Online modeling and adaptive control of robotic manipulators using Gaussian radial basis function networks

Neural Computing and Applications - Radial basis function network (RBFN) is used in this paper for predefined trajectory control of both one-link and two-link robotic manipulators. The updating...     

Object tracking by mean shift and radial basis function neural networks

In this paper, a tracker based on mean shift and radial basis function neural networks called MS-RBF is addressed. As its name implies, two independent trackers have been combined and linked together. The mean shift algorithm estimates the target’s location within only two iterations. The scale and orientation of target are computed by exploiting 2-D correlation coefficient between reference and target candidate histograms instead of using Bhattacharyya coefficient. A code optimization strategy, named multiply–add–accumulate (MAC), is proposed to remove useless memory occupation and programmatic operations. MAC implementation has reduced computational load and made overall tracking process faster. The second tracker “RBFNN” has an input feature vector that contains variables such as local contrast, color histogram, gradient, intensity, and spatial frequency. The neural network learns the color and texture features from the target and background. Then, this information is used to detect and track the object in other frames. The neural network employs Epanechnikov activation functions. The features extracted in any frame are clustered by Fuzzy C-Means clustering which produces the means and variances of the clusters. The experimental results show that the proposed tracker can resist to different types of occlusions, sudden movement, and shape deformations.     

Robust radial basis function neural networks

Function approximation has been found in many applications. The radial basis function (RBF) network is one approach which has shown a great promise in this sort of problems because of its faster learning capacity. A traditional RBF network takes Gaussian functions as its basis functions and adopts the least-squares criterion as the objective function, However, it still suffers from two major problems. First, it is difficult to use Gaussian functions to approximate constant values. If a function has nearly constant values in some intervals, the RBF network will be found inefficient in approximating these values. Second, when the training patterns incur a large error, the network will interpolate these training patterns incorrectly. In order to cope with these problems, an RBF network is proposed in this paper which is based on sequences of sigmoidal functions and a robust objective function. The former replaces the Gaussian functions as the basis function of the network so that constant-valued functions can be approximated accurately by an RBF network, while the latter is used to restrain the influence of large errors. Compared with traditional RBF networks, the proposed network demonstrates the following advantages: (1) better capability of approximation to underlying functions; (2) faster learning speed; (3) better size of network; (4) high robustness to outliers.     

Online learning and fusion of orientation appearance models for robust rigid object tracking

We introduce a robust framework for learning and fusing of orientation appearance models based on both texture and depth information for rigid object tracking. Our framework fuses data obtained from a standard visual camera and dense depth maps obtained by low-cost consumer depth cameras such as the Kinect. To combine these two completely different modalities, we propose to use features that do not depend on the data representation: angles. More specifically, our framework combines image gradient orientations as extracted from intensity images with the directions of surface normals computed from dense depth fields. We propose to capture the correlations between the obtained orientation appearance models using a fusion approach motivated by the original Active Appearance Models (AAMs). To incorporate these features in a learning framework, we use a robust kernel based on the Euler representation of angles which does not require off-line training, and can be efficiently implemented online. The robustness of learning from orientation appearance models is presented both theoretically and experimentally in this work. This kernel enables us to cope with gross measurement errors, missing data as well as other typical problems such as illumination changes and occlusions. By combining the proposed models with a particle filter, the proposed framework was used for performing 2D plus 3D rigid object tracking, achieving robust performance in very difficult tracking scenarios including extreme pose variations.     

Learning identity with radial basis function networks

Radial basis function (RBF) networks are compared with other neural network techniques on a face recognition task for applications involving identification of individuals using low-resolution video information. The RBF networks are shown to exhibit useful shift, scale and pose (y-axis head rotation) invariance after training when the input representation is made to mimic the receptive field functions found in early stages of the human vision system. In particular, representations based on difference of Gaussian (DoG) filtering and Gabor wavelet analysis are compared. Extensions of the techniques to the case of image sequence analysis are described and a time delay (TD) RBF network is used for recognising simple movement-based gestures. Finally, we discuss how these techniques can be used in real-life applications that require recognition of faces and gestures using low-resolution video images.     

