Multivariate Dispersion Research Articles

Multivariate hierarchical multiscale fluctuation dispersion entropy: Applications to fault diagnosis of rotating machinery

With a view to completing the fault diagnosis of rotating machinery efficiently and accurately, this paper presents a novel fault diagnosis model that combines multivariate hierarchical multiscale fluctuation dispersion entropy (MHMFDE), multi-cluster feature selection (MCFS) and gray wolf optimization-based kernel extreme learning machine(GWO-KELM). Firstly, MHMFDE is presented to capture the high-dimensional fault features hidden in the attained multichannel vibration signals. Integrating the multiscale entropy-based method and the hierarchical entropy-based method that are currently popular in the domain of fault identification, MHMFDE can simultaneously extract affluent fault features from multivariate vibration signals in-depth as well as overcoming the problem of information loss in the existing single-channel data analysis methods. Afterward, MCFS is used to pick sensitive features from the attained raw fault features to form the sensitive feature vectors, thereby reducing the impact of redundant features. Finally, GWO-KELM is adopted to quantitatively analyze the diagnostic effect. Three examples reveal that the presented approach enjoys excellent performance in the fault diagnosis domain. Especially for the identification of compound faults of rotating machinery, the performance of the presented method is significantly superior to that of existing methods.

Automated classification of fauna in seabed photographs: The impact of training and validation dataset size, with considerations for the class imbalance

Machine learning is rapidly developing as a tool for gathering data from imagery and may be useful in identifying (classifying) visible specimens in large numbers of seabed photographs. Application of an automated classification workflow requires manually identified specimens to be supplied for training and validating the model. These training and validation datasets are generally generated by partitioning the available manual identified specimens; typical ratios of training to validation dataset sizes are 75:25 or 80:20. However, this approach does not facilitate the desired scalability, which would require models to successfully classify specimens in hundreds of thousands to millions of images after training on a relatively small subset of manually identified specimens. A second problem is related to the ‘class imbalance’, where natural community structure means that fewer specimens of rare morphotypes are available for model training. We investigated the impact of independent variation of the training and validation dataset sizes on the performance of a convolutional neural network classifier on benthic invertebrates visible in a very large set of seabed photographs captured by an autonomous underwater vehicle at the Porcupine Abyssal Plain Sustained Observatory. We tested the impact of increasing training dataset size on specimen classification in a single validation dataset, and then tested the impact of increasing validation set size, evaluating ecological metrics in addition to computer vision metrics. Computer vision metrics (recall, precision, F1-score) indicated that classification improved with increasing training dataset size. In terms of ecological metrics, the number of morphotypes recorded increased, while diversity decreased with increasing training dataset size. Variation and bias in diversity metrics decreased with increasing training dataset size. Multivariate dispersion in apparent community composition was reduced, and bias from expert-derived data declined with increasing training dataset size. In contrast, classification success and resulting ecological metrics did not differ significantly with varying validation dataset sizes. Thus, the selection of an appropriate training dataset size is key to ensuring robust automated classifications of benthic invertebrates in seabed photographs, in terms of ecological results, and validation may be conducted on a comparatively small dataset with confidence that similar results will be obtained in a larger production dataset. In addition, our results suggest that automated classification of less common morphotypes may be feasible, providing that the overall training dataset size is sufficiently large. Thus, tactics for reducing class imbalance in the training dataset may produce improvements in the resulting ecological metrics.

On the multivariate progressive control chart for effective monitoring of covariance matrix

AbstractWith the development of modern acquisition techniques, data with several correlated quality characteristics are increasingly accessible. Thus, multivariate control charts can be employed to detect changes in the process. This study proposes two multivariate control charts for monitoring process variability (MPVC) using a progressive approach. First, when the process parameters are known, the performance of the MPVC charts is compared with some multivariate dispersion schemes. The results showed that the proposed MPVC charts outperform their counterparts irrespective of the shifts in the process dispersion. The effects of the Phase I estimated covariance matrix on the efficiency of the MPVC charts were also evaluated. The performances of the proposed methods and their counterparts are evaluated by calculating some useful run length properties. An application of the proposed chart is also considered for the monitoring of a carbon fiber tubing process.

