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Nobuyuki Matsui - One of the best experts on this subject based on the ideXlab platform.

  • quaternionic multistate Hopfield Neural Network with extended projection rule
    Artificial Life and Robotics, 2016
    Co-Authors: Toshifumi Minemoto, Teijiro Isokawa, Haruhiko Nishimura, Nobuyuki Matsui
    Abstract:

    The aim of this paper is to investigate storing and recalling performances of embedded patterns on associative memory. The associative memory is composed of quaternionic multistate Hopfield Neural Network. The state of a neuron in the Network is described by three kinds of discretized phase with fixed amplitude. These phases are set to discrete values with arbitrary divide size. Hebbian rule and projection rule are used for storing patterns to the Network. Recalling performance is evaluated through storing random patterns with changing the divide size of the phases in a neuron. Color images are also embedded and their noise tolerance is explored.

  • associative memory in quaternionic Hopfield Neural Network
    International Journal of Neural Systems, 2008
    Co-Authors: Teijiro Isokawa, Haruhiko Nishimura, Naotake Kamiura, Nobuyuki Matsui
    Abstract:

    Associative memory Networks based on quaternionic Hopfield Neural Network are investigated in this paper. These Networks are composed of quaternionic neurons, and input, output, threshold, and connection weights are represented in quaternions, which is a class of hypercomplex number systems. The energy function of the Network and the Hebbian rule for embedding patterns are introduced. The stable states and their basins are explored for the Networks with three neurons and four neurons. It is clarified that there exist at most 16 stable states, called multiplet components, as the degenerated stored patterns, and each of these states has its basin in the quaternionic Networks.

  • fundamental properties of quaternionic Hopfield Neural Network
    International Joint Conference on Neural Network, 2006
    Co-Authors: Teijiro Isokawa, Haruhiko Nishimura, Naotake Kamiura, Nobuyuki Matsui
    Abstract:

    Associative memory by Hopfield-type recurrent Neural Networks with quaternionic algebra, called quaternionic Hopfield Neural Network, is proposed in this paper. The variables in the Network are represented by quaternions of four dimensional hypercomplex numbers. The neuron model, the energy function, and the Hebbian rule for embedding patterns into the Network are introduced. The properties of this Network are analyzed concretely through examples of the Network with 3 and 4 quaternion neurons. It is demonstrated that there exist fixed attractors in the Network, i.e., the pattern association from test pattern close to a stored pattern is possible in the quaternionic Network, as in real-valued Hopfield Networks.

Eliang Chen - One of the best experts on this subject based on the ideXlab platform.

  • polygonal approximation using a competitive Hopfield Neural Network
    Pattern Recognition, 1994
    Co-Authors: Pauchoo Chung, Chingtsorng Tsai, Eliang Chen
    Abstract:

    Abstract Polygonal approximation plays an important role in pattern recognition and computer vision. In this paper, a parallel method using a Competitive Hopfield Neural Network (CHNN) is proposed for polygonal approximation. Based on the CHNN, the polygonal approximation is regarded as a minimization of a criterion function which is defined as the arc-to-chord deviation between the curve and the polygon. The CHNN differs from the original Hopfield Network in that a competitive winner-take-all mechanism is imposed. The winner-take-all mechanism adeptly precludes the necessity of determining the values for the weighting factors in the energy function in maintaining a feasible result. The proposed method is compared to several existing methods by the approximation error norms L2 and L∞ with the result that promising approximation polygons are obtained.

Teijiro Isokawa - One of the best experts on this subject based on the ideXlab platform.

  • quaternionic multistate Hopfield Neural Network with extended projection rule
    Artificial Life and Robotics, 2016
    Co-Authors: Toshifumi Minemoto, Teijiro Isokawa, Haruhiko Nishimura, Nobuyuki Matsui
    Abstract:

    The aim of this paper is to investigate storing and recalling performances of embedded patterns on associative memory. The associative memory is composed of quaternionic multistate Hopfield Neural Network. The state of a neuron in the Network is described by three kinds of discretized phase with fixed amplitude. These phases are set to discrete values with arbitrary divide size. Hebbian rule and projection rule are used for storing patterns to the Network. Recalling performance is evaluated through storing random patterns with changing the divide size of the phases in a neuron. Color images are also embedded and their noise tolerance is explored.

  • associative memory in quaternionic Hopfield Neural Network
    International Journal of Neural Systems, 2008
    Co-Authors: Teijiro Isokawa, Haruhiko Nishimura, Naotake Kamiura, Nobuyuki Matsui
    Abstract:

    Associative memory Networks based on quaternionic Hopfield Neural Network are investigated in this paper. These Networks are composed of quaternionic neurons, and input, output, threshold, and connection weights are represented in quaternions, which is a class of hypercomplex number systems. The energy function of the Network and the Hebbian rule for embedding patterns are introduced. The stable states and their basins are explored for the Networks with three neurons and four neurons. It is clarified that there exist at most 16 stable states, called multiplet components, as the degenerated stored patterns, and each of these states has its basin in the quaternionic Networks.

  • fundamental properties of quaternionic Hopfield Neural Network
    International Joint Conference on Neural Network, 2006
    Co-Authors: Teijiro Isokawa, Haruhiko Nishimura, Naotake Kamiura, Nobuyuki Matsui
    Abstract:

    Associative memory by Hopfield-type recurrent Neural Networks with quaternionic algebra, called quaternionic Hopfield Neural Network, is proposed in this paper. The variables in the Network are represented by quaternions of four dimensional hypercomplex numbers. The neuron model, the energy function, and the Hebbian rule for embedding patterns into the Network are introduced. The properties of this Network are analyzed concretely through examples of the Network with 3 and 4 quaternion neurons. It is demonstrated that there exist fixed attractors in the Network, i.e., the pattern association from test pattern close to a stored pattern is possible in the quaternionic Network, as in real-valued Hopfield Networks.

Lei Wang - One of the best experts on this subject based on the ideXlab platform.

  • hopf bifurcation and stability analysis on discrete time Hopfield Neural Network with delay
    Nonlinear Analysis-real World Applications, 2008
    Co-Authors: Hongyong Zhao, Lei Wang
    Abstract:

    Abstract In this paper, a discrete-time Hopfield Neural Network with delay is considered. We give some sufficient conditions ensuring the local stability of the equilibrium point for this model. By choosing the delay as a bifurcation parameter, we demonstrated that Neimark–Sacker bifurcation (or Hopf bifurcation for map) would occur when the delay exceeds a critical value. A formula for determining the direction bifurcation and stability of bifurcation periodic solutions is given by applying the normal form theory and the center manifold theorem. Some numerical simulations for justifying the theoretical results are also provided.

Yan Hong-liang - One of the best experts on this subject based on the ideXlab platform.

  • Application of Hopfield Neural Network in unit commitment problem
    Journal of Computer Applications, 2009
    Co-Authors: Yan Hong-liang
    Abstract:

    This paper presented an algorithm,based on multi-layer Hopfield Neural Network,for determining unit commitment.By constructing an appropriate energy function,a single layer Hopfield Neural Network can solve the problem of assigning output power of generators at any given time.Based on this single layer Hopfield Neural Network,a multi-layer Hopfield Neural Network was presented.The multi-layer Hopfield Neural Network can solve the problem of power system unit commitment.The energy functions of single layer and multi-layer Hopfield Neural Network and the corresponding algorithm were given.The restricted conditions of the balance between power supply and demand,maximum and minimum outputs of power plants were considered in the energy function.An example shows that the result got by Hopfield Neural Network is like to that got by genetic algorithm,but the calculation time is much less.