Lihua Fu

Sparse RBF Networks with Multi-kernels

While the conventional standard radial basis function (RBF) networks are based on a single kernel, in practice, it is often desirable to base the networks on combinations of multiple kernels. In this paper, a multi-kernel function is introduced by combining several kernel functions linearly. A novel RBF network with the multi-kernel is constructed to obtain a parsimonious and flexible regression model. The unknown centres of the multi-kernels are determined by an improved k-means clustering algorithm. And orthogonal least squares (OLS) algorithm is used to determine the remaining parameters. The complexity of the newly proposed algorithm is also analyzed. It is demonstrated that the new network can lead to a more parsimonious model with much better generalization property compared with the traditional RBF networks with a single kernel.

Harmonic retrieval in complex noises based on wavelet transform

A novel approach for frequency estimation of one-dimensional harmonics in multiplicative and additive noises is presented. To overcome the resolution limitation inherent to the traditional Fourier-based algorithms, a wavelet transform is utilized. In this new approach, we use a wavelet mother function with a tunable parameter, which is constructed by modulating a window function. For a given harmonic retrieval problem, the tunable parameter can be adaptively adjusted to achieve a good performance. Some numerical experiments are included to illustrate the merits of this new approach.

Improved Orthogonal Least-Squares Regression With Tunable Kernels Using a Tree Structure Search Algorithm

Orthogonal least-squares (OLS) regression with tunable kernels has been recently introduced, in which a greedy scheme is utilized to tune the parameters of each individual regressor term by term using a global search algorithm. To improve the performance of the greedy-scheme-based OLS algorithm, a tree structure search algorithm is constructed. At each regressor stage, this proposed OLS algorithm is realized by keeping multiple best regressors rather than using the optimal one only. Numerical results show that this new scheme is capable of producing a much sparser regression model with better generalization than the conventional approaches.

Tree Based Orthogonal Least Squares Regression with Repeated Weighted Boosting Search

Orthogonal Least Squares Regression (OLSR) selects each regressor by repeated weighted boosting search (RWBS). This kind of OLSR is known to be capable of producing a much sparser model than many other kernel methods. With the aid of tree structure search, this paper is to construct an even sparser regression model in the framework of OLSR with RWBS. When RWBS being used to solve the optimization at each regression stage, OLSR is extended by keeping the k ( k >1)excellent regressors, which minimize the modeling MSE, rather than only choose the best one at each iteration. In this way, the next regressor will be searched in k subspaces instead of in only one subspace as the conventional method. Furthermore we propose a subtree search to decrease experimental time complexity, by specifying the total number of children in every tree depth. The new schemes are shown to outperform the traditional method in the applications, such as component detection, sparse representation for ECG signal and 2-d time series modeling. Besides, experimental results also indicate that subtree based algorithm is with much lower time complexity than tree based one.

Robust Frequency Estimation of Multi-sinusoidal Signals Using Orthogonal Matching Pursuit with Weak Derivatives Criterion

In this paper, the weak derivatives (WD) criterion is introduced to solve the frequency estimation problem of multi-sinusoidal signals corrupted by noises. The problem is therefore modeled as a new least squares optimization task combined with WD. To overcome the potential basis mismatch effect caused by discretization of the frequency parameters, a modified orthogonal matching pursuit algorithm is proposed to solve the optimization problem by coupling it with a novel multi-grid dictionary training strategy. The proposed algorithm is validated on a set of simulated datasets with white noise and stationary colored noise. The comprehensive simulation studies show that the proposed algorithm can achieve more accurate and robust estimation than state-of-the-art algorithms.

A Computationally Efficient Iterative Algorithm for Estimating the Parameter of Chirp Signal Model

The parameter estimation of Chirp signal model in additive noises when all the noises are independently and identically distributed (i.i.d.) has been considered. A novel iterative algorithm is proposed to estimate the frequency rate of the considered model by constructing the iterative statistics with one-lag and multilag differential signals. It is observed that the estimator for the iterative algorithm is consistent and works quite well in terms of biases and mean squared errors. Moreover, the convergence rate of the estimator is improved from of the initial estimator to for one-lag differential signal condition and from of the initial estimator to for multilag differential signal condition, respectively, by only three iterations. The range of the lag is discussed and the optimal lag is obtained for the multilag differential signal condition when the lag is of order . The estimator of frequency rate with optimal lag is very close to Cramer-Rao lower bound (CRLB) as well as the asymptotic variance of least-squares estimator (LSE) at moderate signal-to-noise ratio (SNR). Finally, simulation experiments are performed to verify the effectiveness of the algorithm.

Harmonic Retrieval in Complex Noise Based on Group Delay

Group delay (GD), the negative derivative of Fourier Transform phase, is regarded as a good tool for spectral estimation in additive noise, for its sharp peak and high resolution. However, as far, GD has not been utilized in the case involving complex noises. In this paper, a novel GD is proposed to the time-varying cumulants of harmonics in complex noises, termed as CGD. A simple and practical algorithm is also derived. Numerical results show that, for the problems in complex noises, the new approach outperforms some traditional methods greatly.

Wavelet-based Approach for Frequency Estimation in Complex Noises

This paper discusses the problem of frequency estimation of one-dimensional harmonics in multiplicative and additive noises. To alleviate the resolution limitation of the traditional Fourier-based algorithms, we introduce a novel wavelet based approach to harmonic retrieval. A wavelet mother function with tunable parameter is constructed by modulating a window function, which makes it easier to get the good performance for the given harmonic retrieval problems by tuning the parameter. Simulations performed on synthetic signals confirmed the gain in performance of the proposed method

Harmonic Retrieval Based on LS-SVM with Wavelet Kernel

In this paper, a novel harmonic retrieval scheme is proposed, which is based on least squares support vector machines (LS-SVM). We consider harmonic signals corrupted by additive noises. The harmonic model is expended by wavelet series, and the corresponding parameters are estimated by weighted LS-SVM approach. Wavelet kernel is adopted to enhance the resolution. Simulations performed on synthetic signals show some merits of the proposed method