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Conventional convergence analysis on mini-batch learning is usually based on the stochastic gradient concept, in which we assume that the training data are presented in a random order. Also, some convergence results require that the learning rate should decrease with the number of training cycles, and that the objective function is a smooth function. Practically speaking, a deterministic presentation scheme with a fixed learning rate is more preferable. Hence, there is a gap between theoretical results and actual implementation. This paper aims at filling the gap. We use the radial basis function (RBF) model for nonlinear regression problems as an example to analyze the convergence properties of mini-batch learning. This paper considers a nonsmooth objective function, which consists of three terms. The coexistence of these three terms is able to handle a number of situations. The first term is a conventional training set error. The second term is a quadratic term which is used to suppress the effect of imperfections in the implementation. The last term is an ℓ 1 -norm term which is used to select important RBF nodes for the resultant network. Note that the ℓ 1 -norm term is a nonsmooth function. Although a nonsmooth ℓ 1 -norm is included and the mini-batch algorithm is deterministic, we are still able to derive the convergence properties, including the sufficient conditions for convergence and range of learning rate. With our results, we have a better theoretical understanding on the behaviour of mini-batch learning and obtain some guidelines on choosing the learning rate. The analysis results can be extended to other flat structural neural network models and other objective functions, which are with quadratic terms and ℓ 1 -norm. [ABSTRACT FROM AUTHOR]

The single-layer perceptron, introduced by Rosenblatt in 1958, is one of the earliest and simplest neural network models. However, it is incapable of classifying linearly inseparable patterns. A new era of neural network research started in 1986, when the backpropagation (BP) algorithm was rediscovered for training the multilayer perceptron (MLP) model. An MLP with a large number of hidden nodes can function as a universal approximator. To date, the MLP model is the most fundamental and important neural network model. It is also the most investigated neural network model. Even in this AI or deep learning era, the MLP is still among the few most investigated and used neural network models. Numerous new results have been obtained in the past three decades. This survey paper gives a comprehensive and state-of-the-art introduction to the perceptron model, with emphasis on learning, generalization, model selection and fault tolerance. The role of the perceptron model in the deep learning era is also described. This paper provides a concluding survey of perceptron learning, and it covers all the major achievements in the past seven decades. It also serves a tutorial for perceptron learning. [ABSTRACT FROM AUTHOR]

The aim of this research is to use continuous time neural networks for solving the sparse portfolio problem, where the objective function includes a non-differentiable ℓ 1 -norm regularization term. To address the non-differentiable issue, we introduce two novel continuous time neural models that are based on the Lagrange programming neural network (LPNN) framework. The proposed neural models have the ability to control the number of the assets in the resulting portfolio and adjust the weighting between risk and return. The first model, called LPNN-Approximation, handles the non-differentiable ℓ 1 -norm term by utilizing a differentiable approximation. The second model merges the locally competitive algorithm (LCA) concept with the LPNN framework to address the non-differentiable term. It is called LPNN-LCA. For the LPNN-Approximation, we prove that the state of the network globally converges to the optimal solution of the sparse portfolio problem. Meanwhile, for the LPNN-LCA, we prove that all the equilibrium points of its dynamics correspond to the optimal solution of the sparse portfolio problem and are asymptotically stable. In addition, the realizations of the two models are discussed. Specifically, a thorough circuit realization for the thresholding elements of the LPNN-LCA model is presented. The effectiveness of the proposed approaches is verified by a number of numerical experiments, which show that the two proposed models outperform two state-of-the-art analog models. [ABSTRACT FROM AUTHOR]

In the construction of a radial basis function (RBF) network, one of the most important issues is the selection of RBF centers. However, many selection methods are designed for the fault free situation only. This paper first assumes that all the training samples are used for constructing a fault tolerant RBF network. We then add an l 1 norm regularizer into the fault tolerant objective function. According to the nature of the l 1 norm regularizer, some unnecessary RBF nodes are removed automatically during training. Based on the local competition algorithm (LCA) concept, we propose an analog method, namely fault tolerant LCA (FTLCA), to minimize the fault tolerant objective function. We prove that the proposed fault tolerant objective function has a unique optimal solution, and that the FTLCA converges to the global optimal solution. Simulation results show that the FTLCA is better than the orthogonal least square approach and the support vector regression approach. [ABSTRACT FROM AUTHOR]

