A Novel Method for Fast Change-Point Detection on Simulated Time Series and Electrocardiogram Data

Although Kolmogorov-Smirnov (KS) statistic is a widely used method, some weaknesses exist in investigating abrupt Change Point (CP) problems, e.g. it is time-consuming and invalid sometimes. To detect abrupt change from time series fast, a novel method is proposed based on Haar Wavelet (HW) and KS statistic (HWKS). First, the two Binary Search Trees (BSTs), termed TcA and TcD, are constructed by multi-level HW from a diagnosed time series; the framework of HWKS method is implemented by introducing a modified KS statistic and two search rules based on the two BSTs; and then fast CP detection is implemented by two HWKS-based algorithms. Second, the performance of HWKS is evaluated by simulated time series dataset. The simulations show that HWKS is faster, more sensitive and efficient than KS, HW, and T methods. Last, HWKS is applied to analyze the electrocardiogram (ECG) time series, the experiment results show that the proposed method can find abrupt change from ECG segment with maximal data fluctuation more quickly and efficiently, and it is very helpful to inspect and diagnose the different state of health from a patient''s ECG signal.     

A Multivariate Procedure for Comparing Mean Vectors for Populations with Unequal Regression Coefficient and Residual Covariance Matrices

In fisheries research there is a need to compare vectors of means of continuous random response variables adjusted for concomitant variations of covariables for populations that have unequal regression coefficient and residual covariance matrices. A multivariate procedure that provides an extended comparison of vectors of adjusted means is presented. An example is presented using a real data set. The procedure is quite general and applicable to many other fields of research.     

A Four-Stage Hybrid Model for Hydrological Time Series Forecasting

Hydrological time series forecasting remains a difficult task due to its complicated nonlinear, non-stationary and multi-scale characteristics. To solve this difficulty and improve the prediction accuracy, a novel four-stage hybrid model is proposed for hydrological time series forecasting based on the principle of ‘denoising, decomposition and ensemble’. The proposed model has four stages, i.e., denoising, decomposition, components prediction and ensemble. In the denoising stage, the empirical mode decomposition (EMD) method is utilized to reduce the noises in the hydrological time series. Then, an improved method of EMD, the ensemble empirical mode decomposition (EEMD), is applied to decompose the denoised series into a number of intrinsic mode function (IMF) components and one residual component. Next, the radial basis function neural network (RBFNN) is adopted to predict the trend of all of the components obtained in the decomposition stage. In the final ensemble prediction stage, the forecasting results of all of the IMF and residual components obtained in the third stage are combined to generate the final prediction results, using a linear neural network (LNN) model. For illustration and verification, six hydrological cases with different characteristics are used to test the effectiveness of the proposed model. The proposed hybrid model performs better than conventional single models, the hybrid models without denoising or decomposition and the hybrid models based on other methods, such as the wavelet analysis (WA)-based hybrid models. In addition, the denoising and decomposition strategies decrease the complexity of the series and reduce the difficulties of the forecasting. With its effective denoising and accurate decomposition ability, high prediction precision and wide applicability, the new model is very promising for complex time series forecasting. This new forecast model is an extension of nonlinear prediction models.     

A Kernel-Based Multivariate Feature Selection Method for Microarray Data Classification

High dimensionality and small sample sizes, and their inherent risk of overfitting, pose great challenges for constructing efficient classifiers in microarray data classification. Therefore a feature selection technique should be conducted prior to data classification to enhance prediction performance. In general, filter methods can be considered as principal or auxiliary selection mechanism because of their simplicity, scalability, and low computational complexity. However, a series of trivial examples show that filter methods result in less accurate performance because they ignore the dependencies of features. Although few publications have devoted their attention to reveal the relationship of features by multivariate-based methods, these methods describe relationships among features only by linear methods. While simple linear combination relationship restrict the improvement in performance. In this paper, we used kernel method to discover inherent nonlinear correlations among features as well as between feature and target. Moreover, the number of orthogonal components was determined by kernel Fishers linear discriminant analysis (FLDA) in a self-adaptive manner rather than by manual parameter settings. In order to reveal the effectiveness of our method we performed several experiments and compared the results between our method and other competitive multivariate-based features selectors. In our comparison, we used two classifiers (support vector machine, -nearest neighbor) on two group datasets, namely two-class and multi-class datasets. Experimental results demonstrate that the performance of our method is better than others, especially on three hard-classify datasets, namely Wang''s Breast Cancer, Gordon''s Lung Adenocarcinoma and Pomeroy''s Medulloblastoma.     

