New Method of Generating Solutions in PBIL for MLFS. In Jun Yu( 유인준 )

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1 New Method of Generating Solutions in PBIL for MLFS In Jun Yu( 유인준 )

2 1. Introduction Evolutionary Algorithms(EA) have recently received much attention from the Feature Selection community because of their global search ability [1]. One of EAs, PBIL is effective for feature selection because of simplicity and more accurate and faster than Genetic Algorithm(GA) [2].

3 1. Introduction The characteristic of PBIL is replacing the population to probability vector [2]. The probability vector can be viewed as a prototype vector for generating solution vectors which have high evaluation [2]. So, unlike GA, operations are not defined on the population. Rather, operations take place directly on the probability vector [2].

4 1. Introduction Limitation of PBIL It is unlikely that the population members would be regenerated by sampling the probability vector [2]. It can also be a disadvantage as the collective knowledge accumulated from other searched individuals are not used properly [3]. Consequently

5 1. Introduction Limitation of PBIL

6 1. Introduction The Aim of This Paper

7 2. Related Work 1. In [3] multiple probability vectors and an adaptive updating strategy are proposed and the resulting algorithm is tested on the geometrical design of the end region of power transformers. 2. In [4] a new probability update rule and sampling procedure are proposed using opposition based computing for maintaining diversity.

8 3. References [1] B Xue, M Zhang, W Browne, X Yao, A Survey on Evolutionary Computation Approaches to Feature Selection, Evolutionary Computation, IEEE Transactions on 20 (4), [2] Shumeet Baluja, Population Based Incremental Learning: a method for integrating genetic search based function optimization and competitive learning, Technical report CMU CS [3] Yang, S. Y., et al. "A new implementation of population based incremental learning method for optimizations in electromagnetics." IEEE Transactions on Magnetics 43.4 (2007): [4] Ventresca, Mario, and Hamid R. Tizhoosh. "A diversity maintaining population based incremental learning algorithm." Information Sciences (2008):

9 Appendix A Competitive Learning A competitive learning network The inhibitory connections, between output units, ensure that only one output is turned on at a time. The output unit that is turned on is the one which has the largest net input. The excitatory connections contribute to the net input of the outputs.

10 Appendix A Competitive Learning The activation of the output units is calculated by thefollowing formula: During training, the weights of the winning output unit are moved closer to the presented point by adjusting the weights according to the following rule (LR is the learning rate parameter):

11 Appendix A Competitive Learning After the network training is complete, the weight vectors for each of the output units can be considered prototype vectors for one of the discovered classes. The attributes with the large weights are the defining characteristics of the class represented by the output. It is the notion of creating a prototype vector which will be central to the discussions of PBIL.

12 Appendix B Genetic Algorithm GA is search technique inspired by the evolutionary process of the natural world. Populations f1 f2 f3 f4 f loop Mutation Evaluation Function Crossover offspting Genetic Algorithm Procedure

13 Appendix B Genetic Algorithm Limitation of GA Once the population has converged, the ability for crossover operators to aid in exploring new portions of the function space is greatly hindered. The entire population may come to be dominated by very similar solution vectors when several consecutive generations do not develop novel high evaluation solution vectors. Can Not Maintain Dissimilarity!!!

14 Appendix C The Role of Mutation The role of mutation is to prevent the prototype vector from too quickly converging to an extreme value (either 0.0 or 1.0) in each of the bit positions.

15 Appendix D Standard PBIL [ Baluja, 1994 ] P ini alize probability vector. (Each posi on = 0.5) For (generations++) 1 Generate Samples 2 Find Best Sample 3 Update Probability Vector 4 Mutate Probability Vector End (Generations)

16 Appendix D Standard PBIL [ Baluja, 1994 ] 1 Generate Samples for ( i++ ) # iis sample size generate sample vector according to probabili es in P end evaluate ( ) 2 Find Best Sample find vector corresponding to maximum evalua on

17 Appendix D Standard PBIL [ Baluja, 1994 ] 3 Update Probability Vector for ( j++ ) # j is Probability Vector Length End User Defined Constants LR : Learning Rate. (= 0.1)

18 Appendix D Standard PBIL [ Baluja, 1994 ] 4 Mutate Probability Vector for ( j++ ) # j is Probability Vector Length if ( ramdom (0,1] < )... end End User Defined Constants MP : Probability of mutation occurring in each position. (= 0.02) MS : Mutation Shift amout for mutation to affect the probability. (= 0.05)

19 Appendix E PBIL Issues Changing the Learning Rate The learning rate affects which portions of the function space will be explored. The setting of the learning rate has a direct impact on the trade off between exploration of the function space and exploitation of the exploration already conducted. exploration is the ability of the algorithm to search the function space thoroughly. exploitation refers to the algorithm s ability to use the information it has gained about the function space to narrow its future search.

20 Appendix E PBIL Issues Extension to the prototype vector the prototype vector is only adjusted based upon the single best solution vector generated in the current generation. Alternatives 1 The first is to move the probability vector in the direction of the best M vectors, where M << N. 2 The second method, moving away from bad vectors. But both introduce more parameters to the algorithm.

Direct Memory Schemes for Population-based Incremental Learning in Cyclically Changing Environments

Direct Memory Schemes for Population-based Incremental Learning in Cyclically Changing Environments Michalis Mavrovouniotis and Shengxiang Yang Centre for Computational Intelligence (CCI) School of Computer