Abstract: This paper develops two neural network models, based on Lagrange programming neural networks (LPNNs), for recovering sparse signals in compressive sampling. The first model is for the standard recovery of sparse signals. The second one is for the recovery of sparse signals from noisy observations. Their properties, including the optimality of the solutions and the convergence behavior of the networks, are analyzed. We show that for the first case, the network converges to the global minimum of the objective function. For the second case, the convergence is locally stable. [Copyright &y& Elsevier]

Soft shadows play an important role in photo-realistic rendering. Although there are many efficient soft shadow algorithms, most of them focus on the one-side light source situation, where a planar light source is on the outside of the scene. In fact, in many situations, such as games, light sources are omnidirectional. They may be surrounded by a number of 3D objects. This paper proposes a soft shadow algorithm for the omnidirectional situation. We develop a concentric spherical representation to model the behaviour of omnidirectional light sources. To provide better rendering results, a novel summed area table based filtering scheme for spherical functions is proposed. In addition, we utilize unicube mapping, which samples the spherical space more uniformly, to further improve the filtering quality. [ABSTRACT FROM AUTHOR]

An illumination adjustable image (IAI), containing a set of pre-captured reference images under various light directions, represents the appearance of a scene with adjustable illumination. One of drawbacks of using the IAI representation is that an IAI consumes a lot of memory. Although some previous works proposed to use blockwise principal component analysis for compressing IAIs, they did not consider the spherical nature of the extracted eigen-coefficients. This paper utilizes the spherical nature of the extracted eigen-coefficients to improve the compression efficiency. Our compression scheme consists of two levels. In the first level, the reference images are converted into a few eigen-images (floating point images) and a number of eigen-coefficients. In the second level, the eigen-images are compressed by a wavelet-based method. The eigen-coefficients are organized into a number of spherical functions. Those spherical coefficients are then compressed by the proposed HEALPIX discrete cosine transform technique. [ABSTRACT FROM AUTHOR]

Many analog neural network approaches for sparse recovery were based on using ℓ 1 -norm as the surrogate of ℓ 0 -norm. This paper proposes an analog neural network model, namely the Lagrange programming neural network with ℓ p objective and quadratic constraint (LPNN-LPQC), with an ℓ 0 -norm sparsity measurement for solving the constrained basis pursuit denoise (CBPDN) problem. As the ℓ 0 -norm is non-differentiable, we first use a differentiable ℓ p -norm-like function to approximate the ℓ 0 -norm. However, this ℓ p -norm-like function does not have an explicit expression and, thus, we use the locally competitive algorithm (LCA) concept to handle the nonexistence of the explicit expression. With the LCA approach, the dynamics are defined by the internal state vector. In the proposed model, the thresholding elements are not conventional analog elements in analog optimization. This paper also proposes a circuit realization for the thresholding elements. In the theoretical side, we prove that the equilibrium points of our proposed method satisfy Karush Kuhn Tucker (KKT) conditions of the approximated CBPDN problem, and that the equilibrium points of our proposed method are asymptotically stable. We perform a large scale simulation on various algorithms and analog models. Simulation results show that the proposed algorithm is better than or comparable to several state-of-art numerical algorithms, and that it is better than state-of-art analog neural models. [ABSTRACT FROM AUTHOR]

High-dynamic range (HDR) images are commonly used in computer graphics for accurate rendering. However, it is inefficient to store these images because of their large data size. Although vector quantization approach can be used to compress them, a large number of representative colors are still needed to preserve acceptable image quality. This paper presents an efficient color quantization approach to compress HDR images. In the proposed approach, a 1D/2D neighborhood structure is defined for the self-organizing map (SOM) approach and the SOM approach is then used to train a color palette. Afterward, a virtual color palette that has more codevectors is simulated by interpolating the trained color palette. The interpolation process is hardware supported in the current graphics hardware. Hence, there is no need to store the virtual color palette as the representative colors are constructed on the fly. Experimental results show that our approach can obtain good image quality with a moderate color palette. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, an objective function for training a radial basis function (RBF) network to handle single node open fault is presented. Based on the definition of this objective function, we propose a training method in which the computational complexity is the same as that of the least mean squares (LMS) method. Simulation results indicate that our method could greatly improve the fault tolerance of RBF networks, as compared with the one trained by LMS method. Moreover, even if the tuning parameter is misspecified, the performance deviation is not significant. [Copyright &y& Elsevier]