COMPLEXITY ANALYSIS OF TIME SERIES BASED ON GENERALIZED FRACTIONAL ORDER DUAL-EMBEDDED DIMENSIONAL MULTIVARIATE MULTISCALE DISPERSION ENTROPY

Based on the theories of multivariate multiscale dispersion entropy, we propose an improved new model — dual-embedded dimensional multivariate multiscale dispersion entropy (mvMDE), and generalize the new model to fractional order (GmvMDE). The mvMDE and GmvMDE simultaneously consider the cross-correlation between multiple channels, and they provide a dynamic complexity measure for measuring the multivariable data observed in one system. We introduce dual embedded dimensions to construct subsequences, which makes the model more flexible and applicable to a variety of application scenarios. Through empirical analysis of simulated data and stock market data, this paper verifies that both mvMDE and GmvMDE can effectively measure and distinguish the sequence complexity, and GmvMDE can better capture the small evolution of sequences, with higher stability and accuracy. On the basis of mvMDE research, we also propose the multiscale system dispersion entropy (MSDE) and its fractional order form (GMSDE). Using the vector-to-vector distance quantization method, the relationship between individuals in the system can be better extracted, and the systemic complexity of financial portfolio can be measured from the time dimension and the space dimension simultaneously. The empirical analysis based on the data of major industries in Chinese stock market shows that MSDE and GMSDE can accurately capture the structural information in the system and effectively distinguish the complexity of financial portfolios.

Assessment of Outliers and Detection of Artifactual Network Segments Using Univariate and Multivariate Dispersion Entropy on Physiological Signals.

Network physiology has emerged as a promising paradigm for the extraction of clinically relevant information from physiological signals by moving from univariate to multivariate analysis, allowing for the inspection of interdependencies between organ systems. However, for its successful implementation, the disruptive effects of artifactual outliers, which are a common occurrence in physiological recordings, have to be studied, quantified, and addressed. Within the scope of this study, we utilize Dispersion Entropy (DisEn) to initially quantify the capacity of outlier samples to disrupt the values of univariate and multivariate features extracted with DisEn from physiological network segments consisting of synchronised, electroencephalogram, nasal respiratory, blood pressure, and electrocardiogram signals. The DisEn algorithm is selected due to its efficient computation and good performance in the detection of changes in signals for both univariate and multivariate time-series. The extracted features are then utilised for the training and testing of a logistic regression classifier in univariate and multivariate configurations in an effort to partially automate the detection of artifactual network segments. Our results indicate that outlier samples cause significant disruption in the values of extracted features with multivariate features displaying a certain level of robustness based on the number of signals formulating the network segments from which they are extracted. Furthermore, the deployed classifiers achieve noteworthy performance, where the percentage of correct network segment classification surpasses 95% in a number of experimental setups, with the effectiveness of each configuration being affected by the signal in which outliers are located. Finally, due to the increase in the number of features extracted within the framework of network physiology and the observed impact of artifactual samples in the accuracy of their values, the implementation of algorithmic steps capable of effective feature selection is highlighted as an important area for future research.

Multiple analyses redirect management and restoration priorities for a critically endangered ecological community

AbstractAccurately assessing community diversity patterns across distributional ranges is critically important for informed and effective management of ecological communities. Yet, for many wide‐ranging communities diversity patterns across broad ranges are poorly known. We apply a range of analytical approaches to an extensively studied ecological community to determine the relative utility and complementarity of these analytical approaches and their applicability for improved management. White Box Yellow Box Blakely’s Red Gum Woodland (herein abbreviated to BGW) occurs across seven bioregions in New South Wales, eastern Australia. Previous work has suggested either small levels of regional variation in floristic patterns or, contrastingly, up to ~80 variants determined by expert‐driven assessment. We undertook floristic survey and analysed floristic patterns using multivariate dispersion, diversity metrics (alpha (α) diversity, beta (β) diversity, gamma (γ) diversity and zeta (ζ) diversity; including assessments of β turnover and nestedness and higher order ζ diversity). Expert‐derived BGW variants were not clearly related to patterns of floristic variation. In this study, multivariate interactions were critical to identifying patterns of floristic variation. ζ diversity provided insights into bioregional variation not detected via other analytics and was more robust to unbalanced data than β diversity. However, β diversity provided important insights, detecting changing community patterns within a bioregion that would otherwise not be detected and allowing for some comparison of our results with other studies. This study highlights the value of applying multiple analytical approaches to the understanding of floristic patterns. Conservation of floristic diversity in BGW requires protection and management across its range, something which has not previously been adequately addressed.

