‡We describe the use of singular value decomposition in transforming genome-wide expression data from genes 3 arrays space to reduced diagonalized ‘‘eigengenes’’ 3 ‘‘eigenarrays’’ space, where the eigengenes (or eigenarrays) are unique orthonormal superpositions of the genes (or arrays). Normalizing the data by filtering out the eigengenes (and eigenarrays) that are inferred to represent noise or experimental artifacts enables meaningful comparison of the expression of different genes across different arrays in different experiments. Sorting the data according to the eigengenes and eigenarrays gives a global picture of the dynamics of gene expression, in which individual genes and arrays appear to be classified into groups of similar regulation and function, or similar cellular state and biological phenotype, respectively. After normalization and sorting, the significant eigengenes and eigenarrays can be associated with observed genome-wide effects of regulators, or with measured samples, in which these regulators are overactive or underactive, respectively.

Singular Value Decomposition for Genome-Wide Expression Data Processing and Modeling

: This thesis applies neural network feature selection techniques to multivariate time series data to improve prediction of a target time series. Two approaches to feature selection are used. First, a subset enumeration method is used to determine which financial indicators are most useful for aiding in prediction of the S&P 500 futures daily price. The candidate indicators evaluated include RSI, Stochastics and several moving averages. Results indicate that the Stochastics and RSI indicators result in better prediction results than the moving averages. The second approach to feature selection is calculation of individual saliency metrics. A new decision boundary-based individual saliency metric, and a classifier independent saliency metric are developed and tested. Ruck's saliency metric, the decision boundary based saliency metric, and the classifier independent saliency metric are compared for a data set consisting of the RSI and Stochastics indicators as well as delayed closing price values. The decision based metric and the Ruck metric results are similar, but the classifier independent metric agrees with neither of the other metrics. The nine most salient features, determined by the decision boundary based metric, are used to train a neural network and the results are presented and compared to other published results. (AN)

/pdf/nonlinear-time-series-analysis-1j3a35n4y3.pdf

Nonlinear Time Series Analysis.

Since the early 1980s, short-term traffic forecasting has been an integral part of most Intelligent Transportation Systems (ITS) research and applications; most effort has gone into developing methodologies that can be used to model traffic characteristics and produce anticipated traffic conditions. Existing literature is voluminous, and has largely used single point data from motorways and has employed univariate mathematical models to predict traffic volumes or travel times. Recent developments in technology and the widespread use of powerful computers and mathematical models allow researchers an unprecedented opportunity to expand horizons and direct work in 10 challenging, yet relatively under researched, directions. It is these existing challenges that we review in this paper and offer suggestions for future work.

Short-term traffic forecasting: Where we are and where we’re going

Part I. Examples and Fundamental Concepts Introduction 1. First examples 2. Equivalence, classification, and invariants 3. Principle classes of asymptotic invariants 4. Statistical behavior of the orbits and introduction to ergodic theory 5. Smooth invariant measures and more examples Part II. Local Analysis and Orbit Growth 6. Local hyperbolic theory and its applications 7. Transversality and genericity 8. Orbit growth arising from topology 9. Variational aspects of dynamics Part III. Low-Dimensional Phenomena 10. Introduction: What is low dimensional dynamics 11. Homeomorphisms of the circle 12. Circle diffeomorphisms 13. Twist maps 14. Flows on surfaces and related dynamical systems 15. Continuous maps of the interval 16. Smooth maps of the interval Part IV. Hyperbolic Dynamical Systems 17. Survey of examples 18. Topological properties of hyperbolic sets 19. Metric structure of hyperbolic sets 20. Equilibrium states and smooth invariant measures Part V. Sopplement and Appendix 21. Dynamical systems with nonuniformly hyperbolic behavior Anatole Katok and Leonardo Mendoza.

Introduction to the Modern Theory of Dynamical Systems: EQUILIBRIUM STATES AND SMOOTH INVARIANT MEASURES

/pdf/analysis-of-observed-chaotic-data-3spe9uweeb.pdf

Analysis of observed chaotic data

In this paper, we present an adaptive measurement to quantify the complexity of time series, called q-sample entropy difference mean ( q SEDiffAve), and apply this method to heart rate time series. It quantifies the structural information of the signals and helps identify different conditions of the heart systems. Experiments show that compared with the traditional sample entropy (SampEn), q SEDiffAve has significant advantages in reflecting the inherent information of sequences. It also reveals that the q SEDiffAve curves of healthy subjects are significantly different from the atrial fibrillation (AF) and congestive heart failure (CHF) groups, because the CHF signals tend to fluctuate between narrow ranges while the atrial fibrillation (AF) signals are random, and the signals of healthy subjects are usually mixed by signals with different dynamic characteristics, showing higher complexity. In addition, the most important parameter in the model, q, can enlarge the differences between q SEDiffAve curves of healthy and pathological states.

A complexity measure for heart rate signals

• We use the MDDM to construct the dependence index (DI) from the perspective of MDC. • The phase space reconstruction is adopted to depict the nonlinear dependency of data. • The DI can recognize and distinguish different complex systems more effectively. • Our method can extract the detailed inner features of different complex data. • The DI is applied to multidimensional scaling and gets good clustering results. For the study of complex systems, the existing correlation measures suffer from deficiencies and may lead to the loss of information and inefficient characterizations of complex systems. We aim to capture detailed dynamical characteristics from complex systems effectively, including periodical features, chaotic features, and mixed features. Our objectives also include discriminating different complex systems and performing clustering of complex data with higher efficiency. So in this paper, we propose the dependence index (DI) based on the martingale difference correlation (MDC), the synchronization index, and the phase space reconstruction. Through simulation experiments, we demonstrate that our proposed method is effective in detecting different and subtle dynamical features, including periodic, chaotic, and mixed behaviors. For applications, we apply our method to analyze real-world data, including heartbeat signals, stock indices, bearing fault data, image outline data, CBF data, and food spectrum data. To achieve our objectives and demonstrate the applicability of our method, the DI is applied to multidimensional scaling (MDS) to cluster reality-based data with better performance when compared with the MDS based on other measures. We affirm that our method can distinguish different complex systems more effectively and obtain detailed information. 

The dependence index based on martingale difference correlation: An efficient tool to distinguish different complex systems

Intelligent detection of rail corrugation using ACMP-based energy entropy and LSSVM

Diversity index based on entropy such as Emlen index ( E I ) is suggested as a highly effective algorithm to detect complexity in nonlinear systems. In this paper, a method considering the amplitude information, called Weighted Emlen index ( W E I ) is proposed to extract the amplitude information and track the signal changes. And then, we expand E I ∕ W E I methods to multiple time scales. Thus, multiscale Emlen index ( M S E I ) and multiscale Weighted Emlen index ( M S W E I ) will be used to discuss the complexity of traffic time series under different scales. Results show that there are differences between the complexity of weekend traffic time series and workday time series, which gives a better classification of traffic systems for making prediction.

Diversity analysis based on ordered patterns

In this paper we pay attention to the preprocessing of time series and its application. We apply Empirical Mode Decomposition (EMD) to decompose three kinds of series into their components in order to study the data and forecast more efficiently. We try to unite EMD analysis and autoregressive integrated moving average processes (ARIMA) into a new forecasting technique which we call EMD-ARIMA. We find that our method is extraordinarily close to the original data.

Pengjian Shang

Papers

A complexity measure for heart rate signals

The dependence index based on martingale difference correlation: An efficient tool to distinguish different complex systems

Intelligent detection of rail corrugation using ACMP-based energy entropy and LSSVM

Diversity analysis based on ordered patterns

Time Series Preprocessing and Forecasting Based on EMD