Injecting weight noise during training has been a simple strategy to improve the fault tolerance of multilayer perceptrons (MLPs) for almost two decades, and several online training algorithms have been proposed in this regard. However, there are some misconceptions about the objective functions being minimized by these algorithms. Some existing results misinterpret that the prediction error of a trained MLP affected by weight noise is equivalent to the objective function of a weight noise injection algorithm. In this brief, we would like to clarify these misconceptions. Two weight noise injection scenarios will be considered: one is based on additive weight noise injection and the other is based on multiplicative weight noise injection. To avoid the misconceptions, we use their mean updating equations to analyze the objective functions. For injecting additive weight noise during training, we show that the true objective function is identical to the prediction error of a faulty MLP whose weights are affected by additive weight noise. It consists of the conventional mean square error and a smoothing regularizer. For injecting multiplicative weight noise during training, we show that the objective function is different from the prediction error of a faulty MLP whose weights are affected by multiplicative weight noise. With our results, some existing misconceptions regarding MLP training with weight noise injection can now be resolved. [ABSTRACT FROM AUTHOR]

Abstract: Image-based relighting allows us to efficiently light a scene under complicated illumination conditions. However, the traditional cubemap based multi-resolution analysis unevenly samples the spherical surface, with a higher sampling rate near the face corners and a lower one near the face centers. The non-uniformity penalizes the efficiency of data representation. This paper presents a uniformly sampling multi-resolution analysis approach, namely the icosahedron spherical wavelets (ISW), for image-based relighting under time-varying distant environment. Since the proposed ISW approach provides a highly uniform sampling distribution over the spherical domain, we thus can efficiently handle high frequency variations locally in the illumination changes as well as reduce the number of wavelet coefficients needed in the renderings. Furthermore, visual artifacts are demonstrated to be better suppressed in the proposed ISW approach. Compared with the traditional cubemap based multi-resolution analysis approach, we show that our approach can effectively produce higher quality image sequences that are closer to the ground truth in terms of percentage square errors. [Copyright &y& Elsevier]

Abstract: In image-based relighting (IBR), a set of reference images is pre-captured under various light directions. These reference images represent the appearance of a scene with an adjustable illumination. This paper describes a graphics process unit (GPU) favor relighting scheme for IBR. The scheme consists of two levels. In the first level, the reference images are converted into a number of lightmaps (floating point images) based on the proposing HEALPIX discrete cosine transform (HDCT). In the second level, the lightmaps are compressed with a GPU favor compression method. Novel images with complicated lighting conditions can be directly generated from those compressed lightmaps. The GPU accelerated relighting methods for the directional source and the point source are discussed. Compared with the spherical harmonic scheme and the radial basis function scheme, the proposed HDCT scheme offers the similar rendering speed and much better rendering quality. [Copyright &y& Elsevier]

