Chapter 6 Comparisons and Discussions
6.2 Discussions
In the IPSO and BFPSO approaches, we investigated hybridization by combining PSO with IA and BFO, respectively. In IPSO method, the major parameter learning process is achieved by IA. In order to avoid trapping in a local optimal solution and ensure the search capability of near global optimal solution, we employ the advantages of the PSO to improve mutation mechanism of IA. In addition, the balance between exploration of the search space and exploitation of potentially good solutions is considered as a fundamental problem in nature-inspired systems. Too much stress on exploration results in a pure random search whereas too much exploitation results in a pure local search. Clearly, intelligent search must self-adaptively combine exploration of the new regions of the space with evaluation of potential solutions already identified. The BFPSO combines both algorithms BFO and PSO to balance the exploration and exploitation abilities of the search space.
Unlike IPSO and BFPSO approaches that use PSO as the enhance mechanism to improve the performance of basic IA and BFO. In DMPSO approach, the parameter learning method is based on the PSO algorithm and the distance-based mutation operator is introduced to increase the population diversity, which strongly encourages a global search giving the particles more chance of escaping from local optimum and converging to the global optimum.
It should be notice that due to the PSO plays different role between the proposed IPSO, BFPSO and DMPSO methods, the parameters of PSO are not totally the same for these three parameter learning algorithms. The functions of IA, BFO and PSO are summarized in Table 6.3. Furthermore, the predefined fuzzy rule number in IPSO method is set to be 4 which were different from others.
Table 6.3: The roles of IA, BFO and PSO in the proposed learning algorithm.
Method IPSO BFPSO DMPSO
Fuzzy Rule Numbers 4 3 3
Basic/Main Algorithm IA BFO PSO
Mechanism PSO PSO Mutation operator
Enhancement
Function
Increase population
diversity
Improve global search
ability
Increase population
diversity
Moreover, in order to obtain better simulation results, the proposed learning algorithms always require training data to be sufficient and proper. However, there is no procedure or rule suitable for all cases in choosing training data. One rule of thumb is that training data should cover the entire expected input space and then during the training process select training-vector pairs randomly from the set.
Chapter 7
Conclusions and Future Works
Fuzzy logic and artificial neural networks are complementary technologies in the design of intelligent systems. The combination of these two technologies into an integrated system appears to be a promising path toward the development of intelligent systems capable of capturing qualities characterizing the human brain.
Both neural networks and fuzzy logic are powerful design techniques that have their strengths and weaknesses. The integrated neuro-fuzzy systems possess the advantages of both neural networks (e.g. learning abilities, optimization abilities and connectionist structures) and fuzzy systems (e.g. humanlike IF-THEN rules thinking and ease of incorporating expert knowledge). In this way, it is possible to bring the low-level learning and computational power of neural networks into fuzzy systems and also high-level humanlike IF-THEN thinking and reasoning of fuzzy systems into neural networks.
A neuro-fuzzy system is a fuzzy system, whose parameters are learned by a learning algorithm. It has a neural network architecture constructed from fuzzy reasoning, and can always be interpreted as a system of fuzzy rules. Learning is used to adaptively adjust the rules in the rule base, and to produce or optimize the membership functions of a fuzzy system. Structured knowledge is codified as fuzzy rules. Modern neuro-fuzzy systems are usually represented as special multilayer feedforward neural networks. Hayashi et al. [126] showed that a feedforward neural network could approximate any fuzzy rule based system and any feedforward neural network may be approximated by a rule based fuzzy inference system.
In this dissertation, the neuro-fuzzy architecture we used is called
functional-link-based neuro-fuzzy network (FLNFN) model. The FLNFN model uses a functional link neural network to the consequent part of the fuzzy rules. FLNFN is a multilayer feedforward network in which each node performs a particular function (node function) based on incoming signals and a set of parameters pertaining to this node. The FLNFN model can automatically be constructed and the FLNFN parameters can be adjusted by performing structure/parameter learning schemes.
