Unlike most conventional techniques with static model assumption, this paper aims to estimate the time-varying model parameters and identify significant genes involved at different timepoints from time course gene microarray data. We first formulate the parameter identification problem as a new maximum a posteriori probability estimation problem so that prior information can be incorporated as regularization terms to reduce the large estimation variance of the high dimensional estimation problem. Under this framework, sparsity and temporal consistency of the model parameters are imposed using L1-regularization and novel continuity constraints, respectively. The resulting problem is solved using the L-BFGS method with the initial guess obtained from the partial least squares method. A novel forward validation measure is also proposed for the selection of regularization parameters, based on both forward and current prediction errors. The proposed method is evaluated using a synthetic benchmark testing data and a publicly available yeast Saccharomyces cerevisiae cell cycle microarray data. For the latter particularly, a number of significant genes identified at different timepoints are found to be biological significant according to previous findings in biological experiments. These suggest that the proposed approach may serve as a valuable tool for inferring time-varying gene regulatory networks in biological studies.

This paper proposes a new visual object tracking algorithm using a novel Bayesian Kalman filter (BKF) with simplified Gaussian mixture (BKF-SGM). The new BKF-SGM employs a GM representation of the state and noise densities and a novel direct density simplifying algorithm for avoiding the exponential complexity growth of conventional KFs using GM. Together with an improved mean shift (MS) algorithm, a new BKF-SGM with improved MS (BKF-SGM-IMS) algorithm with more robust tracking performance is also proposed. Experimental results show that our method can successfully handle complex scenarios with good performance and low arithmetic complexity.

This paper proposes a new variable regularized QR decompPosition (QRD)-based recursive least M-estimate (VR-QRRLM) adaptive filter and studies its convergence performance and acoustic applications. Firstly, variableL2regularization is introduced to an efficient QRD-based implementation of the conventional RLM algorithm to reduce its variance and improve the numerical stability. Difference equations describing the convergence behavior of this algorithm in Gaussian inputs and additive contaminated Gaussian noises are derived, from which new expressions for the steady-state excess mean square error (EMSE) are obtained. They suggest that regularization can help to reduce the variance, especially when the input covariance matrix is ill-conditioned due to lacking of excitation, with slightly increased bias. Moreover, the advantage of the M-estimation algorithm over its least squares counterpart is analytically quantified. For white Gaussian inputs, a new formula for selecting the regularization parameter is derived from the MSE analysis, which leads to the proposed VR-QRRLM algorithm. Its application to acoustic path identification and active noise control (ANC) problems is then studied where a new filtered-x (FX) VR-QRRLM ANC algorithm is derived. Moreover, the performance of this new ANC algorithm under impulsive noises and regularization can be characterized by the proposed theoretical analysis. Simulation results show that the VR-QRRLM-based algorithms considerably outperform the traditional algorithms when the input signal level is low or in the presence of impulsive noises and the theoretical predictions are in good agreement with simulation results.

This paper proposes a new state-regularized (SR) and QR decomposition based recursive least squares (QRRLS) algorithm with variable forgetting factor (VFF) for recursive coefficient estimation of time-varying autoregressive (AR) models. It employs the estimated coefficients as prior information to minimize the exponentially weighted observation error, which leads to reduced variance and bias over traditional regularized RLS algorithm. It also increases the tracking speed by introducing a new measure of convergence status to control the FF. Simulations using synthetic and real speech signals show that the proposed method has improved tracking performance and reduced estimation error variance than conventional TVAR modeling methods during rapid changing of AR coefficients.

This paper addresses the problem of beamforming for antenna arrays in the presence of mismatches between the true and nominal steering vectors. A new method for robust beamforming is proposed by minimizing the array output power while controlling the array mainlobe response. Due to the presence of the non-convex response constraints, a new approach based on iteratively linearizing the non-convex constraints is proposed to reformulate the non-convex problem to a series of second-order cone programming (SOCP) subproblems, each of which can be optimally solved by well-established convex optimization techniques. Simulation results show that the proposed method offers better performance than conventional methods tested.

The Logistic Principal Component Regression (LPCR) has found many applications in classification of high-dimensional data, such as tumor classification using microarray data. However, when the measurements are contaminated and/or the observations are mislabeled, the performance of the LPCR will be significantly degraded. In this paper, we propose a new robust LPCR based on M-estimation, which constitutes a versatile framework to reduce the sensitivity of the estimators to outliers. In particular, robust detection rules are used to first remove the contaminated measurements and then a modified Huber function is used to further remove the contributions of the mislabeled observations. Experimental results show that the proposed method generally outperforms the conventional LPCR under the presence of outliers, while maintaining a performance comparable to that obtained under normal condition.

