Chunqi Chang

A matrix-pencil approach to blind separation of colored nonstationary signals

For many signal sources such as speech with distinct, nonwhite power spectral densities, second-order statistics of the received signal mixture can be exploited for signal separation. Without knowledge of the noise correlation matrix, we propose a simple and yet effective signal extraction method for signal source separation under unknown temporally white noise. This new and unbiased signal extractor is derived from the matrix pencil formed between output autocorrelation matrices at different delays. Based on the matrix pencil, an ESPRIT-type algorithm is derived to get an optimal solution in the least square sense. Our method is well suited for systems with colored sensor noises and for nonstationary signals.

Fast network component analysis (FastNCA) for gene regulatory network reconstruction from microarray data

MOTIVATION Recently developed network component analysis (NCA) approach is promising for gene regulatory network reconstruction from microarray data. The existing NCA algorithm is an iterative method which has two potential limitations: computational instability and multiple local solutions. The subsequently developed NCA-r algorithm with Tikhonov regularization can help solve the first issue but cannot completely handle the second one. Here we develop a novel Fast Network Component Analysis (FastNCA) algorithm which has an analytical solution that is much faster and does not have the above limitations. RESULTS Firstly FastNCA is compared to NCA and NCA-r using synthetic data. The reconstruction of FastNCA is more accurate than that of NCA-r and comparable to that of properly converged NCA. FastNCA is not sensitive to the correlation among the input signals, while its performance does degrade a little but not as dramatically as that of NCA. Like NCA, FastNCA is not very sensitive to small inaccuracies in a priori information on the network topology. FastNCA is about several tens times faster than NCA and several hundreds times faster than NCA-r. Then, the method is applied to real yeast cell-cycle microarray data. The activities of the estimated cell-cycle regulators by FastNCA and NCA-r are compared to the semi-quantitative results obtained independently by Lee et al. (2002). It is shown here that there is a greater agreement between the results of FastNCA and Lees, which is represented by the ratio 23/33, than that between the results of NCA-r and Lees, which is 14/33. AVAILABILITY Software and supplementary materials are available from http://www.eee.hku.hk/~cqchang/FastNCA.htm

Order Statistics Correlation Coefficient as a Novel Association Measurement With Applications to Biosignal Analysis

In this paper, we propose a novel correlation coefficient based on order statistics and rearrangement inequality. The proposed coefficient represents a compromise between the Pearsons linear coefficient and the two rank-based coefficients, namely Spearmans rho and Kendalls tau. Theoretical derivations show that our coefficient possesses the same basic properties as the three classical coefficients. Experimental studies based on four models and six biosignals show that our coefficient performs better than the two rank-based coefficients when measuring linear associations; whereas it is well able to detect monotone nonlinear associations like the two rank-based coefficients. Extensive statistical analyses also suggest that our new coefficient has superior anti-noise robustness, small biasedness, high sensitivity to changes in association, accurate time-delay detection ability, fast computational speed, and robustness under monotone nonlinear transformations.

Asymptotic Properties of Order Statistics Correlation Coefficient in the Normal Cases

We have previously proposed a novel order statistics correlation coefficient (OSCC), which possesses some desirable advantages when measuring linear and monotone nonlinear associations between two signals. However, the understanding of this new coefficient is far from complete. A lot of theoretical questions, such as the expressions of its distribution and moments, remain to be addressed. Motivated by this unsatisfactory situation, in this paper we prove that for samples drawn from bivariate normal populations, the distribution of OSCC is asymptotically equivalent to that of the Pearsons product moment correlation coefficient (PPMCC). We also reveal its close relationships with the other two coefficients, namely, Gini correlation (GC) and Spearmans rho (SR). Monte Carlo simulation results agree with the theoretical findings.

Real-time data-reusing adaptive learning of a radial basis function network for tracking evoked potentials

Tracking variations in both the latency and amplitude of evoked potential (EP) is important in quantifying properties of the nervous system. Adaptive filtering is a powerful tool for tracking such variations. In this paper, a data-reusing nonlinear adaptive filtering method, based on a radial basis function network (RBFN), is implemented to estimate EP. The RBFN consists of an input layer of source nodes, a single hidden layer of nonlinear processing units and an output layer of linear weights. It has built-in nonlinear activation functions that allow learning of function mappings. Moreover, it produces satisfactory estimates of signals against a background noise without a priori knowledge of the signal, provided that the signal and noise are independent. In clinical situations where EP responses change rapidly, the convergence rate of the algorithm becomes a critical factor. A carefully designed data-reusing RBFN can accelerate the convergence rate markedly and, thus, enhance its performance. Both theoretical analysis and simulation results support the improved performance of our new algorithm.