Generalised Gaussian radial basis function neural networks

The mixed use of different shapes of radial basis functions (RBFs) in radial basis functions neural networks (RBFNNs) is investigated in this paper. For this purpose, we propose the use of a generalised version of the standard RBFNN, based on the generalised Gaussian distribution. The generalised radial basis function (GRBF) proposed in this paper is able to reproduce other different radial basis functions (RBFs) by changing a real parameter τ. In the proposed methodology, a hybrid evolutionary algorithm (HEA) is employed to estimate the number of hidden neuron, the centres, type and width of each RBF associated with each radial unit. In order to test the performance of the proposed methodology, an experimental study is presented with 20 datasets from the UCI repository. The GRBF neural network (GRBFNN) was compared to RBFNNs with Gaussian, Cauchy and inverse multiquadratic RBFs in the hidden layer and to other classifiers, including different RBFNN design methods, support vector machines (SVMs), a sparse probabilistic classifier (sparse multinominal logistic regression, SMLR) and other non-sparse (but regularised) probabilistic classifiers (regularised multinominal logistic regression, RMLR). The GRBFNN models were found to be better than the alternative RBFNNs for almost all datasets, producing the highest mean accuracy rank.     

Output value-based initialization for radial basis function neural networks

The use of Radial Basis Function Neural Networks (RBFNNs) to solve functional approximation problems has been addressed many times in the literature. When designing an RBFNN to approximate a function, the first step consists of the initialization of the centers of the RBFs. This initialization task is very important because the rest of the steps are based on the positions of the centers. Many clustering techniques have been applied for this purpose achieving good results although they were constrained to the clustering problem. The next step of the design of an RBFNN, which is also very important, is the initialization of the radii for each RBF. There are few heuristics that are used for this problem and none of them use the information provided by the output of the function, but only the centers or the input vectors positions are considered. In this paper, a new algorithm to initialize the centers and the radii of an RBFNN is proposed. This algorithm uses the perspective of activation grades for each neuron, placing the centers according to the output of the target function. The radii are initialized using the center’s positions and their activation grades so the calculation of the radii also uses the information provided by the output of the target function. As the experiments show, the performance of the new algorithm outperforms other algorithms previously used for this problem.     

Numerical solution of PDEs via integrated radial basis function networks with adaptive training algorithm

This paper develops a mesh-free numerical method for solving PDEs, based on integrated radial basis function networks (IRBFNs) with adaptive residual subsampling training scheme. The multiquadratic function is chosen as the transfer function of the neurons. The nonlinear algebraic equation systems for weights training are solved by Levenberg–Marquardt algorithm. The performance of the proposed method is demonstrated in numerical examples by approximating several functions and solving nonlinear PDEs. The result of numerical experiments shows that the IRBFNs with the adaptive procedure requires less neurons to attain the desired accuracy than conventional radial basis function networks.     

A fast identification algorithm with outliers under Box-Cox transformation-based annealing robust radial basis function networks

In this article, a Box-Cox transformation-based annealing robust radial basis function networks (ARRBFNs) is proposed for an identification algorithm with outliers. Firstly, a fixed Box-Cox transformation-based ARRBFN model with support vector regression (SVR) is derived to determine the initial structure. Secondly, the results of the SVR are used as the initial structure in the fixed Box-Cox transformation-based ARRBFNs for the identification algorithm with outliers. At the same time, an annealing robust learning algorithm (ARLA) is used as the learning algorithm for the fixed Box-Cox transformation-based ARRBFNs, and applied to adjust the parameters and weights. Hence, the fixed Box-Cox transformation-based ARRBFNs with an ARLA have a fast convergence speed for an identification algorithm with outliers. Finally, the proposed algorithm and its efficacy are demonstrated with an illustrative example in comparison with Box-Cox transformation-based radial basis function networks.     