Local and regional drivers of macrophyte beta diversity in tropical coastal rivers

Studies on beta diversity across different spatial scales can yield insight into the ecological factors that shape communities and the mechanisms of maintenance and loss of diversity. The coastal rivers in southeast Brazil have different lengths and salinity gradients because of variation in coastal plain width and slope. These differences in environmental characteristics promote natural gradients and patterns of macrophyte assemblage variation within and among rivers. To investigate the drivers of macrophyte beta diversity, we recorded the occurrence of species and life forms and collected limnological variables at 100 sampling sites over 8 unconnected rivers that run directly to the sea. We estimated macrophyte beta diversity, and its nestedness and turnover components, within (local scale) and among (regional scale) coastal rivers using traditional metrics (Jaccard dissimilarity matrix) and a metric that accounts for sampling effect (permutational analysis of multivariate dispersions). At each sampling site, we collected variables from water (nutrients, dissolved oxygen, and pH), sediment (nutrients, salinity, and grain type), and channel (width, littoral declivity, distance from river’s mouth, and coastline). For assessment of regional-scale drivers of macrophyte beta diversity, we measured river length and calculated salinity gradient. We evaluated the potential of environmental variables to explain local and regional beta diversity using distance-based redundancy analysis and multiple linear regression. As expected, at the local scale, high species turnover and life-form nestedness were predominantly explained by the rivers’ longitudinal gradients (mainly salinity, P, and channel width). At the regional scale, we found that river length explained life-form nestedness among rivers (small rivers are subsets of the largest rivers); however, neither river length nor salinity gradient explained the high species turnover among rivers. We suggest that dispersal limitation among rivers and historical colonization shaped the species pool in each river resulting in almost completely distinct assemblage compositions. This high turnover at the regional scale suggests that conservation strategies for macrophytes must consider multiple rivers and not only the largest ones. Overall, our results suggest that environmental variation strongly influences macrophyte beta diversity within and among coastal tropical rivers.

The identification of fractional order systems by multiscale multivariate analysis

Abstract The recognition of complex systems plays a vital role in system dynamics. To distinguish chaotic systems and stochastic processes, the complex-entropy causality plane (CECP) was proposed and received considerable attention. However, few methods have been applied to the identification of fractional order chaotic systems. In this paper, we propose multiscale multivariate fractional dispersion entropy (MMFDE) and MMFDE plane to study the structural complexity of multivariate nonlinear systems. Unlike the ordinal pattern in CECP, the dispersion pattern is used in MMFDE plane to solve the computational burden in fractional order systems. Moreover, the fractional order α in MMFDE can be used to adjust the ability of MMFDE plane to distinguish between different systems. Through simulation data, we find that the MMFDE plane can classify not only chaotic systems and stochastic processes but also different fractional order chaotic systems even if adding noise to the signals. It is then applied to financial time series and epileptic EEG recordings. The results show that the MMFDE plane can identify developed and emerging markets. For epileptic EEG recordings, both the EEG subbands and the original data without filtering can be used to distinguish different states of healthy subjects and patients with epilepsy. The coarse-graining process is also discussed to demonstrate the consequences further.

A Refined Composite Multivariate Multiscale Fluctuation Dispersion Entropy and Its Application to Multivariate Signal of Rotating Machinery.

In the fault monitoring of rotating machinery, the vibration signal of the bearing and gear in a complex operating environment has poor stationarity and high noise. How to accurately and efficiently identify various fault categories is a major challenge in rotary fault diagnosis. Most of the existing methods only analyze the single channel vibration signal and do not comprehensively consider the multi-channel vibration signal. Therefore, this paper presents Refined Composite Multivariate Multiscale Fluctuation Dispersion Entropy (RCMMFDE), a method which extracts the recognition information of multi-channel signals with different scale factors, and the refined composite analysis ensures the recognition stability. The simulation results show that this method has the characteristics of low sensitivity to signal length and strong anti-noise ability. At the same time, combined with Joint Mutual Information Maximisation (JMIM) and support vector machine (SVM), RCMMFDE-JMIM-SVM fault diagnosis method has been proposed. This method uses RCMMFDE to extract the state characteristics of the multiple vibration signals of the rotary machine, and then uses the JMIM method to extract the sensitive characteristics. Finally, different states of the rotary machine are classified by SVM. The validity of the method is verified by the composite gear fault data set and bearing fault data set. The diagnostic accuracy of the method is 99.25% and 100.00%. The experimental results show that RCMMFDE-JMIM-SVM can effectively recognize multiple signals.