A Conversion Formula for Comparing Pulse Oximeter Desaturation Rates Obtained with Different Averaging Times

Objective

The number of desaturations determined in recordings of pulse oximeter saturation (SpO₂) primarily depends on the time over which values are averaged. As the averaging time in pulse oximeters is not standardized, it varies considerably between centers. To make SpO₂ data comparable, it is thus desirable to have a formula that allows conversion between desaturation rates obtained using different averaging times for various desaturation levels and minimal durations.

Methods

Oxygen saturation was measured for 170 hours in 12 preterm infants with a mean number of 65 desaturations <90% per hour of arbitrary duration by using a pulse oximeter in a 2–4 s averaging mode. Using 7 different averaging times between 3 and 16 seconds, the raw red-to-infrared data were reprocessed to determine the number of desaturations (D). The whole procedure was carried out for 7 different minimal desaturation durations (≥1, ≥5, ≥10, ≥15, ≥20, ≥25, ≥30 s) below SpO₂ threshold values of 80%, 85% or 90% to finally reach a conversion formula. The formula was validated by splitting the infants into two groups of six children each and using one group each as a training set and the other one as a test set.

Results

Based on the linear relationship found between the logarithm of the desaturation rate and the logarithm of the averaging time, the conversion formula is: D₂ = D₁ (T₂/T₁)^c, where D₂ is the desaturation rate for the desired averaging time T₂, and D₁ is the desaturation rate for the original averaging time T₁, with the exponent c depending on the desaturation threshold and the minimal desaturation duration. The median error when applying this formula was 2.6%.

Conclusion

This formula enables the conversion of desaturation rates between different averaging times for various desaturation thresholds and minimal desaturation durations.     

Comparing Trials with Multiple Outcomes: The Multivariate One-Sided Hypothesis with Unknown Covariances

The paper deals with a problem arising for tests in clinical trials. The outcomes of a standard and a new treatment to be compared are multivariate normally distributed with common but unknown covariance matrix. Under the null hypothesis the means of the outcomes are equal, under the alternative the new treatment is assumed to be superior, i.e. the means are larger without further quantification. For known covariance matrix there is a variety of tests for this problem. Some of these procedures can be extended to the case of unknown covariances if one is willing to accept a bias. There is, however, also an efficient unbiased test. The paper contains some numerical comparisons of these different procedures and takes a look on the minimax properties of the unbiased test.     

A Concordance Method For Analyzing Categorical Time Series. An Application For The Search of Periodicities

A simple method for searching for periods in biological series is proposed. Because it is based on an auto-comparison of the observations within a series we call it the concordance method. It requires few theoritical assumptions. In fact, even the ever present stationarity condition is not used. The method is compared with competing methods based on the khi-square periodogram. It is shown that the concordance method is much better for analyzing multimodal and noisy series. Rhythms presenting simultaneously circadian and ultradian components can also be analyzed with this method.     

A Concordance Method For Analyzing Categorical Time Series. An Application For The Search of Periodicities

A simple method for searching for periods in biological series is proposed. Because it is based on an auto-comparison of the observations within a series we call it the concordance method. It requires few theoritical assumptions. In fact, even the ever present stationarity condition is not used. The method is compared with competing methods based on the khi-square periodogram. It is shown that the concordance method is much better for analyzing multimodal and noisy series. Rhythms presenting simultaneously circadian and ultradian components can also be analyzed with this method.     

A Generalized Interrupted Time Series Model for Assessing Complex Health Care Interventions

Statistics in Biosciences - Assessing the impact of complex interventions on measurable health outcomes is a growing concern in health care and health policy. Interrupted time series (ITS) designs...     

A Platform for Processing Expression of Short Time Series (PESTS)

Background  

Time course microarray profiles examine the expression of genes over a time domain. They are necessary in order to determine the complete set of genes that are dynamically expressed under given conditions, and to determine the interaction between these genes. Because of cost and resource issues, most time series datasets contain less than 9 points and there are few tools available geared towards the analysis of this type of data.     