Multi-step prediction method for robust object tracking

In this paper, multi-step ahead prediction method for object tracking based on chaos theory is introduced. The chaos theory is used to preserve the information of object's movement and to model uncertainty and nonlinearity of movement in video sequences. The methodology of the algorithm includes three steps. First, adaptive pseudo-orbit data assimilation is applied to estimate the next state by using the previous states of object. Second, the ensemble members of the state are generated to predict multi-step prediction. Then, the likelihood function of members selects candidate patch for target detection using color information. The algorithm significantly reduces the prediction error because of high-order dynamical information of motion and chaotic prediction. To verify the efficiency of the tracker, the tracking algorithm is compared with the stochastic and deterministic methods under two datasets. The results demonstrate that the chaotic-based tracker outperforms other state-of-the-art methods on the abrupt motion, occlusion, and out of view. The algorithm is about two times faster than the particle filter method while the error of particle filter is about two times more than the error of the chaotic-based tracking method.     

用于目标跟踪的智能群体优化滤波算法

针对目标跟踪中的状态估计，提出一种智能群体优化滤波算法。算法在贝叶斯滤波的基础上，运用智能群体优化的3种运动模型估计目标的后验状态，其中内聚运动在保持了粒子多样性的情况下增加了样本的权值，分离运动和排列运动相协调能够更加准确地预测下一时刻目标的先验状态。实验结果表明:与标准粒子滤波相比，该算法能够更加准确地估计非线性系统中的后验状态，在复杂多变的场景环境中，表现出更高的跟踪准确性。     

Descartes' rule of signs for radial basis function neural networks

We establish versions of Descartes' rule of signs for radial basis function (RBF) neural networks. The RBF rules of signs provide tight bounds for the number of zeros of univariate networks with certain parameter restrictions. Moreover, they can be used to infer that the Vapnik-Chervonenkis (VC) dimension and pseudodimension of these networks are no more than linear. This contrasts with previous work showing that RBF neural networks with two or more input nodes have superlinear VC dimension. The rules also give rise to lower bounds for network sizes, thus demonstrating the relevance of network parameters for the complexity of computing with RBF neural networks.     

梯度算法下RBF网的参数变化动态

分析神经网络学习过程中各参数的变化动态,对理解网络的动力学行为,改进网络的结构和性能等具有积极意义.本文讨论了用梯度算法优化误差平方和损失函数时RBF网隐节点参数的变化动态,即算法收敛后各隐节点参数的可能取值.主要结论包括:如果算法收敛后损失函数不为零,则各隐节点将位于样本输入的加权聚类中心;如果损失函数为零,则网络中的冗余隐节点将出现萎缩、衰减、外移或重合现象.进一步的试验发现,对结构过大的RBF网,冗余隐节点的萎缩、外移、衰减和重合是频繁出现的现象.     

Probabilistic self-organizing map and radial basis function networks

We propose in this paper a new learning algorithm probabilistic self-organizing map (PRSOM) using a probabilistic formalism for topological maps. This algorithm approximates the density distribution of the input set with a mixture of normal distributions. The unsupervised learning is based on the dynamic clusters principle and optimizes the likelihood function. A supervised version of this algorithm based on radial basis functions (RBF) is proposed. In order to validate the theoretical approach, we achieve regression tasks on simulated and real data using the PRSOM algorithm. Moreover, our results are compared with normalized Gaussian basis functions (NGBF) algorithm.     

GPS orbit approximation using radial basis function networks

We present solutions for GPS orbit computation from broadcast and precise ephemerides using a group of artificial neural networks (ANNs), i.e. radial basis function networks (RBFNs). The problem of broadcast orbit correction, resulting from precise ephemerides, has already been solved using traditional polynomial and trigonometric interpolation. As an alternative approach RBFN broadcast orbit correction produces results within the accuracy range of the traditional methods. Our study shows RBFN broadcast orbit correction performs well also near the end of data intervals and for short data spans (～20 min). Regarding limitations of polynomial and trigonometric extrapolation, the most significant advantage of using RBFNs over the traditional methods for GPS broadcast orbit approximation arises from its short time prediction capability.     