KINERJA METODE MAHALANOBIS DISTANCE YANG DIBENTUK DARI DUA UKURAN PUSAT DAN DUA DISPERSI MULTIVARIAT (UNTUK UKURAN SIMILARITAS KLASIFIKASI IMAGE)

Distance is a space that connects two points or two locations which can be calculated by length and time. Distance is used to measure the similarity of two objects (for example, an image object). An image can be considered to be similar to another image if the similarity size value is small. On the contrary, if the value of the similarity distance between the training object and the object being tested is large, the object can be said to be different or not. In this design, the image classification of Lakes, Forests and Settlements will be carried out by taking the Color feature using the Color Moment extraction method and the Texture feature using the GLCM (Gray Level Co-occurrence Matrix) extraction method and taking the method of calculating the distance between one data and another data that has High similiarity using the Mahalanobis Distance calculation method with two center sizes namely Mean and Median and three multivariate dispersions, namely the covariance matrix formed by the mean center value, the covariance matrix formed by the value of Median, and the covariance matrix formed by the value of Grand Median. From the research conducted, the performance results that can be considered for use are the Mahalanobis Distance with a median center size with a covariance matrix formed by the Median center value with an accuracy of 69.855% and a covariant matrix formed by the Grand Median center value with an accuracy of 69.565%. In this case the percentage is taken from testing images based on color characteristics using the Color Moment extraction method.

Anuran assemblage changes along small-scale phytophysiognomies in natural Brazilian grasslands

ABSTRACT We studied the species composition of frogs in two phytophysiognomies within Pampa biome (grassland and forest) of a Ramsar site in southern Brazil to assess the distribution of species and dissimilarities in community composition on a small spatial scale. We tested the hypothesis that the vegetation structure and the types of land cover present in each physiognomy influence species distribution and the compositional dissimilarity patterns between locations. We sampled individuals using pitfall traps and active search in the areas around the traps. We evaluated the existence of these differences by using permutational multivariate analysis of variance and multivariate dispersion. We found that the compositional dissimilarity was higher between the sampling sites from different phytophysiognomies than within the same phytophysiognomy. Also, the difference in anuran species composition between the sampling sites within the forest was considerably high. These differences were mainly due to the type of land cover present in each sampled site. Based on our results, we could assume that the phytophysiognomies evaluated here offer quite different colonization opportunities for anurans, especially those related to microhabitat characteristics, such as microclimate variables. Still, the presence of different types of land cover seems to be a decisive factor for the maintenance of some anuran species, since these can serve as an important source for obtaining food resources, in addition to facilitating the dispersion of individuals within and between locals, serve as sites for the regulation of physiological functions and also refuges against predators.

Complexity Analysis of Three-Dimensional Fractional-Order Chaotic System Based on Entropy Theory

Complexity analysis of fractional-order chaotic system is an interesting topic in recent years. How to measure the complexity of fractional-order chaotic system correctly and effectively is the basis of its theoretical analysis and engineering application. In this paper, complexity analysis of three-dimensional fractional-order chaotic system based on multivariate multiscale fuzzy entropy (mvMFE), multivariate multiscale sample entropy (mvMSE) and multivariate multiscale dispersion entropy (mvMDE) respectively is proposed. In the case of single parameter change, different entropy such as mvMFE, mvMSE and mvMDE are used to analyze how complexity varies with parameter. In the case of two parameters change, the change of complexity is analyzed by the chromatomap which takes two parameters as independent variable, and mvMFE, mvMSE, and mvMDE as the dependent variable when the two parameters change simultaneously. Aiming at the performance problem when the complexity of three-dimensional fractional-order chaotic system is analyzed by mvMFE, mvMSE, and mvMDE, the maximum complexity under single parameter and the detection area under two parameters are used as indicators. The result shows that the performance of mvMDE is the best, and the nonlinear term in the mathematical model of fractional-order chaotic system is positively correlated with the complexity of the system. This will provide a new method for measuring the complexity of fractional-order chaotic system, and lay the basis of theoretical analysis and practical application of fractional chaotic system in the fields of image encryption, sound encryption, image compression-encryption technique, and secure communication.