• This paper formally analyzes the properties of multi-bit quanta image sensor (QIS) systems. It derives the log likelihood function of the received photon counts in a spatiotemporal jot kernel, and introduces the concept of the probability of all jots being saturated. • From the likelihood function result, we can have a maximum likelihood (ML) estimate for the exposure level and present a construction algorithm, namely ML multi-bit (MLM). As our estimate is ML based, the variance of the estimated exposure achieves the Cramér-Rao bound (CRB) asymptotically. • From the Fisher information concept, this paper derives the CRB on the variance of the estimated exposure. This CRB value can be considered as a performance indicator for different hardware settings. • From the jot saturation result, we can accurately formulate the relationship between maximum exposure and the kernel size, as well as i.e., the relationship between dynamic range and the kernel size. • From two analysis results, we can model the relationships between sensor design parameters and performance metrics (variance of the estimated exposure and the dynamic range). Since the analysis results are independent of the construction algorithm used, they give us some guidelines to vary the spatiotemporal jot kernel size and the bit resolution of QIS jots to control dynamic range, and signal to noise ratio of constructed images. • This paper empirically studies the effect of readout Gaussian noise. • With our framework in likelihood function, we can develop some joint-construction-and-denosing algorithms for MBQIS. We use an enhanced version of MLM, namely MLM with denoising (MLMDN), to demonstrate this joint-construction-and-denosing concept. A new breed of photon-counting sensors, called quanta image sensor (QIS), enables the detection of light with precision represented by the number of photons arriving within a time period. However, most existing analysis results on QIS systems are formulated for the single-bit case only. Directly extending the existing single-bit analysis to the multi-bit case leads to the situation that the variance of the estimated exposure is greater than the Cramér-Rao bound (CRB). Also, the existing dynamic range analysis leads to a strange situation that the maximum exposure level is not a function of the spatiotemporal jot kernel size. This paper formally analyzes the properties of multi-bit QIS (MBQIS) systems. It derives the log likelihood function of the received photon counts in a spatiotemporal jot kernel, and introduces the concept of the probability of all jots being saturated. From the likelihood function result, we can obtain a maximum likelihood (ML) estimate for the exposure level and present an image construction algorithm, namely ML multi-bit (MLM). Since the estimate is ML based, the variance of the estimated exposure achieves the CRB asymptotically and the MLM is an asymptotically unbiased estimator. Also, based on the Fisher information concept, this paper derives the CRB on the variance of the estimated exposure. Hence the CRB given by this paper can be considered as a performance indicator for all algorithms. From the jot saturation analysis result, we can accurately formulate the relationship between dynamic range and spatiotemporal kernel size. Specifically, with our two analysis results, we can model the relationships between sensor design parameters and performance metrics (variance of the estimated exposure and the dynamic range). Since the two analysis results are independent of the construction algorithms used, they give us some guidelines to design a QIS system. In addition, this paper empirically studies the effect of the readout Gaussian noise. Finally, to demonstrate another application of the likelihood analysis result, we develop an enhanced version of MLM, namely MLM with denoising (MLMDN), based on the proposed likelihood function and the regularization concept. [ABSTRACT FROM AUTHOR]

In the image-based relighting (IBL), tremendous reference images are needed to provide a high quality rendering. Therefore, a data compression is a must for its real applications. In this paper, two global analysis methods, the principal component analysis (PCA) and the independent component analysis (ICA), are used to compress the huge IBL data by exploiting its correlation properties. Both approaches approximate the raw data with a small number of global base images, and they follow a similar algorithm structure: base images extraction, raw data representation, and further compression on the base images and the representing coefficients. What differs is that PCA only removes the second-order data correlation, but ICA reduces nearly all order statistics data dependence, which should benefit the data compression. Simulations are given to evaluate their performance. Comparisons are also made between them and JPEG2000 and MPEG. The evaluation results show that both approaches are superior to JPEG2000 and MPEG. Although ICA tends to remove higher order dependence than PCA, it is a little inferior to PCA in terms of compression ratio/reconstruction error performance. [Copyright &y& Elsevier]

In image-based rendering with adjustable illumination, the data set contains a large number of pre-captured images under different sampling lighting directions. Instead of individually compressing each pre-captured image, we propose a two-level compression method. Firstly, we use a few spherical harmonic (SH) coefficients to represent the plenoptic property of each pixel. The classical discrete summation method for extracting SH coefficient requires that the sampling lighting directions should be uniformly distributed on the whole spherical surface. It cannot handle the case that the sampling lighting directions are irregularly distributed. A constrained least-squares algorithm is proposed to handle this case. Afterwards, embedded zero-tree wavelet coding is used for removing the spatial redundancy in SH coefficients. Simulation results show our approach is much superior to the JPEG, JPEG2000, MPEG2, and 4D wavelet compression method. The way to allow users to interactively control the lighting condition of a scene is also discussed. [Copyright &y& Elsevier]

