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Lecture 10

Lecture 10. Hybrid intelligent systems:. Introduction Neural expert systems Evolutionary neural networks Fuzzy evolutionary systems Summary. Introduction.

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Lecture 10

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  1. Lecture 10 Hybrid intelligent systems: • Introduction • Neural expert systems • Evolutionary neural networks • Fuzzy evolutionary systems • Summary

  2. Introduction • A hybrid intelligent system is one that combinesat least two intelligent technologies. For example, combining a fuzzy system with evolutionary computation. • The combination of probabilistic reasoning, fuzzylogic, neural networks and evolutionarycomputation forms the core of soft computing, anemerging approach to building hybrid intelligentsystems capable of reasoning and learning in anuncertain and imprecise environment. One character of soft computing is the using of words but not numbers in systems.

  3. Although words are less precise than numbers, precision carries a high cost. We use wordswhen there is a tolerance for imprecision. Softcomputing exploits the tolerance for uncertaintyand imprecision to achieve greater tractabilityand robustness, and lower the cost of solutions. • We also use words when the available data isnot precise enough to use numbers. This isoften the case with complex problems, andwhile “hard” computing fails to produce anysolution, soft computing is still capable offinding good solutions.

  4. LotfiZadehis reputed to have said that a goodhybrid would be “British Police, GermanMechanics, French Cuisine, Swiss Banking andItalian Love”. But “British Cuisine, GermanPolice, French Mechanics, Italian Banking andSwiss Love” would be a bad one. Likewise, ahybrid intelligent system can be good or bad – itdepends on which components constitute thehybrid. So our goal is to select the rightcomponents for building a good hybrid system.

  5. Comparison of Expert Systems, FuzzySystems, Neural Networks and Genetic Algorithms

  6. Neural expert systems • Let’s compare neural networks with expert systems: • Expert systems rely on logical inferences anddecision trees and focus on modelling humanreasoning. Neural networks rely on parallel dataprocessing and focus on modelling a human brain. • Expert systems treat the brain as a black-box. Neural networks look at its structure and functions, particularly at its ability to learn. • Knowledge in a rule-based expert system isrepresented by IF-THEN production rules. Knowledge in neural networks is stored assynaptic weights between neurons.

  7. In expert systems, knowledge can be divided intoindividual rules and the user can see andunderstand the piece of knowledge applied by thesystem. • In neural networks, one cannot select a singlesynaptic weight as a discrete piece of knowledge. Here knowledge is embedded in the entirenetwork; it cannot be broken into individualpieces, and any change of a synaptic weight maylead to unpredictable results. A neural network is,in fact, a black-boxfor its user.

  8. Can we combine advantages of expert systemsand neural networks to create a more powerfuland effective expert system? A hybrid system that combines a neural networkand a rule-based expert system is called aneuralexpert system(or a connectionist expert system).

  9. Basic structure of a neural expert system

  10. The heart of a neural expert system is theinference engine. It controls the informationflow in the system and initiates inference overthe neural knowledge base. Based on the neural knowledge base (a special neural network), inference derive the outputs based on the inputs. The most important thing about neural expert system is that it can derive the rules from the neural network. That’s why the it is called a neural expert system but not a neural network

  11. Example: The neural knowledge base (a special NN)

  12. If we set each input of the input layer to either +1(true), -1 (false), or 0 (unknown), we can give asemantic interpretation for the activation ofany outputneuron. For example, we can have following IF-THEN rule: if the object has Wings (+1), Beak (+1) and Feathers (+1), but does not haveEngine (-1), then we can conclude that this object isBird (+1):

  13. We can similarly conclude that this object is notPlane: and not Glider:

  14. By attaching a corresponding question to each inputneuron, we can enable the system to prompt the userfor initial values of the input variables: Neuron: WingsQuestion: Does the object have wings? Neuron: TailQuestion: Does the object have a tail? Neuron: BeakQuestion: Does the object have a beak? Neuron: FeathersQuestion: Does the object have feathers? Neuron: EngineQuestion: Does the object have an engine? Based on these inputs, we can determine the type of objects.

  15. More interestingly, we do not need all the answers of questions to make the decision. An inference can be made if the known netweighted input to a neuron is greater than thesum of the absolute values of the weights ofthe unknown inputs. where iÎ known, j Ï known and nis the numberof neuron inputs.