Evaluation of the influence of sowing time on yield and quality of the wheat grain using Multivariate dispersion analysis

The statistical analysis of the results of studies on the effect of sowing time on the yield and quality of winter wheat grains, from the perspective of multivariate variance analysis and multiple comparison of averages, is carried out in the article. It was found that the application of the procedure of a multivariate generalized linear model allows comparing the variants of experiments for all indicators in the aggregate. An important advantage of multiple comparisons over paired Student comparisons is also the ability to isolate homogeneous subgroups of experiments. In this study, post hoc comparisons according to the Tukey criterion were applied, the results of which are presented in tables of homogeneous experiment subgroups and multiple comparisons of indicators’ differences. The distribution of experiment variants by zones of desirability of Harrington functions of yield and generalized indicator of grain quality, depending on shift of sowing time is also presented. It is justified that the maxima of yield and quality of winter wheat grains provide a sowing period of 10 days later than previously recommended for the region. The use of multivariate dispersion analysis and multiple comparison of average increases the reliability of statistical conclusions, allows you to distinguish homogeneous versions of experiments in agricultural production.

Using generalised dissimilarity modelling and targeted field surveys to gap‐fill an ecosystem surveillance network

Abstract Effective ecosystem management requires spatially distributed measurements that are representative of ecological diversity. When considering which sites complement existing conservation or monitoring networks, there are many strategies for optimising ecological coverage in the absence of ground observations. However, such optimisation is often implemented theoretically in conservation prioritisation frameworks and real‐world implementation is rarely assessed, particularly for monitoring networks. We assessed the performance of adding new survey sites informed by predictive modelling in gap‐filling the ecological coverage of the Terrestrial Ecosystem Research Network's (TERN) continental network of ecosystem surveillance plots, Ausplots. We constructed a generalised dissimilarity model (GDM) in which plant species composition in 531 sites was fitted to environmental parameters. We combined predicted nearest‐neighbour ecological distances for locations across Australia with practical considerations to select regions for gap‐filling surveys of 181 new plots across 18 expeditions. We iteratively tracked the reduction in mean nearest‐neighbour distances in GDM space, and increases in the actual sampling of ecological space, using cumulative multivariate dispersion. The generalised dissimilarity model explained 34% of deviance in species compositional turnover as a function of geographic distance, soil P, aridity, actual evapotranspiration and rainfall seasonality, among 17 significant predictors. We targeted identified gap regions in the Australian jurisdictions of Queensland, New South Wales and Western Australia for surveys in addition to opportunistic or project‐based gap‐filling over 2 years. Approximately 20% of the land area of Australia received increased servicing of biological representation, corresponding to a reduction in mean nearest‐neighbour ecological distances from 0.38 to 0.33 in units of compositional dissimilarity. The corresponding increase in sampled ecological space was 172% more than that achieved from the previous 181 plots. Synthesis and applications. Increases in the representation of ecosystems included in surveillance networks can be achieved efficiently using objective methods for site selection and appraisal. Scaling of environmental variables through ecological models supports practical sampling decisions, while optimising putative survey locations via their ecological distance to a nearest neighbour is useful when the aim is to increase inclusion of habitats. Iterations between modelled gaps and field campaigns provide a pragmatic compromise between theoretical optima and real‐world decision‐making.

