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    X - /ife - Is Smaller Than The Width, A . Then For Any Given Input, Only The Small

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    Tiu Ton
    The document discusses radial basis function (RBF) neural networks. It explains that RBF networks have a hidden layer with locally tuned units that each have a receptive field. The hidden units produce Gaussian activations based on the distance between the input and the center of their receptive field. The output layer performs a weighted sum of the hidden unit activations. The network is trained using a hybrid method where the hidden unit properties are determined first using self-organization, then the output weights are optimized using supervised learning to minimize error.

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    X - /ife - Is Smaller Than The Width, A . Then For Any Given Input, Only The Small

    Uploaded by

    Tiu Ton
    22 views1 page
    The document discusses radial basis function (RBF) neural networks. It explains that RBF networks have a hidden layer with locally tuned units that each have a receptive field. The hidden units produce Gaussian activations based on the distance between the input and the center of their receptive field. The output layer performs a weighted sum of the hidden unit activations. The network is trained using a hybrid method where the hidden unit properties are determined first using self-organization, then the output weights are optimized using supervised learning to minimize error.

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    00311___3757e9b8bcebe03ddd65548e8f17252f.pdf

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    The document discusses radial basis function (RBF) neural networks. It explains that RBF networks have a hidden layer with locally tuned units that each have a receptive field. The hidden units produce Gaussian activations based on the distance between the input and the center of their receptive field. The output layer performs a weighted sum of the hidden unit activations. The network is trained using a hybrid method where the hidden unit properties are determined first using self-organization, then the output weights are optimized using supervised learning to minimize error.

    Copyright:

    Attribution Non-Commercial (BY-NC)
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    22 views1 page

    X - /ife - Is Smaller Than The Width, A . Then For Any Given Input, Only The Small

    Uploaded by

    Tiu Ton
    The document discusses radial basis function (RBF) neural networks. It explains that RBF networks have a hidden layer with locally tuned units that each have a receptive field. The hidden units produce Gaussian activations based on the distance between the input and the center of their receptive field. The output layer performs a weighted sum of the hidden unit activations. The network is trained using a hybrid method where the hidden unit properties are determined first using self-organization, then the output weights are optimized using supervised learning to minimize error.

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    of 1

    Manufacturing

    Systems

    Estimation

    Using Neural Network Models

    295

    where /x^ and < 7 f c are the center and width, respectively, of the receptive field in the input space for unit k. The value of Zk will be appreciable only when the "distance" \\x /ife|| is smaller than the width, a^. Then for any given input, only the small fraction of basis functions with centers very close will respond with activations that differ significantly from zero. This leads to the notion of locality of RBF networks. A commonly used RBF network assumes a Gaussian basis function for the locally-tuned units: >-Mfc|l (2) zk = exp

    where the norm is Euclidean. No bias terms are needed when Gaussian basis functions are used. The output layer of the RBF network is linear and produces a weighted sum of the outputs of the hidden layer, where the sum is calculated by the matrix multiplication given in Eq. (3).
    Wn W21 W22 WK1 WK2 Zl

    d2

    Wl2

    z% (3)

    dL

    WlL

    W2L

    WKL

    ZK

    The strength of the connections between the fcth hidden unit and the Zth output unit is denoted by weight wu- Term di, where I = 1 , . . . , L, is the Ith component of the network output vector for one input/output pair. The linear output layer function may also include a bias term Aoi- An allowance for nonlinearity in the output layer is possible, provided the transfer function is invertible. Moody and Darken (1989), Broomhead and Lowe (1988), and Hassoun (1995) are popular citations for theory on Radial Basis Function networks. Training the Network

    Training of RBF networks is most computationally efficient when a hybrid learning method, combining linear supervised learning and linear self-organized learning is used. Supervised learning rules adjust the network parameters to move network outputs closer to target outputs and self-organized learning rules modify parameters in response to network inputs only. The combination of local representation and linear learning offers tremendous speed advantages relative to other architectures such as backpropagation. The hybrid learning method is an example of a training strategy that decouples learning at the hidden and the output layers, made possible for RBF networks because of the local receptive field nature of the hidden units. Under the hybrid learning method, receptive field centers and widths are first determined using a self-organizing or feedforward technique. Then, a supervised feedback procedure that optimizes total error is used to adjust the network weights and biases that connect the hidden and output layers.

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