This paper presents a principal component analysis (PCA) based data compression method for the image-base relighting (IBL) technology, which needs tremendous reference images to produce high quality rendering. The method contains two main steps, eigen-image based representation and eigen-image compression. We extract eigen-images by the cascade recursive least squared (CRLS) networks based PCA due to the large data dimension. By keeping only a few important eigen-images, which are enough to describe the IBL data set, the data size can be drastically reduced. To further reduce the data size, we use the embedded zero wavelet (EZW) approach to compress those retained eigen-images, and use uniform quantization plus arithmetic coding to compress the representing coefficients. Simulation results demonstrate that our approach is superior to that of compressing reference images separately with JPEG or EZW. [Copyright &y& Elsevier]

In the classical deterministic Elman model, the estimation of parameters must be very accurate. Otherwise, the system performance is very poor. To improve the system performance, we can use a Kalman filtering algorithm to guide the operation of a trained recurrent neural network (RNN). In this case, during training, we need to estimate the state of hidden layer, as well as the weights of the RNN. This paper discusses how to use the dual extended Kalman filtering (DEKF) for this dual estimation and how to use our proposing DEKF for removing some unimportant weights from a trained RNN. In our approach, one Kalman algorithm is used for estimating the state of the hidden layer, and one recursive least square (RLS) algorithm is used for estimating the weights. After training, we use the error covariance matrix of the RLS algorithm to remove unimportant weights. Simulation showed that our approach is an effective joint-learning–pruning method for RNNs under the online operation. [Copyright &y& Elsevier]

The global extended Kalman filtering (EKF) algorithm for recurrent neural networks (RNNs) is plagued by the drawback of high computational cost and storage requirement. In this paper, we present a local EKF training-pruning approach that can solve this problem. In particular, the by-products, obtained along with the local EKF training, can be utilized to measure the importance of the network weights. Comparing with the original global approach, the proposed local approach results in much lower computational cost and storage requirement. Hence, it is more practical in solving real world problems. Simulation showed that our approach is an effective joint-training-pruning method for RNNs under online operation. [ABSTRACT FROM AUTHOR]

The training of neural networks using the extended Kalman filter (EKF) algorithm is plagued by the drawback of high computational complexity and storage requirement that may become prohibitive even for networks of moderate size. In this paper, we present a local EKF training and pruning approach that can solve this problem. In particular, the by-products obtained along with the local EKF training can be utilized to measure the importance of the network weights. Comparing with the original global approach, the proposed local EKF training and pruning approach results in a much lower computational complexity and storage requirement. Hence, it is more practical in solving real world problems. The performance of the proposed algorithm is demonstrated on one medium- and one large-scale problems, namely, sunspot data prediction and handwritten digit recognition. [ABSTRACT FROM AUTHOR]

The concept of randomized neural networks (RNNs), such as the random vector functional link network (RVFL) and extreme learning machine (ELM), is a widely accepted and efficient network method for constructing single-hidden layer feedforward networks (SLFNs). Due to its exceptional approximation capabilities, RNN is being extensively used in various fields. While the RNN concept has shown great promise, its performance can be unpredictable in imperfect conditions, such as weight noises and outliers. Thus, there is a need to develop more reliable and robust RNN algorithms. To address this issue, this paper proposes a new objective function that addresses the combined effect of weight noise and training data outliers for RVFL networks. Based on the half-quadratic optimization method, we then propose a novel algorithm, named noise-aware RNN (NARNN), to optimize the proposed objective function. The convergence of the NARNN is also theoretically validated. We also discuss the way to use the NARNN for ensemble deep RVFL (edRVFL) networks. Finally, we present an extension of the NARNN to concurrently address weight noise, stuck-at-fault, and outliers. The experimental results demonstrate that the proposed algorithm outperforms a number of state-of-the-art robust RNN algorithms. [ABSTRACT FROM AUTHOR]

Provides information on a study which deals with error control scheme for transmitting vector-quantized data over noisy channels. Self-organizing feature maps; Background on vector quantization for noisy channels; Conclusion.