Genome-scale cluster analysis of replicated microarrays using shrinkage correlation coefficient

BackgroundCurrently, clustering with some form of correlation coefficient as the gene similarity metric has become a popular method for profiling genomic data. The Pearson correlation coefficient and the standard deviation (SD)-weighted correlation coefficient are the two most widely-used correlations as the similarity metrics in clustering microarray data. However, these two correlations are not optimal for analyzing replicated microarray data generated by most laboratories. An effective correlation coefficient is needed to provide statistically sufficient analysis of replicated microarray data.ResultsIn this study, we describe a novel correlation coefficient, shrinkage correlation coefficient (SCC), that fully exploits the similarity between the replicated microarray experimental samples. The methodology considers both the number of replicates and the variance within each experimental group in clustering expression data, and provides a robust statistical estimation of the error of replicated microarray data. The value of SCC is revealed by its comparison with two other correlation coefficients that are currently the most widely-used (Pearson correlation coefficient and SD-weighted correlation coefficient) using statistical measures on both synthetic expression data as well as real gene expression data from Saccharomyces cerevisiae. Two leading clustering methods, hierarchical and k-means clustering were applied for the comparison. The comparison indicated that using SCC achieves better clustering performance. Applying SCC-based hierarchical clustering to the replicated microarray data obtained from germinating spores of the fern Ceratopteris richardii, we discovered two clusters of genes with shared expression patterns during spore germination. Functional analysis suggested that some of the genetic mechanisms that control germination in such diverse plant lineages as mosses and angiosperms are also conserved among ferns.ConclusionThis study shows that SCC is an alternative to the Pearson correlation coefficient and the SD-weighted correlation coefficient, and is particularly useful for clustering replicated microarray data. This computational approach should be generally useful for proteomic data or other high-throughput analysis methodology.

A matrix-pencil approach to blind separation of non-white sources in white noise

The problem of blind source separation in additive white noise is an important problem in speech, array and acoustic signal processing. In general this problem requires the use of higher order statistics of the received signals. However for many signal sources, such as speech with distinct non-white power spectral densities, second order statistics of the received signal mixture can be exploited for signal separation. While previous approaches often assume that additive noise is absent or that the noise correlation matrix is known, we propose a simple and yet effective signal extraction method for signal source separation under unknown white noise. This new and unbiased signal extractor is derived from the matrix pencil formed between output auto-correlation matrices at different delays. Simulation examples are presented.

Order Statistic Correlation Coefficient and Its Application to Association Measurement of Biosignals

In this paper we propose a novel and fast nonlinear association measure based on order statistics and rearrangement inequality. We employ one episode of heart signal, one episode of EEG signal and 1000 white Gaussian noises in our study. Extensive statistical analysis are performed based on one linear model and one nonlinear model. Comparative studies with three other prominent methods are presented. Theoretical derivations and experimental results suggest that our new method has small biasedness, high sensitivity to changes in association, fast computational speed, and robustness under monotone nonlinear transformations

Sequential approach to blind source separation using second order statistics

A general result on identifiability for the blind source separation problem, based on second order statistics only, is presented. The separation principle using second order statistics is first proposed. This is followed by a discussion on a number of algorithms to separate the sources one by one.

Linear Precoder Optimization for MIMO Systems with Joint Power Constraints

This paper considers linear precoder optimization problems for multiple-input multiple-output (MIMO) systems. In addition to the conventionally used sum-power constraint, maximum eigenvalue constraint on the precoding matrix is also considered so as to account for power limitations imposed on each antenna by the linearity of its own power amplifier in practical implementations. A framework employing directional derivative is developed to obtain optimal precoder designs for different criteria including maximizing the information rate and minimizing the sum of mean-square error (MSE). It turns out that power allocations in such situations are piecewise linear in sum-power space. The piecewise linear property allows us to generate the entire path of solution through finding out a finite number of breakpoints. A Homotopy-type algorithm is then proposed to obtain the solution for an arbitrary sum-power constraint. The number of breakpoints to be determined in our exact piecewise linear solution is in fact only about two times of the number of transmit antennas, so that our method is super fast and outperforms existing approximate solutions in the literature in both effectiveness and efficiency. Simulated experiments are performed to verify our theoretical analysis.