Search

In this paper, inspired by Multiscale Geometric Analysis (MGA), a Sparse Ridgelet Kernel Regressor (SRKR) is constructed by combing ridgelet theory with kernel trick. Considering the preferable future of sequential learning over batch learning, we exploit the kernel method in an online setting using the sequential extreme learning scheme to predict nonlinear time-series successively. By using the dimensionality non-separable ridgelet kernels, SRKR is capable of processing the high-dimensional data more efficiently. The online learning algorithm of the examples, named Online Sequential Extreme Learning Algorithm (OS-ELA) is employed to rapidly produce a sequence of estimations. OS-ELA learn the training data one-by-one or chunk by chunk (with fixed or varying size), and discard them as long as the training procedure for those data is completed to keep the memory bounded in online learning. Evolution scheme is also incorporated to obtain a ‘good' sparse regressor. Experiments are taken on some nonlinear time-series prediction problems, in which the examples are available one by one. Some comparisons are made and the experimental results show its efficiency and superiority to its counterparts.

Kernel Matching Pursuit Machine (KMPM) is a relatively new learning algorithm utilizing Mercer kernels to produce non-linear version of conventional supervised and unsupervised learning algorithm. But the commonly used Mercer kernels can't expand a set of complete bases in the feature space (subspace of the square and integrable space). Hence the decision-function found by the machine can't approximate arbitrary objective function in feature space as precise as possible. Multiresolution analysis (MRA) shows promise for both nonstationary signal approximation and pattern recognition, so we combine KMPM with multiresolution analysis technique to improve the performance of the machine, and put forward a MRA shift-invariant kernel, which is a Mercer admissive kernel by theoretical analysis. An MRA kernel matching pursuit machine (MKMPM) is constructed in this paper by Shannon MRA shift-invariant kernel. It is shown that MKMPM is much more effective in the problems of regression and pattern recognition by a large number of comparable experiments.

Most existing object segmentation algorithms suffer from a so-called under-segmentation problem, where parts of the segmented object are missing and holes often occur inside the object region. This problem becomes even more serious when the object pixels have similar intensity values as that of backgrounds. To resolve the problem, we propose a constrained region-growing and contrast enhancement to recover those missing parts and fill in the holes inside the segmented objects. Our proposed scheme consists of three elements: (i) a simple linear transform for contrast enhancement to enable stronger edge detection; (ii) an 8-connected linking regional filter for noise removal; and (iii) a constrained region-growing for elimination of those internal holes. Our experiments show that the proposed scheme is effective towards revolving the under-segmentation problem, in which a representative existing algorithm with edge-map based segmentation technique is used as our benchmark.

In this paper, a new kind of neural network is proposed by combining ridgelet with feed-forward neural network (FNN). The network adopts ridgelet as the activation function in hidden layer of a three-layer FNN. Ridgelet is a good basis for describing the directional information in high dimension and it proves to be optimal in representing the functions with hyperplane singularity. So the network can approximate quite a wide range of multivariate functions in a more stable and efficient way, especially those with certain kinds of spatial inhomogeneities. Both theoretical analysis and experimental results of function approximation prove its superiority to wavelet neural network.

To get a high-ratio compression of remote sensing images, we advanced a new compression method using neural network (NN) and a geometrical multiscale analysis (GMA) tool-ridgelet. Ridgelet is powerful in dealing with linear singularity (or curvilinear singularity with a localized version), so it can represent the edges of images more efficiently. Thus a network for remote sensing image compression is constructed by taking ridgelet as the activation function of hidden layer in a standard three-layer feed-forward NN. Using the characteristics of self-learning, parallel processing, and distributed storage of NN, we get high-ratio compression with satisfying result. Experiment results indicate that the proposed network not only outperforms the classical multilayer perceptron, but also is quite competitive on training of time.

An adaptive beamforming method based on radial-basis function (RBF) neural network is examined for ultra-wideband (UWB) array illuminated by nearfield source in this paper. An analysis of the principle of space-time processing employing Gaussian monocycle model as UWB signal is conducted. The nearfield regionally constrain of UWB beamformer is reflected by a set of samples exerted on neural network training sample space. The recursive least square algorithm has been used for network weights updating. It improves the robustness against large errors in distance and directions of arrival. The efficiency and feasibility of presented approach is proved through the experimental results.

In this paper, a ridgelet kernel regression model is proposed for approximation of multivariate functions, especially those with certain kinds of spatial inhomogeneities. It is based on ridgelet theory, kernel and regularization technology from which we can deduce a regularized kernel regression form. Using the objective function solved by quadratic programming to define a fitness function, we adopt particle swarm optimization algorithm to optimize the directions of ridgelets. Theoretical analysis proves the superiority of ridgelet kernel regression for multivariate functions. Experiments in regression indicate that it not only outperforms support vector machine for a wide range of multivariate functions, but also is robust and quite competitive on training of time.