Native plant turnover and limited exotic spread explain swamp biotic differentiation with urbanization

AbstractQuestionsDoes urbanization promote biotic differentiation or homogenization of swamp plant communities? What is the contribution of natives and exotics to swamp response to urbanization?LocationQuebec City, Canada.MethodsPlant communities of 34 swamps located in low, moderately or highly urbanized landscapes were sampled, and species classified into three exclusive groups: native wetland, native upland and exotic plants. Urbanization’s influence on the richness of each plant group was assessed using mixed models. Between‐site compositional similarities were calculated to identify variations in beta diversity with urbanization level using tests for homogeneity in multivariate dispersion. Beta diversity was further partitioned into species replacement and richness difference for each plant group. Finally, the relationships of ten environmental variables representing soil water saturation and microtopography with plant assemblages were determined by redundancy analysis.ResultsAlthough the richness of exotics increased with urbanization intensity, revealing increasing propagule pressure, it remained six to 27 times lower compared to the richness of natives, which remained stable with urbanization. On the other hand, beta diversity increased with urbanization, with higher dissimilarities in species composition between highly urbanized swamps than between low‐urbanized ones. This pattern resulted from high species replacement among natives, while richness difference mainly contributed to exotic beta diversity. Changes in plant assemblages were mostly associated with bryophyte cover and soil drainage and red mottle size, suggesting that hydrological conditions likely acted as a strong driver of swamp plant community response to urbanization.ConclusionsSwamp plant communities experienced biotic differentiation with increasing urbanization. This differentiation pattern likely was linked to the unpredictable effect of urbanization on hydrological regimes, which promoted high native turnover while limiting exotic spread. Long‐term monitoring is recommended to ensure that exotics do not outcompete natives through time. Designing sustainable cities requires a greater understanding of the multifaceted effect of urbanization on biodiversity.

Stocktaking the environmental coverage of a continental ecosystem observation network

AbstractField‐based sampling of terrestrial habitats at continental scales is required to build ecosystem observation networks. A key challenge for detecting change in ecosystem composition, structure, and function within these observatories is to obtain a representative sample of habitats. Representative sampling across a continent contributes to ecological validity when analyzing spatially distributed data. However, field resources are limited, and actual representativeness may differ markedly from theoretical expectations. Here, we report a post hoc evaluation of the coverage of environmental gradients as a surrogate for ecological representativeness by a continental‐scale survey undertaken by the Australian Terrestrial Ecosystem Research Network (TERN). TERN’s surveillance program maintains a network of ecosystem observation plots initially established in the rangelands through a stratification method (clustering of bioregions by environment) and application of the Ausplots survey methodology. Subsequent site selection comprised gap‐filling and opportunistic sampling. We confirmed that environmental coverage was a good surrogate for ecological representativeness. The cumulative sampling of environments and plant species composition over time were strongly correlated (based on mean multivariate dispersion; r = 0.93). We compared environmental sampling of Ausplots to 100,000 background points and a set of retrospective (virtual) sampling schemes: systematic grid, simple random, stratified random, and generalized random‐tessellation stratified (GRTS). Differences were assessed according to sampling densities along environmental gradients, and multivariate dispersion. Ausplots outperformed systematic grid, simple random, and GRTS in coverage of environmental space (Tukey HSD of mean dispersion, P < 0.001). GRTS site selection obtained similar coverage to Ausplots when employing the same bioregional stratification. Stratification by climatic zones generated the highest environmental coverage (P < 0.001), although resulting sampling densities over‐represented mesic coastal habitats. The Ausplots bioregional stratification implemented under practical constraints represented complex environments well, compared to statistically oriented or spatially even samples. Potential statistical power also depends on replication, unbiased site selection, and accuracy of field measurements relative to the magnitude of change. Consistent with previous studies, our stocktake analysis confirmed that environmental, rather than spatial, stratification is required to maximize ecological coverage across continental ecosystem observation networks, and the approach to establishing TERN Ausplots was robust. We recommend targeted gap‐filling to complete sampling.

On linear dimension reduction based on diagonalization of scatter matrices for bioinformatics downstream analyses

Dimension reduction is often a preliminary step in the analysis of data sets with a large number of variables. Most classical, both supervised and unsupervised, dimension reduction methods such as principal component analysis (PCA), independent component analysis (ICA) or sliced inverse regression (SIR) can be formulated using one, two or several different scatter matrix functionals. Scatter matrices can be seen as different measures of multivariate dispersion and might highlight different features of the data and when compared might reveal interesting structures. Such analysis then searches for a projection onto an interesting (signal) part of the data, and it is also important to know the correct dimension of the signal subspace. These approaches usually make either no model assumptions or work in wide classes of semiparametric models. Theoretical results in the literature are however limited to the case where the sample size exceeds the number of variables which is hardly ever true for data sets encountered in bioinformatics. In this paper, we briefly review the relevant literature and explore if the dimension reduction tools can be used to find relevant and interesting subspaces for small-n-large-p data sets. We illustrate the methods with a microarray dataset of prostate cancer patients and healthy controls.

