Weichao Xu

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.

Asymptotic Mean and Variance of Gini Correlation for Bivariate Normal Samples

This paper derives the asymptotic analytical forms of the mean and variance of the Gini correlation (GC) with respect to samples drawn from bivariate normal populations. The asymptotic relative efficiency (ARE) of the Gini correlation to Pearsons product moment correlation coefficient (PPMCC) is investigated under the normal assumptions. To gain further insight into GC, we also compare the Gini correlation to other two closely related correlation coefficients, namely, the order statistics correlation coefficient (OSCC) and Spearmans rho (SR). Theoretical and simulation results suggest that the performance of GC lies in between those of OSCC and SR when estimating the correlation coefficient of the bivariate normal population. The newly found theoretical results along with other desirable properties enable GC to be a useful alternative to the existing coefficients, especially when one wants to make a trade-off between the efficiency and robustness to monotone nonlinearity.

New Bayesian Discriminator for Detection of Atrial Tachyarrhythmias

Background—Accurate, rapid detection of atrial tachyarrhythmias has important implications in the use of implantable devices for treatment of cardiac arrhythmia. Currently available detection algorithms for atrial tachyarrhythmias, which use the single-index method, have limited sensitivity and specificity. Methods and Results—In this study, we evaluated the performance of a new Bayesian discriminator algorithm in the detection of atrial fibrillation (AF), atrial flutter (AFL), and sinus rhythm (SR). Bipolar recording of 364 rhythms (AF=156, AFL=88, SR=120) at the high right atrium were collected from 20 patients who underwent electrophysiological procedures. After initial signal processing, a column vector of 5 features for each rhythm were established, based on the regularity, rate, energy distribution, percent time of quiet interval, and baseline reaching of the rectified autocorrelation coefficient functions. Rhythm identification was obtained by use of Bayes decision rule and assumption of Gaussian distribution. For the new Bayesian discriminator, the overall sensitivity for detection of SR, AF, and AFL was 97%, 97%, and 94%, respectively; and the overall specificity for detection of SR, AF, and AFL was 98%, 98%, and 99%, respectively. The overall accuracy of detection of SR, AF, and AFL was 98%, 97% and 98%, respectively. Furthermore, sensitivity, specificity, and accuracy of this algorithm were not affected by a range of white Gaussian noises with different intensities. Conclusions—This new Bayesian discriminator algorithm, based on Bayes decision of multiple features of atrial electrograms, allows rapid on-line and accurate (98%) detection of AF with robust anti-noise performance.

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

Segmentation-based retrospective shading correction in fluorescence microscopy E. coli images for quantitative analysis

Due to the inherent imperfections in the imaging process, fluorescence microscopy images often suffer from spurious intensity variations, which is usually referred to as intensity inhomogeneity, intensity non uniformity, shading or bias field. In this paper, a retrospective shading correction method for fluorescence microscopy Escherichia coli (E. Coli) images is proposed based on segmentation result. Segmentation and shading correction are coupled together, so we iteratively correct the shading effects based on segmentation result and refine the segmentation by segmenting the image after shading correction. A fluorescence microscopy E. Coli image can be segmented (based on its intensity value) into two classes: the background and the cells, where the intensity variation within each class is close to zero if there is no shading. Therefore, we make use of this characteristics to correct the shading in each iteration. Shading is mathematically modeled as a multiplicative component and an additive noise component. The additive component is removed by a denoising process, and the multiplicative component is estimated using a fast algorithm to minimize the intra-class intensity variation. We tested our method on synthetic images and real fluorescence E.coli images. It works well not only for visual inspection, but also for numerical evaluation. Our proposed method should be useful for further quantitative analysis especially for protein expression value comparison.

Quantifying organization during atrial fibrillation based on order statistics correlation coefficient

Atrial fibrillation (AF) is a type of abnormal heart rhythm exhibiting rapid and irregular patterns. Quantifying the extent of organization (regularity) is of great clinical importance for assessing the effectiveness of antiarrhythmic drugs as well as AF detection. In this paper we propose an organization index (OIX) that quantifies AF organization based on the order statistics correlation coefficient (OSCC) previously developed by the present authors. For comparison, we also construct another similar index (OIP ) based on the classical Pearsonpsilas product-moment correlation coefficient (PPMCC). Statistical evidences suggest that (a) OIX is capable of distinguishing fibrillatory rhythms (AF) from nonfibrillatory rhythms, such as Atrial flutter (AFL); (b) OIX can reflect the effectiveness of adenosine, a drug commonly used during electrophysiological procedures; and (c) OIX performs better than OIP .