In this study, we propose a robust approach for blind source separation (BSS) by using radial basis function networks (RBFNs) and higher-order statistics (HOS). The RBFN is employed to estimate the inverse of a hypothetical complicated mixing procedure. It transforms the observed signals into high-dimensional space, in which one can simply separate the transformed signals by using a cost function. Recently, Tan et al. proposed a nonlinear BSS method, in which higher-order moments between source signals and observations are matched in the cost function. However, it has a strict restriction that it requires the higher-order statistics of sources to be known. We propose a cost function that consists of higher-order cumulants and the second-order moment of signals to remove the constraint. The proposed approach has the capacity of not only recovering the complicated mixed signals, but also reducing noise from observed signals. Simulation results demonstrate the validity of the proposed approach. Moreover, a result of application to X-ray image separation also shows its practical applicability.

In this paper, we present the method for identifying an Adaptive Neuro-Fuzzy Networks (ANFN) with Takagi-Sugeno-Kang (TSK) fuzzy type based on fuzzy granulation. We also develop a systematic approach to generating fuzzy if-then rules from a given input-output data. The proposed ANFN is designed by the use of fuzzy granulation realized via context-based fuzzy clustering. This clustering technique builds information granules in the form of fuzzy sets and develops clusters by preserving the homogeneity of the clustered patterns associated with the input and output space. The experimental results reveal that the proposed model yields a better performance in comparison with Linguistic Models (LM) and Radial Basis Function Networks (RBFN) based on context-based fuzzy clustering introduced in the previous literature for Box-Jenkins gas furnace data and automobile MPG prediction.

This paper deals with an on-line identification method based on a radial basis function (RBF) network model for continuous-time nonlinear systems. The nonlinear term of the objective system is represented by the RBF network. In order to track the time-varying system parameters and nonlinear term, the recursive least-squares (RLS) method is combined in a bootstrap manner with the genetic algorithm (GA). The centers of the RBF are coded into binary bit strings and searched by the GA, while the system parameters of the linear terms and the weighting parameters of the RBF are updated by the RLS method. Numerical experiments are carried out to demonstrate the effectiveness of the proposed method.

Partial face images, e.g., eyes, nose, and ear images are significant for face recognition. In this paper, we present a method for partial face extraction and recognition based on Radial Basis Function (RBF) networks. Focus has been centered on using ear images because they are not influenced by facial expression, and the influences of aging are negligible. Original human side face image with 320240 pixels is input, and then the RBF network locates the ear and extracts it with a 200120 pixel image. Next, another RBF network is constructed for the purpose of recognition. An algorithm that determines the radius of an RBF function is proposed. Dynamic radius, so called as compared to static one, is found through the algorithm that makes RBF functions adaptable to the training samples. We built a database that contains 600 side face images, from 100 people, to test the method and the results of both extraction and recognition are satisfied.

In content-based image retrieval (CBIR), the content of an image can be expressed in terms of different features such as color, texture, shape, or text annotations. Retrieval methods based on these features can be varied depending on how the feature values are combined. Many of the existing approaches assume linear relationships between different features, and also require users to assign weights to features for themselves. Other nonlinear approaches have mostly concentrated on indexing technique. While the linearly combining approach establishes the basis of CBIR, the usefulness of such systems is limited due to the lack of the capability to represent high-level concepts using low-level features and human perception subjectivity. In this paper, we introduce a Neural Network-based Image Retrieval (NNIR) system, a human-computer interaction approach to CBIR using the Radial Basis Function (RBF) network. The proposed approach allows the user to select an initial query image and incrementally search target images via relevance feedback. The experimental results show that the proposed approach has the superior retrieval performance over the existing linearly combining approach, the rank-based method, and the BackPropagation-based method.

A generalized radial basis function network consisting of (1 + cosh x)-1 as the basis function of the same class as Gaussian functions is investigated in terms of the feasibility of analog-hardware implementation. A simple way of hardware-implementing (1 + cosh x)-1 is proposed to generate the exact input-output response curve on an analog circuit constructed with bipolar transistors. To demonstrate that networks consisting of the basis function proposed actually work, the networks are applied to numerical experiments of forecasting chaotic time series contaminated with observational random noise. Stochastic gradient descent is used as learning rule. The networks are capable of learning and making short-term forecasts about the dynamic behavior of the time series with comparable performance to Gaussian radial basis function networks.

In fully connected Multilayer perceptron (MLP), all the hidden units are activated by samples from the whole input space. For complex problems, due to interference and cross coupling of hidden units' activations, the network needs many hidden units to represent the problem and the error surface becomes highly non-linear. Searching for the minimum is then complex and computationally expensive, and simple gradient descent algorithms usually fail. We propose a network, where the input space is partitioned into local sub-regions. Subsequently, a number of smaller networks are simultaneously trained by overlapping subsets of the input samples. Remarkable improvement of training efficiency as well as generalization performance of this combined network are observed through various simulations.

Deterministic nonlinear prediction is applied to both artificial and real time series data in order to investigate orbital-instabilities, short-term predictabilities and long-term unpredictabilities, which are important characteristics of deterministic chaos. As an example of artificial data, bimodal maps of chaotic neuron models are approximated by radial basis function networks, and the approximation abilities are evaluated by applying deterministic nonlinear prediction, estimating Lyapunov exponents and reconstructing bifurcation diagrams of chaotic neuron models. The functional approximation is also applied to squid giant axon response as an example of real data. Two metnods, the standard and smoothing interpolation, are adopted to construct radial basis function networks; while the former is the conventional method that reproduces data points strictly, the latter considers both faithfulness and smoothness of interpolation which is suitable under existence of noise. In order to take a balance between faithfulness and smoothness of interpolation, cross validation is applied to obtain an optimal one. As a result, it is confirmed that by the smoothing interpolation prediction performances are very high and estimated Lyapunov exponents are very similar to actual ones, even though in the case of periodic responses. Moreover, it is confirmed that reconstructed bifurcation diagrams are very similar to the original ones.