Generalized entropy plane based on multiscale weighted multivariate dispersion entropy for financial time series

Abstract In recent years, complexity-entropy causality plane, Shannon-Fisher information plane and Renyi-Tsalli entropy plane methods have been proposed to study one-dimensional nonlinear complex systems and widely applied in many fields. However, it is much less common for these definitions to extend to two-dimensional or higher-dimensional data. Dispersion entropy shows superior performance in complex system analysis. We propose the above three generalized entropy plane methods based on multivariate dispersion entropy (MDE) and weighted multivariate dispersion entropy (WMDE) to evaluate the complexity of two-dimensional data. The performance of these methods is compared by analyzing the simulated data. Applying these methods to the study of multivariate stock time series, the complexity-entropy causality plane shows more great performance, not only obtains the classification of the stock market indices, but distinguishes the development states of different stock market indices. At the same time, we also propose multiscale multivariate dispersion entropy (MMDE) and multiscale weighted multivariate dispersion entropy (MWMDE), and reveal the ordinal structure of stock market indices from the view of multiscale.

Meroplankton seasonal dynamics in the high Arctic fjord: Comparison of different sampling methods

Meroplankton comprise mainly of pelagic larvae of benthic invertebrates and play an important role as consumers and prey in coastal ecosystems. During a year-round study in Isfjorden (Svalbard Archipelago; >78°N), two locations (stations North and South) were sampled every third month to capture seasonal dynamics of meroplankton at high-latitudes, using different sampling methods (vertically hauled WP2 plankton net, and SCUBA diver-operated: horizontal towed net and underwater suction pump). Independent of sampling methods, seasonality was the factor that explained the largest part of variation in meroplankton composition (31.8%, PERMANOVA). Distinct seasonal abundance peaks were found of the following taxa: Polychaeta larvae and Cirripedia nauplii in spring; Bivalvia veligers, Echinodermata ophioplutei, and Cirripedia cypris during summer; while Bryozoa cyphonautes in autumn. These changes were driven mainly by water temperature, chlorophyll a concentration, and photoperiod, which according to DistLM routine, jointly explained 36.7% of meroplankton variability. Our results support the theory that planktotrophy is an important larval development strategy in some high Arctic taxa, e.g. Bivalvia and Cirripedia. We also observed that the southern part of Isfjorden was more productive and affected by the advection of Atlantic waters; while the northern location was influenced by the sea ice drift, coming from the north-eastern part of the Isfjord system in winter and spring, and was characterised by higher meroplankton abundances. The comparison of the number of taxa collected by each method and multivariate dispersion index between the standard WP2 plankton net and the remaining devices, operated by SCUBA divers, proved that WP2 is the most optimal method to collect meroplankton, especially from deeper waters. However, an underwater, manually operated suction pump would be a good choice in shallow coastal areas, especially with a dense kelp forest, where using a WP2 net is impossible. The joint use of the WP2 net and suction pump gives the highest value of multivariate dispersion index for the total community, as it additionally allows for the collection of demersal and epibenthic animals which are often omitted by standard net sampling methods, so this combination is worth recommending in studying shallow coastal ecosystems.

Insights into β-diversity of periphytic protozoan fauna along the water column of marine ecosystems

It has been increasingly recognized that there is high relevance in determining the β-diversity of communities along an environmental gradient for bioassessment of environmental quality status. To evaluate the vertical variations in β-diversity of periphytic protozoan fauna, in response to environmental heterogeneity in marine ecosystems, a baseline survey was conducted at the four water depths in the coastal waters of the Yellow Sea, northern China. Results demonstrated that (1) the species distribution presented different patterns at four water depths; (2) both compositional and community structure showed a significant vertical variation in multivariate dispersions from surface layer to the deeper layers; and (3) β-diversity measures generally increased from depths of 1 m to 5 m. These findings suggest that the homogeneity in the periphytic communities are of a high variability along the water column of marine ecosystems.