Presents information on a study which discussed the regularization of employing the forgetting recursive least square (FRLS) training technique on feedforward neural networks. Preliminary on the FRLS method; Results of the study; Derivation of the expected mean prediction error; Comparison between FRLS and recursive least square.

Provides information on a study on the Kalman filtering method in neural network training and pruning. Description of Kalman filtering method in training; Evaluation of weight saliency; Conclusion.

Provides information on a study which analyzed the network response time of a class of winner-take-all neural network which involves self-decay. Network model; Properties; Simulation verification; Design examples; Conclusion.

Pruning a neural network to a reasonable smaller size, and if possible to give a better generalization, has long been investigated. Conventionally the common technique of pruning is based on considering error sensitivity measure, and the nature of the problem being solved is usually stationary. In this article, we present an adaptive pruning algorithm for use in a nonstationary environment. The idea relies on the use of the extended Kalman filter (EKF) training method. Since EKF is a recursive Bayesian algorithm, we define a weight-importance measure in term of the sensitivity of a posteriori probability. Making use of this new measure and the adaptive nature of EKF, we devise an adaptive pruning algorithm called adaptive Bayesian pruning. Simulation results indicate that in a noisy nonstationary environment, the proposed pruning algorithm is able to remove network redundancy adaptively and yet preserve the same generalization ability. [ABSTRACT FROM AUTHOR]

Presents an algorithm to form a topographic map resembling to the self-organizing map. Basis behind idea; How the proposed algorithm is defined; Illustration of simulations on two-dimensional maps; Concluding remarks.

Discusses a possible solution to the problem caused by the separation of the vector quantizer and the communication system in the transmission of vector quantized data. Impact of this separation on the performance of the vector quantizer; Construction of a mapping based on the self-organizing feature map (SOFM); Simulation results.

Reviews a bidirectional associative memory (BAM) model with second-order connections, namely second-order bidirectional associative memory (SOBAM). SOBAM and its stability; Statistical dynamics of SOBAM; Estimation of statistical properties; Numerical results based on theoretical work; Higher order bidirectional associative memories (HOBAM); Conclusion of the study.

Studies the storage behavior of bidirectional associative memory (BAM) under the forgetting learning rule in the associative memory class of neural networks. Properties of forgetting learning; Simulation; Magnitude of the weights.

• This paper develops a noise/fault aware training objective for incremental ELM. • This paper uses two representative algorithms to develop two noise aware ELM. • The two proposed algorithms are much better than existing ones. • The multiple set concept can further enhance the performance. • We can make other non-noise tolerant algorithms to be noise tolerant. This paper investigates noise/fault tolerant incremental algorithms for the extreme learning machine (ELM) concept. Existing incremental ELM algorithms can be classified into two approaches: non-recomputation and recomputation. This paper first formulates a noise/fault aware objective function for nonlinear regression problems. Instead of developing noise/fault aware algorithms for the two computational approaches in a one-by-one manner, this paper uses two representative incremental algorithms, namely incremental ELM (I-ELM) and error minimized ELM (EM-ELM), to develop two noise/fault aware incremental algorithms. The proposed algorithms are called generalized I-ELM (GI-ELM) and generalized EM-ELM (GEM-ELM). The GI-ELM adds k hidden nodes into the existing network at each incremental step without recomputing the existing weights. To have a fair comparison, we consider a modified version of I-ELM as a comparison algorithm. The simulation demonstrates that the noise/fault tolerance of the proposed GI-ELM is better than that of the modified I-ELM. In the GEM-ELM, k hidden nodes are added into the existing network at each incremental step. Meanwhile, all output weights are recomputed based on a recursive formula. We also consider a modified version of EM-ELM as a comparison algorithm. The simulation demonstrates that the noise/fault tolerance of the proposed GEM-ELM is better than that of the modified EM-ELM. Moreover, we demonstrate that the multiple set concept can further enhance the performance of the two proposed algorithms. Following our research results, one can make some non-noise/fault tolerant incremental algorithms to be noise/fault tolerant. [ABSTRACT FROM AUTHOR]