  16. Example: Enter initial value for the input Feathers:> +1 KNOWN = 1.2.8 = 2.8UNKNOWN = ½-0.8½ + ½-0.2½ + ½2.2½ + ½-1.1½ = 4.3KNOWN < UNKNOWN Enter initial value for the input Beak: >+1 KNOWN = 1.2.8 + 1.2.2 = 5.0UNKNOWN = ½-0.8½ + ½-0.2½ + ½-1.1½ = 2.1KNOWN > UNKNOWN CONCLUDE: Bird is TRUE

  17. An example of a multi-layer knowledge base

  18. Evolutionary neural networks • Although neural networks are used for solving a variety of problems, they still have some limitations. • One of the most common is associated with neural network training. The back-propagation learning algorithm cannot guarantee an optimal solution. In real-world applications, the back-propagation algorithm might converge to a set of sub-optimal weights from which it cannot escape. As a result, the neural network is often unable to find a desirable solution to a problem at hand.

  19. Another difficulty is related to selecting an optimal topology for the neural network. The “right” network architecture for a particular problem is often chosen by means of heuristics, and designing a neural network topology is still more art than engineering. • Genetic algorithms are an effective optimisation technique that can guide both weight optimisation and topology selection.

  20. Encoding a set of weights in a chromosome

  21. The second step is to define a fitness function for evaluating the chromosome’s performance. This function must estimate the performance of a given neural network. We can apply here a simple function defined by the sum of squared errors. • The training set of examples is presented to the network, and the sum of squared errors is calculated. The smaller the sum, the fitter the chromosome. The genetic algorithm attempts to find a set of weights that minimises the sum of squared errors.

  22. The third step is to choose the genetic operators – crossover and mutation. A crossover operator takes two parent chromosomes and creates a single child with genetic material from both parents. Each gene in the child’s chromosome is represented by the corresponding gene of the randomly selected parent. • A mutation operator selects a gene in a chromosome and adds a small random value between –1 and 1 to each weight in this gene.

  23. Crossover in weight optimisation

  24. Mutation in weight optimisation

  25. Can genetic algorithms help us in selecting the network architecture? The architecture of the network (i.e. the number of neurons and their interconnections) often determines the success or failure of the application. Usually the network architecture is decided by trial and error; there is a great need for a method of automatically designing the architecture for a particular application. Genetic algorithms may well be suited for this task.

  26. The basic idea behind evolving a suitable network architecture is to conduct a genetic search in a population of possible architectures. • We must first choose a method of encoding a network’s architecture into a chromosome.

  27. Encoding the network architecture • The connection topology of a neural network can be represented by a square connectivity matrix. • Each entry in the matrix defines the type of connection from one neuron (column) to another (row), where 0 means no connection and 1 denotes connection for which the weight can be changed through learning. • To transform the connectivity matrix into a chromosome, we need only to string the rows of the matrix together.

  28. Encoding of the network topology

  29. The cycle of evolving a neural network topology

  30. Fuzzyevolutionary systems • Evolutionary computation is also used in the design of fuzzy systems, particularly for generating fuzzy rules and adjusting membership functions of fuzzy sets. • In this section, we introduce an application of genetic algorithms to select an appropriate set of fuzzy IF-THEN rules for a classification problem. • For a classification problem, a set of fuzzy IF-THEN rules is generated from numerical data. • First, we use a grid-type fuzzy partition of an input space.

  31. Fuzzy partition by a 3´3 fuzzy grid

  32. Fuzzy partition • Black and white dots denote the training patterns of Class 1 and Class 2, respectively. • The grid-type fuzzy partition can be seen as a rule table. • The linguistic values of input x1 (A1, A2 and A3) form the horizontal axis, and the linguistic values of input x2 (B1, B2 and B3) form the vertical axis. • At the intersection of a row and a column lies the rule consequent.

  33. In the rule table, each fuzzy subspace can have only one fuzzy IF-THEN rule, and thus the total number of rules that can be generated in a K´K grid is equal to K´K.