In Chapter 3, the proposed IPSO method combines the IA and PSO to perform parameter learning. The advantages of the proposed IPSO method are summarized as follows: 1) We employed the advantages of PSO to improve the mutation mechanism;
2) The complicated problems can be better solved than IA and PSO; 3) There is more of a likelihood to get a global optimum compared to heuristic methods; 4) The experimental results have shown that our method obtains better results than other existing methods in accuracy rate and convergence speed.
In Chapter 4, an innovative BFPSO algorithm is applied for the design of neuro-fuzzy classifier. Conventional BFO depends on random search directions which may lead to delay in reaching global solution while PSO is prone to be trapped in local optima. In order to get better optimization, the new algorithm combines advantages of both the algorithms i.e. PSO’s ability to exchange social information and BFO’s ability in finding new solutions by elimination and dispersal. The BFPSO algorithm combines PSO-based mutation operator with bacterial chemotaxis in order to make judicious use of exploration and exploitation abilities of search space and to avoid false and premature convergence. The simulation results showed that the overall performance of the hybrid algorithm outperforms conventional BFO and PSO.
Unlike IPSO and BFPSO approaches that use PSO as the enhance mechanism to improve the performance of basic IA and BFO. In chapter 5, the PSO-based learning algorithm, called DMPSO, for the neural fuzzy system is presented. In DMPSO
approach, the parameter learning method is based on the PSO algorithm and the distance-based mutation operator is introduced to increase the population diversity, which strongly encourages a global search giving the particles more chance of escaping from local optimum and converging to the global optimum. The simulation results have shown the proposed DMPSO method yields better performance than other existing models under some circumstances in the nonlinear system control application fields.
In Chapter 6, the well-known skin color detection problem is used as the benchmark to demonstrate the performance and efficiency of the proposed IPSO, BFPSO and DMPSO method. The aim of the skin color detection is to distinguish between skin and non-skin pixels based on the Y, Cb and Cr information. The average accuracy rates of testing and training data with different approaches were depicted in Table 6.2. Since the predefined rule number is not identical, we cannot make the comparison fairly. From the simulation results, we can only conclude that DMPSO outperforms BFPSO and IPSO seems to be over-trained.
Although the proposed algorithms yield better performance in the classification and nonlinear system control applications, but there still some advanced topics should be addressed in future research.
In general, synthesizing a neuro-fuzzy system, two major types of learning are required: structure learning algorithms to find appropriate fuzzy logic rules; and parameter learning algorithms to fine-tune the membership functions and other parameters. There are several ways that structure learning and parameter learning can be combined in a neuro-fuzzy system. They can be performed sequentially: structure learning is used first to find the appropriate structure of a neuro-fuzzy system; and parameter learning is then used to fine-tune the parameters. In some situations, only parameter learning or structure learning is necessary when structure (fuzzy rules) or
parameters (membership functions) are provided by experts, and the structure in some neuro-fuzzy systems is fixed. Identification of fuzzy rules has been one of the most important aspects in the design of neuro-fuzzy sysyem. Identified rules and concise rules can provide an initial structure of networks so that learning processes can be fast, reliable and highly intuitive. To overcome the limitations of using expert knowledge in defining the fuzzy rules, data driven methods to create fuzzy systems are needed.
Therefore, the first advanced research topic is to generate fuzzy rules from numerical data more efficiently.
The choice of the model’s structure is very important, as it determines the flexibility of the model in the approximation of (unknown) systems. Despite of the research that has already been done in the area of neuro-fuzzy systems the recurrent variants of this architecture are still rarely studied. In contrast to pure feed-forward architectures, that have a static input-output behavior, recurrent models are able to store information of the past (e.g. prior system states) and are thus more appropriate for the analysis of dynamic systems. The second advanced research topic is to apply the proposed IPSO, BFPSO and DMPSO into the recurrent neural network to learn and optimize a hierarchical fuzzy rule base with feedback connections.
In this dissertation, a systematic method was not used to determine the initial parameters. The initial parameters are determined by practical experimentation or by trial-and-error. In future works, we will try to develop a well-defined method to automatically determine the initial parameters, and thus inexperienced users could design a neuro-fuzzy system with ease.
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