Kernel Width Optimization for Faulty RBF Neural Networks with Multi-node Open Fault

Many researches have been devoted to select the kernel parameters, including the centers, kernel width and weights, for fault-free radial basis function (RBF) neural networks. However, most are concerned with the centers and weights identification, and fewer focus on the kernel width selection. Moreover, to our knowledge, almost no literature has proposed the effective and applied method to select the optimal kernel width for faulty RBF neural networks. As is known that the node faults inevitably take place in real applications, which results in a great many of faulty networks, it will take a lot of time to calculate the mean prediction error (MPE) for the traditional method, i.e., the test set method. Thus, the letter derives a formula to estimate the MPE of each candidate width value and then use it to select the optimal one with the lowest MPE value for faulty RBF neural networks with multi-node open fault. Simulation results show that the chosen optimal kernel width by our proposed MPE formula is very close to the actual one by the conventional method. Moreover, our proposed MPE formula outperforms other selection methods used for fault-free neural networks.     

Regularizers for fault tolerant multilayer feedforward networks

Fault tolerance is an important issue for multilayer feedforward networks (MFNs). However, in the classical training approach for open node fault and open weight fault, we should consider many potential faulty networks. Clearly, if the number of faulty networks considered in the objective function is large, this training approach would be very time consuming. This paper derives two objective functions for attaining fault tolerant MFNs. One objective function is designed for handling open node fault while another one is designed for handling open weight fault. With the linearization technique, each of these two objective functions can be decomposed into two terms, the training error and a simple regularization term. In our approach, the objective functions are computationally simple. Hence the conventional backpropagation algorithm can be simply applied to handle these fault tolerant objective functions.     

Isocube: exploiting the cubemap hardware

This paper proposes a novel six-face spherical map, isocube, that fully utilizes the cubemap hardware built in most GPUs. Unlike the cubemap, the proposed isocube uniformly samples the unit sphere (uniformly distributed), and all samples span the same solid angle (equally important). Its mapping computation contains only a small overhead. By feeding the cubemap hardware with the six-face isocube map, the isocube can exploit all built-in texturing operators tailored for the cubemap and achieve a very high frame rate. In addition, we develop an anisotropic filtering that compensates aliasing artifacts due to texture magnification. This filtering technique extends the existing hardware anisotropic filtering and can be applied not only to the proposed isocube, but also to other texture mapping applications.     

A finite-element study on constitutive relation HM-V for elastic polycrystals

Through a semi-phenomenological approach, we have recently derived a simple constitutive relation (HM-V) for aggregates of cubic crystallites with arbitrary texture symmetry. This constitutive relation is quadratic in the texture coefficients of the polycrystal, and it carries four elastic constants. The derivation delivers four explicit formulae which express the four elastic constants of the polycrystal in terms of the three elastic constants of the single cubic crystal and one undetermined parameter. In this paper we use finite-element calculations to check the adequacy of constitutive relation HM-V and to determine the undetermined parameter for copper and iron polycrystals, respectively.     

Generalized RLS approach to the training of neural networks

Recursive least square (RLS) is an efficient approach to neural network training. However, in the classical RLS algorithm, there is no explicit decay in the energy function. This will lead to an unsatisfactory generalization ability for the trained networks. In this paper, we propose a generalized RLS (GRLS) model which includes a general decay term in the energy function for the training of feedforward neural networks. In particular, four different weight decay functions, namely, the quadratic weight decay, the constant weight decay and the newly proposed multimodal and quartic weight decay are discussed. By using the GRLS approach, not only the generalization ability of the trained networks is significantly improved but more unnecessary weights are pruned to obtain a compact network. Furthermore, the computational complexity of the GRLS remains the same as that of the standard RLS algorithm. The advantages and tradeoffs of using different decay functions are analyzed and then demonstrated with examples. Simulation results show that our approach is able to meet the design goals: improving the generalization ability of the trained network while getting a compact network.     

The plenoptic illumination function

Image-based modeling and rendering has been demonstrated as a cost-effective and efficient approach to virtual reality applications. The computational model that most image-based techniques are based on is the plenoptic function. Since the original formulation of the plenoptic function does not include illumination, most previous image-based virtual reality applications simply assume that the illumination is fixed. We propose a formulation of the plenoptic function, called the plenoptic illumination function, which explicitly specifies the illumination component. Techniques based on this new formulation can be extended to support relighting as well as view interpolation. To relight images with various illumination configurations, we also propose a local illumination model, which utilizes the rules of image superposition. We demonstrate how this new formulation can be applied to extend two existing image-based representations, panorama representation such as QuickTime VR and two-plane parameterization, to support relighting with trivial modifications. The core of this framework is compression, and we therefore show how to exploit two types of data correlation, the intra-pixel and the inter-pixel correlations, in order to achieve a manageable storage size.     

An error control scheme for transmission of vector quantizationdata over noisy channels

This paper presents an error control scheme for transmitting vector-quantized data over noisy channels. First, we review a self-organizing feature map (SOFM) based approach to construct the mapping from the codebook of the quantizer to the channel signal set of the communication system. This approach is robust with respect to channel noise even if we do not use any error control scheme in the communication system. Afterwards, a new trellis type quantizer, namely, the trellis coded Kohonen (1984) map (TCKM), is presented. The design process of the TCKM, which is based on the neighborhood structure of SOFMs, is simpler than that of conventional trellis coded vector quantizers (TCVQs). Simulation results show that the performance of TCKMs is comparable with that of TCVQs. Last, we introduce the error control scheme based on the concepts of the above two applications of SOFMs. Simulation results show that the proposed error control scheme is more robust with respect to channel noise. The advantage of our approaches mentioned above is that the design processes of transmission systems are predefined before the construction of the codebook. Thus, different codebooks with the same neighborhood structure can share the same design     

An improved optimal bit allocation method for sub-band coding

This paper presents an improved optimal bit allocation method for sub-band coding. To speed up the allocation process, a coarse bit range for each sub-band is firstly obtained using the log–variance method, and then an optimal searching routine is applied to produce the final solution. Good features are showed in the simulations for evaluating the proposed method.     

Soft-Decoding SOM for VQ Over Wireless Channels

A self-organizing map (SOM) approach for vector quantization (VQ) over wireless channels is presented. We introduce a soft decoding SOM-based robust VQ (RVQ) approach with performance comparable to that of the conventional channel optimized VQ (COVQ) approach. In particular, our SOM approach avoids the time-consuming index assignment process in traditional RVQs and does not require a reliable feedback channel for COVQ-like training. Simulation results show that our approach can offer potential performance gain over the conventional COVQ approach. For data sources with Gaussian distribution, the gain of our approach is demonstrated to be in the range of 1–4 dB. For image data, our approach gives a performance comparable to a sufficiently trained COVQ, and is superior with a similar number of training epoches. To further improve the performance, a SOM–based COVQ approach is also discussed.