Given a set of 2-dimensional (2D) scattering points, obtained from the edge detection process, the aim of ellipse fitting is to construct an elliptic equation that best fits the scattering points. However, the 2D scattering points may contain some outliers. To address this issue, we devise a robust ellipse fitting approach based on two analog neural network models, Lagrange programming neural network (LPNN) and locally competitive algorithm (LCA). We formulate the fitting task as a nonsmooth constrained optimization problem, in which the objective function is an approximated l 0 -norm term. As the LPNN model cannot handle non-differentiable functions, we utilize the internal state concept of LCA to avoid the computation of the derivative at non-differentiable points. Simulation results show that the proposed ellipse fitting approach is superior to several state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

Dual paraboloid mapping is an approach for environment mapping. Its major advantage is its fast map generation speed. For graphics applications, when filtering is needed, the filtering tool would naturally be mipmapping. However, directly applying mipmapping to dual paraboloid mapping would give us three problems. They are the discontinuity across the dual paraboloid map boundary, the non‐uniform sampling problem and the depth testing issue. We propose three approaches to solve these problems. Our approaches are based on some closed form equations derived via theoretical analysis. Using these equations, we modify the coordinates involved during the rendering process. In other words, these problems are handled just by using dual paraboloid maps and mipmaps differently, instead of fundamentally altering their data structures. Consequently, we are fixing the problems without damaging the map generation speed advantage. Applying all three approaches, we improve the rendering quality of dual paraboloid map mipmaps to a level equivalent to that of cubemap mipmaps, while preserving its fast map generation speed advantage. This gives dual paraboloid map mipmaps the potential to be a better choice than cubemap mipmaps for the devices with less computational power. The effectiveness and the efficiency of the proposed approaches are demonstrated using a glossy reflection application and an omnidirectional soft shadow generation application. [ABSTRACT FROM AUTHOR]

A new method powered by an artificial neural network (ANN) is studied for resonant-mode recognitions of a rectangular dielectric resonator antenna (DRA). Different rectangular DRAs were simulated with ANSYS HFSS to generate a large dataset for training the model. Their resonance frequencies, dimensions, and 3-D electric fields are input to the ANN. The output end is a 12-element array representing the corresponding probabilities of 12 different resonant modes. Using this trained ANN model, the mode recognition accuracy can reach 96.74%. Apart from identifying the resonant modes, our proposed approach can suggest how to modify a rectangular DRA to improve the purity of a resonant mode for better antenna performance. [ABSTRACT FROM AUTHOR]

In vector graphics, gradient meshes represent an image object by one or more regularly connected grids. Every grid point has attributes as the position, colour and gradients of these quantities specified. Editing the attributes of an existing gradient mesh (such as the colour gradients) is not only non-intuitive but also time-consuming. To facilitate user-friendly colour editing, we develop an optimization-based colour transfer method for gradient meshes. The key idea is built on the fact that we can approximate a colour transfer operation on gradient meshes with a linear transfer function. In this paper, we formulate the approximation as an optimization problem, which aims to minimize the colour distribution of the example image and the transferred gradient mesh. By adding proper constraints, i.e. image gradients, to the optimization problem, the details of the gradient meshes can be better preserved. With the linear transfer function, we are able to edit the colours and colour gradients of the mesh points automatically, while preserving the structure of the gradient mesh. The experimental results show that our method can generate pleasing recoloured gradient meshes. [ABSTRACT FROM AUTHOR]

An integration of particle swarm optimization (PSO) and K-Means algorithm is becoming one of the popular strategies for solving clustering problem, especially unsupervised gene clustering. It is known as PSO-based K-Means clustering algorithm (PSO-KM). However, this approach causes the dimensionality of clustering problem to expand in PSO search space. The sequence of clusters represented in particle is not evaluated. This study proposes an enhanced cluster matching to further improve PSO-KM. In the proposed scheme, prior to the PSO updating process, the sequence of cluster centroids encoded in a particle is matched with the corresponding ones in the global best particle with the closest distance. On this basis, the sequence of centroids is evaluated and optimized with the closest distance. This makes particles to perform better in searching the optimum in collaborative manner. Experimental results show that this proposed scheme is more effective in reducing clustering error and improving convergence rate. [ABSTRACT FROM AUTHOR]