This paper proposes a new method for preliminary identification of gene regulatory networks (GRNs) from gene microarray cancer databased on ridge partial least squares (RPLS) with recursive feature elimination (RFE) and novel Brier and occurrence probability measures. It facilitates the preliminary identification of meaningful pathways and genes for a specific disease, rather than focusing on selecting a small set of genes for classification purposes as in conventional studies. First, RFE and a novel Brier error measure are incorporated in RPLS to reduce the estimation variance using a two-nested cross validation (CV) approach. Second, novel Brier and occurrence probability-based measures are employed in ranking genes across different CV subsamples. It helps to detect different GRNs from correlated genes which consistently appear in the ranking lists. Therefore, unlike most conventional approaches that emphasize the best classification using a small gene set, the proposed approach is able to simultaneously offer good classification accuracy and identify a more comprehensive set of genes and their associated GRNs. Experimental results on the analysis of three publicly available cancer data sets, namely leukemia, colon, and prostate, show that very stable gene sets from different but relevant GRNs can be identified, and most of them are found to be of biological significance according to previous findings in biological experiments. These suggest that the proposed approach may serve as a useful tool for preliminary identification of genes and their associated GRNs of a particular disease for further biological studies using microarray or similar data.

The transform domain normalized least mean squares (TDNLMS) algorithm is an efficient adaptive algorithm, which offers fast convergence speed with a reasonably low arithmetic complexity. However, its convergence speed is usually limited by the fixed step-size so as to achieve a low desired misadjustment. In this paper a new switch-mode noise-constrained TDNLMS (SNC-TDNLMS) algorithm is proposed. It employs a maximum step-size mode in initial convergence and a noise-constrained mode afterwards to improve the convergence speed and steady state performance. The mean and mean square convergence behaviors of the proposed algorithm are studied to characterize its convergence condition and steady-state excess mean square error (EMSE). Based on the theoretical results, an automatic threshold selection scheme for mode switching is developed. Computer simulations are conducted to show the effectiveness of the proposed algorithm and verify the theoretical results.

This paper introduces two new time-frequency analysis methods originated from the minimum variance spectral estimation (MVSE) for nonstationary time-series. First, a windowed MVSE (WMVSE) extends the conventional MVSE by windowing the observation data to obtain a time-frequency distribution for the time-series. Moreover, the window lengths are selected adaptively by the intersection of confidence intervals (ICI) rule to improve the time-frequency resolution. Secondly, a new recursive MVSE (RMVSE) is developed to process the input samples recursively at a lower arithmetic complexity for online time-frequency analysis. Simulation results show that the proposed WMVSE with adaptive windows offers better frequency resolutions than the Fourier-transformed-based time-frequency distributions, and the RMVSE has a good performance when tracking sinusoidal signals

This paper studies the time-frequency analysis of trunk response based on surface electromyography (EMG) under an experimental protocol of sudden load release. Due to difficulties in feature extraction of surface EMG in short-time muscular reflex using conventional time-frequency analysis algorithms, a novel method called adaptive Lomb periodogram (ALP) is employed to improve the time and frequency resolutions by adaptively selecting the window sizes. Experimental results demonstrate the improved time-frequency resolution of the ALP in analyzing the EMG signals compared with conventional methods using scalogram. The findings of this study would provide important information in devising objective and quantitative protocol for neuromuscular function assessment, which are applicable to rehabilitation of low back pain patients, motor control and training, elderly fall prevention and ergonomic studies.

This paper proposes two new methods for optimizing hardware resources in finite wordlength implementation of multiple-output (MO) linear time invariant systems. The hardware complexity is measured by the exact internal wordlength used for each intermediate data. The first method relaxes the wordlength from integer to real-value and formulates the design problem as a geometric programming, from which an optimal solution of the relaxed problem can be determined. The second method is based on a discrete optimization method called the marginal analysis method, and it yields the desired wordlengths in integer values. By combining these two methods, a hybrid method is also proposed, which is found to be very effective for large scale MO systems. Design example shows that the proposed algorithms offer better results and a lower design complexity than conventional methods

This paper proposes a new design method for a class of two-channel 2D non-separable perfect reconstruction (PR) filter banks (FBs) using the multiplet FBs. 1D multiplet FBs are PR FBs that can be obtained by frequency transformation of a prototype PR FB in the conventional lifting structure so that a better frequency characteristics can be obtained and varied online to process different signals. By employing the 1D to 2D transformation of Phoong et al., new 2D PR multiplet FBs with quincunx, hourglass, and parallelogram spectral support are obtained. These nonseparable multiplet FBs can be cascaded to realize new PR directional FB for image processing and motion analysis. The design procedure is very general and it can be applied to both linear-phase and low-delay 2D FBs. Design examples are given to demonstrate the usefulness of the proposed method

Variable digital filters (VDFs) are useful to the implementation of digital receivers because its frequency characteristics such as fractional delays and cutoff frequencies can be varied online. It is shown that the optimal minimax design of VDFs with passband linear-phase can be formulated and solved as a semi-definite programming (SDP) problem, which is a powerful convex optimization method. In addition, other objective functions, such as least squares, and linear and convex quadratic inequality constraints can readily be incorporated. Design examples using a variable fractional delay (VFD) and a variable cutoff frequency (VCF) FIR filters are given to demonstrate the effectiveness of the proposed approach.