is limited and very much less subject to “bloat” =-=[17]-=- than GP tree structures are. In GP, crossover between trees can lead to unlimited tree size unless constrained for example by deductions from fitness due to size. In GEP, the size cannot exceed a lin... |

18 |
ellipsoidal conditions in the real-valued XCS classifier system
- Kernel-based
- 2005
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Citation Context ...many environmental regularities do not have that shape and so will elude representation by single classifiers. Attempts to match regularities more adroitly include conditions based on hyperellipsoids =-=[2]-=- and on convex hulls [15]. Hyperellipsoids are higher-dimensional ellipse-like structures that will evolve to align with regularity boundaries. Convex hulls—depending on the number of points available... |

14 |
Function approximation with XCS: Hyperellipsoidal conditions, recursive least squares, and compaction[J
- Butz, Lanzi, et al.
(Show Context)
Citation Context ...ctually much improved by the fact that regularity-fitting classifiers do evolve, in contrast to the poor fit of rectilinear classifiers for all but rectilinear en8vironments. Considerable work (e.g. =-=[23, 6, 9, 18, 4]-=-) exists on algorithms that reduce evolved populations down to minimal classifier sets that completely and correctly cover the problem environment. If the population consists of poorly fitting classif... |

14 | A modified classifier system compaction algorithm
- Fu, Davis
- 2002
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Citation Context ...ctually much improved by the fact that regularity-fitting classifiers do evolve, in contrast to the poor fit of rectilinear classifiers for all but rectilinear en8vironments. Considerable work (e.g. =-=[23, 6, 9, 18, 4]-=-) exists on algorithms that reduce evolved populations down to minimal classifier sets that completely and correctly cover the problem environment. If the population consists of poorly fitting classif... |

12 |
A rule set reduction algorithm for the XCS learning classifier system
- Dixon, Corne, et al.
- 2003
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11 |
Classifier systems for continuous payoff environments. In: Genetic and Evolutionary Computation GECCO
- Wilson
- 2004
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Citation Context ...(x + y) : x + y ≥ 1 (1) 22-(x+y) x+y P(x,y) 0.8 0.6 0.4 0.2 0 1 0 0.2 0.4 0.6 x 0.8 1 0 1 0.8 0.6 0.4 y 0.2 Figure 1: “Tent” payoff landscape P(x,y). The landscape of Figure 1 can be learned by XCSF =-=[24]-=- in its function approximation version [21, 22]. XCSF approximates non-linear functions by covering the landscape with classifiers that compute local linear approximations to the function’s value. Eac... |

5 | Three architectures for continuous action
- Wilson
- 2007
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Citation Context ... will make these ideas clear. Figure 1 shows a tent-like two-dimensional payoff landscape where the projection of each side of the tent onto the x-y plane is a triangle (the landscape is adapted from =-=[25]-=-). The two sides represent different regularities: each is a linear function of x and y but the slopes are different. The equation for the payoff function is { P(x,y) = x + y : x + y ≤ 1 2 − (x + y) :... |

5 |
Expression Programming: Mathematical Modeling by an Artificial Intelligence. 2nd Edn
- Gene
- 2006
(Show Context)
Citation Context ...and have the ability to ignore unneeded inputs or add ones that become relevant. This paper seeks to advance understanding of functional conditions by exploring the use of gene expression programming =-=[7, 8]-=- to define LCS conditions. Gene expression programming (GEP) is partially similar to genetic programming (GP) [11] in that their phenotype structures are both trees of functions and terminals. However... |

4 | Using convex hulls to represent classifier conditions
- Lanzi, Wilson
- 2006
(Show Context)
Citation Context ...arities do not have that shape and so will elude representation by single classifiers. Attempts to match regularities more adroitly include conditions based on hyperellipsoids [2] and on convex hulls =-=[15]-=-. Hyperellipsoids are higher-dimensional ellipse-like structures that will evolve to align with regularity boundaries. Convex hulls—depending on the number of points available 1to define them—can be ... |

3 | Towards clustering with xcs
- Tamee, Bull, et al.
- 2007
(Show Context)
Citation Context ... actually much improved by the fact that regularity-fitting classifiers do evolve, in contrast to the poor fit of rectilinear classifiers for all but rectilinear environments. Considerable work (e.g. =-=[23,6, 9,18,4]-=-) exists on algorithms that reduce evolved populations down to minimal classifier sets that completely and correctly cover the problem environment. If the population consists of poorly fitting classif... |

2 | Prefix gene expression programming
- Li, Zhou, et al.
- 2005
(Show Context)
Citation Context ...h a different technique for translating the chromosome. Ferreira calls the breadthfirst technique “Karva” whereas it is also possible to translate in a depth-first fashion called “prefix” (see, e.g., =-=[16]-=-). Like Karva, prefix has the property that every chromosome translates to a valid expression tree. Figure 2, right side, shows the translation of the chromosome of Sect. 3.1 using prefix. Looking at ... |

2 | O.: Towards clustering with xcs
- Tamee, Bull, et al.
- 2007
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1 |
expression programming: a new algorithm for solving problems
- Gene
(Show Context)
Citation Context ...and have the ability to ignore unneeded inputs or add ones that become relevant. This paper seeks to advance understanding of functional conditions by exploring the use of gene expression programming =-=[7, 8]-=- to define LCS conditions. Gene expression programming (GEP) is partially similar to genetic programming (GP) [11] in that their phenotype structures are both trees of functions and terminals. However... |