一类灰色项时间序列模型及其应用

利用灰色系统理论与时间序列分析,提出了带灰色项的时间序列模型,对这类模型进行了分析,给出了建模与预报方法,并将其应用于我国农业产值问题的预报与研究之中,模型的正确性得到了检验．     

Equidirection: A Measure of Similarity Among Time Series

In the present paper we investigate the concept of equidirection, i.e. similarity in the direction of variation, or parallelism in the broader sense, among m (m ≧ 2) times series, especially under the assumption that the time series are realizations of processes with independent increments. However, the processes need not be stationary. Furthermore, the probabilities for the direction of variation may be unstable, in which case only upper and lower bounds are known. A measure based on the concept of equidirection was developed that enables identification of clusters of similar time series and analysis of relationships among variables.     

A Robust Measurement of Correlation in Dependent Time Series

A special problem in behavioral sciences are time series where the data points of one series are dependent on the just prior values of the other series. The data structure may additionally exhibit an interdependence between the variables that changes over time. Pfanzagl's T provides a robust test of trend independence between such data sets. At the same time the applicability of Pearson's r can be extended by using the statistical considerations for T. For this purpose, the time series are transformed into binary series, consisting either of the values 1 or 0. These series may show distinct trend patterns of consecutive data points with the value 1 or with the value 0. Data points belonging to the same trend pattern are regarded as cohering values for any further mathematical operation applied. Based on the trend identifcation the T-value is derived, providing information on the coherent development of trend patterns in the two series. Additionally Pearson's r together with a modified sampling theory offers a standard measure of linear association between the time series. The procedures are described and a computer program is provided, combining Pfanzagl's T and Pearson's r with a bootstrap procedure for the statistical evaluation of the correlation coefficients.     

A Simple Approach for the Computation of Multiple Periodicities in Biological Time Series

We have described a simple approach for the analysis and isolation of multiple periodicities from a biological time series. For the estimation of the periodicities, we used simulated data and data from ongoing experiments in our laboratory. Two time series were simulated, one which consisted of only white noise and the other consisted white noise along with periodicities of 6, 11, 17 and 23 h, to demonstrate that our method can successfully isolate multiple patterns in a time series. Our method of analysis is objective, simple, flexible and adaptive since it distinctly delineates the individual contribution from an overlap of multiple periodicities. The key features of our method are: (i) identification of a reliable phase reference point, (ii) scanning the time series using a moving window in increments, (iii) use of Siegel's modification of Fisher's method to detect significant periodicit(y)ies in the time series. The use of window sizes of increasing length to examine the time series elegantly reduces noise while identifying periodicities that are otherwise not apparent. Finally, the periodogram can be smoothed in order to normalize the contribution by attendant frequency components within the waveform. A minimum critical value for relative contribution of various frequencies was calculated to delineate the periodicities that contributed significantly to the time series. We executed this method of time series analysis using MS Excel and C.     

A Simple Approach for the Computation of Multiple Periodicities in Biological Time Series

We have described a simple approach for the analysis and isolation of multiple periodicities from a biological time series. For the estimation of the periodicities, we used simulated data and data from ongoing experiments in our laboratory. Two time series were simulated, one which consisted of only white noise and the other consisted white noise along with periodicities of 6, 11, 17 and 23 h, to demonstrate that our method can successfully isolate multiple patterns in a time series. Our method of analysis is objective, simple, flexible and adaptive since it distinctly delineates the individual contribution from an overlap of multiple periodicities. The key features of our method are: (i) identification of a reliable phase reference point, (ii) scanning the time series using a moving window in increments, (iii) use of Siegel's modification of Fisher's method to detect significant periodicit(y)ies in the time series. The use of window sizes of increasing length to examine the time series elegantly reduces noise while identifying periodicities that are otherwise not apparent. Finally, the periodogram can be smoothed in order to normalize the contribution by attendant frequency components within the waveform. A minimum critical value for relative contribution of various frequencies was calculated to delineate the periodicities that contributed significantly to the time series. We executed this method of time series analysis using MS Excel and C.     

时间序列数据记忆性的判别方法

目的：发展时间序列数据记忆的判别方法并用于离子通道数据记忆性的判别研究。方法：应用Pearson检验与曲线拟合的方法,识别数据的记忆性。结果：得到数据记忆性的判别方法,讨论了离子通道记忆性。结论：Pearson检验与曲线拟合法简单易用,离子通道具有记忆性。