Kernel orthonormalization in radial basis function neural networks

This paper deals with optimization of the computations involved in training radial basis function (RBF) neural networks. The main contribution of the reported work is the method for network weights calculation, in which the key idea is to transform the RBF kernels into an orthonormal set of functions (using the standard Gram-Schmidt orthogonalization). This significantly reduces the computing time if the RBF training scheme, which relies on adding one kernel hidden node at a time to improve network performance, is adopted. Another property of the method is that, after the RBF network weights are computed, the original network structure can be restored back. An additional strength of the method is the possibility to decompose the proposed computing task into a number of parallel subtasks so gaining further savings on computing time. Also, the proposed weight calculation technique has low storage requirements. These features make the method very attractive for hardware implementation. The paper presents a detailed derivation of the proposed network weights calculation procedure and demonstrates its validity for RBF network training on a number of data classification and function approximation problems.     

Training radial basis function networks using biogeography-based optimizer

Training artificial neural networks is considered as one of the most challenging machine learning problems. This is mainly due to the presence of a large number of solutions and changes in the search space for different datasets. Conventional training techniques mostly suffer from local optima stagnation and degraded convergence, which make them impractical for datasets with many features. The literature shows that stochastic population-based optimization techniques suit this problem better and are reliably alternative because of high local optima avoidance and flexibility. For the first time, this work proposes a new learning mechanism for radial basis function networks based on biogeography-based optimizer as one of the most well-regarded optimizers in the literature. To prove the efficacy of the proposed methodology, it is employed to solve 12 well-known datasets and compared to 11 current training algorithms including gradient-based and stochastic approaches. The paper considers changing the number of neurons and investigating the performance of algorithms on radial basis function networks with different number of parameters as well. A statistical test is also conducted to judge about the significance of the results. The results show that the biogeography-based optimizer trainer is able to substantially outperform the current training algorithms on all datasets in terms of classification accuracy, speed of convergence, and entrapment in local optima. In addition, the comparison of trainers on radial basis function networks with different neurons size reveal that the biogeography-based optimizer trainer is able to train radial basis function networks with different number of structural parameters effectively.

     

Accurate and robust image registration based on radial basis neural networks

Neural network-based image registration using global image features is relatively a new research subject, and the schemes devised so far use a feedforward neural network to find the geometrical transformation parameters. In this work, we propose to use a radial basis function neural network instead of feedforward neural network to overcome lengthy pre-registration training stage. This modification has been tested on the neural network-based registration approach using discrete cosine transformation features in the presence of noise. The experimental registration work is conducted in two different levels: estimation of transformation parameters from a local range for fine registration and from a medium range for coarse registration. For both levels, the performances of the feedforward neural network-based and radial basis function neural network-based schemes have been obtained and compared to each other. The proposed scheme does not only speed up the training stage enormously but also increases the accuracy and gives robust results in the presence of additive Gaussian noise owing to the better generalization ability of the radial basis function neural networks.     

径向基函数神经网络的一种两级学习方法

建立RBF(radial basis function)神经网络模型关键在于确定网络隐中心向量、基宽度参数和隐节点数.为设计结构简单,且具有良好泛化性能径向基网络结构,本文提出了一种RBF网络的两级学习新设计方法.该方法在下级由正则化正交最小二乘法与D-最优试验设计结合算法自动构建结构节俭的RBF网络模型;在上级通过粒子群优化算法优选结合算法中影响网络泛化性能的3个学习参数,即基宽度参数、正则化系数和D-最优代价系数的最佳参数组合.仿真实例表明了该方法的有效性.     

Logical radial basis function networks a hybrid intelligent model for function approximation

The aim of this article is to introduce a new approach for fuzzy neural network models which can be used effectively in function approximation problems. The proposed model is introduced as an adaptive two-level fuzzy inference system. The architecture of the model is basically a two-layer network of new types of fuzzy-neurons which act as fuzzy IF–THEN rules. The model can be considered as a logical version of the Radial Basis Function networks (RBF). Genetic Algorithms have been adopted as the learning mechanism of the proposed model. Simulations show both highly nonlinear mapping and reasoning capabilities together with simpler structure and better performance when compared with classical neural networks.