Fundamentals of Computational Intelligence. NEURAL NETWORKS, by James M. Keller, Derong Liu, David B. Fogel

By James M. Keller, Derong Liu, David B. Fogel

Provides an in-depth or even remedy of the 3 pillars of computational intelligence and the way they relate to 1 another 

This ebook covers the 3 basic subject matters that shape the root of computational intelligence:  neural networks, fuzzy platforms, and evolutionary computation. The textual content specializes in concept, layout, concept, and sensible elements of enforcing methods to resolve real-world difficulties. whereas different books within the 3 fields that contain computational intelligence are written by way of experts in a single self-discipline, this ebook is co-written through present former Editor-in-Chief of IEEE Transactions on Neural Networks and studying platforms, a former Editor-in-Chief of IEEE Transactions on Fuzzy platforms, and the founding Editor-in-Chief of IEEE Transactions on Evolutionary Computation. The insurance around the 3 issues is either uniform and constant common and notation.

  • Discusses single-layer and multilayer neural networks, radial-basis functionality networks, and recurrent neural networks
  • Covers fuzzy set concept, fuzzy relatives, fuzzy common sense interference, fuzzy clustering and category, fuzzy measures and fuzzy integrals
  • Examines evolutionary optimization, evolutionary studying and challenge fixing, and collective intelligence
  • Includes end-of-chapter perform difficulties that may support readers observe equipment and methods to real-world problems

Fundamentals of Computational intelligence is written for complicated undergraduates, graduate scholars, and practitioners in electric and machine engineering, desktop technological know-how, and different engineering disciplines.

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Additional info for Fundamentals of Computational Intelligence. NEURAL NETWORKS, FUZZY SYSTEMS, AND EVOLUTIONARY COMPUTATION

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8. Notice that the following two assumptions are required. • Each neuron is represented by a McCulloch–Pitts model, which utilizes the threshold function as activation function. 7 Architectural graph of network for solving the XOR problem. 8 Signal flow graph of network for solving the XOR problem. • Bits 0 and 1 are represented by the levels 0 and ‡1, respectively. 9. 10. 7. 7. 7. The function of the output neuron is to construct a linear combination of the decision boundaries formed by the two hidden neurons.

Consider a two-layer network containing no hidden neurons. Assume that the network has q inputs and a single output neuron. Let xi denote the ith input signal and define the corresponding output as q yˆϕ wi xi iˆ0 where wi is a threshold and ϕ…v† ˆ 1 1 ‡ exp … v† Show that this network implements a linear decision boundary that consists of a hyperplane in the input space ℜq . Illustrate your conclusion when q ˆ 2. 3. 12 has been trained to classify correctly a set of two-dimensional, two-class patterns.

2. Assume the input and the desired responses of the network are x ˆ 1; d ˆ 1, respectively. 1. Calculate the total instantaneous error energyE. 2. Compute @E=@w1 based on the result of 1. 3. Recompute @E=@w1 by using the backpropagation algorithm and compare the result with (2). 7. 15 have to be classified into two categories by using a layered network. Construct the separating planes in the pattern space and draw patterns in the image space. 6. 7. 9. threshold values of related units. Use the minimum number of threshold units to perform the classification.

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