  34. Fuzzy rules that correspond to the K´K fuzzy partition can be represented in a general form as: where xp is a training pattern on input space X1´X2, P is the total number of training patterns, Cnis the rule consequent (either Class 1 or Class 2), and is the certainty factor that a pattern in fuzzy subspace AiBj belongs to class Cn. Cn CFAi Bj

  35. To determine the rule consequent and the certainty factor, we use the following procedure: Step 1: Partition an input space into K´K fuzzy subspaces, and calculate the strength of each class of training patterns in every fuzzy subspace. Each class in a given fuzzy subspace is represented by its training patterns. The more training patterns, the stronger the class - in a given fuzzy subspace, the rule consequent becomes more certain when patterns of one particular class appear more often than patterns of any other class.

  36. The Strength of class Cn in fuzzy subspace AiBj can be determined as:

  37. Step 2: Determine the rule consequent and the certainty factor in each fuzzy subspace. As the rule consequent is determined by the strongest class we need to find class Cm such that,

  38. The certainty factor can be interpreted as follows: • If all the training patterns in fuzzy subspace Ai Bjbelong to the same class, then the certainty factor is maximum and it is certain that any new pattern in this subspace will belong to this class. • If, however, training patterns belong to different classes and these classes have similar strengths, then the certainty factor is minimum and it is uncertain that a new pattern will belong to any particular class.

  39. This means that patterns in a fuzzy subspace can be misclassified. Moreover, if a fuzzy subspace does not have any training patterns, we cannot determine the rule consequent at all. • If a fuzzy partition is too coarse, many patterns may be misclassified. On the other hand, if a fuzzy partition is too fine, many fuzzy rules cannot be obtained, because of the lack of training patterns in the corresponding fuzzy subspaces.

  40. Training patterns are not necessarily distributed evenly in the input space. As a result, it is often difficult to choose an appropriate density for the fuzzy grid. To overcome this difficulty, we use multiple fuzzy rule tables.

  41. Multiple fuzzy rule tables Fuzzy IF-THEN rules are generated for each fuzzy subspace of multiple fuzzy rule tables, and thus a complete set of rules for our case can be specified as: 22 + 33 + 44 + 55 + 66 = 90 rules.

  42. Once the set of rules SALLis generated, a new pattern, x = (x1, x2), can be classified by the following procedure: Step 1: In every fuzzy subspace of the multiple fuzzy rule tables, calculate the degree of compatibility of a new pattern with each class.

  43. Step 2: Determine the maximum degree of compatibility of the new pattern with each class.

  44. Step 3: Determine the class with which the new pattern has the highest degree of compatibility, and assign the pattern to this class.

  45. The number of multiple fuzzy rule tables required for an accurate pattern classification may be large. • Consequently, a complete set of rules can be enormous. • Meanwhile, these rules have different classification abilities, and thus by selecting only rules with high potential for accurate classification, we reduce the number of rules.

  46. Can we use genetic algorithms for selecting fuzzy IF-THEN rules ? • The problem of selecting fuzzy IF-THEN rules can be seen as a combinatorial optimisation problem with two objectives. • The first, more important, objective is to maximise the number of correctly classified patterns. • The second objective is to minimise the number of rules. • Genetic algorithms can be applied to this problem.

  47. A basic genetic algorithm for selecting fuzzy IF-THEN rules includes the following steps: • Step 1: Randomly generate an initial population of chromosomes. The population size may be relatively small, say 10 or 20 chromosomes. Each gene in a chromosome corresponds to a particular fuzzy IF-THEN rule in the rule set defined by SALL. • e.g. the chromosome can be specified by a 90-bit string. Each bit can assume 1, -1, 0. • 1 for a particular rule belongs to set S, -1 for not belonging, and 0 for dummy rule. • Step 2: Calculate the performance, or fitness, of each individual chromosome in the current population.

  48. The problem of selecting fuzzy rules has two objectives: to maximise the accuracy of the pattern classification and to minimise the size of a rule set. • The fitness function has to accommodate both these objectives. This can be achieved by introducing two respective weights, wPand wN, in the fitness function: where PSthe number of patterns classified successfully, PALLis the total number of patterns presented to the classification system, NSand NALLare the numbers of fuzzy IF-THEN rules in set S and set SALL, respectively.

  49. The classification accuracy is more important than the size of a rule set. That is,

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