Correlation-based Measures Research Articles

Comparison of correlation-based measures of concordance in terms of asymptotic variance

We compare measures of concordance that arise as Pearson’s linear correlation coefficient between two random variables transformed so that they follow the so-called concordance-inducing distributions. The class of such transformed rank correlations includes Spearman’s rho, Blomqvist’s beta and van der Waerden’s coefficient. When only the standard axioms of measures of concordance are required, it is not always clear which transformed rank correlation is most suitable to use. To address this question, we compare measures of concordance in terms of their best and worst asymptotic variances of some canonical estimators over a certain set of dependence structures. A simple criterion derived from this approach is that concordance-inducing distributions with smaller fourth moment are more preferable. In particular, we show that Blomqvist’s beta is the optimal transformed rank correlation in this sense, and Spearman’s rho outperforms van der Waerden’s coefficient. Moreover, we find that Kendall’s tau, although it is not a transformed rank correlation of that nature, shares a certain optimal structure with Blomqvist’s beta.

Evaluating the impact of higher-mode and inelastic dynamic responses of concrete frames on the performance of seismic intensity measures

The accuracy of seismic risk-based evaluation depends on the selected seismic intensity measures (IMs). The performance of the selected IM is commonly assessed based on efficiency and sufficiency criteria, which reflect the ability of the IM to reduce epistemic uncertainty and avoid bias, respectively. Although various characteristics of structural dynamic response affect IM performance to different extents, the current literature determines IM suitability based on the overall response. This study examines the impact of two dynamic response characteristics, namely higher-mode effect and nonlinearity, on the efficiency and sufficiency of a comprehensive set of common and advanced IMs. Two correlation-based measures are then proposed to explicitly evaluate the effect of higher-mode effect and nonlinearity using statistical tests. The results show that the developed statistical measures can explain the inefficiency and insufficiency of an IM based on dynamic characteristics of response. In addition, while the IM’s efficiency and sufficiency changes for different structures and ground motion sets, vector-valued and energy-based scalar IMs provide more consistent performance. Lastly, the impact of higher-mode response and nonlinearity is more pronounced on IMs efficiency than IM sufficiency.

Investigating the effects of healthy cognitive aging on brain functional connectivity using 4.7T resting-state functional magnetic resonance imaging.

Functional changes in the aging human brain have been previously reported using functional magnetic resonance imaging (fMRI). Earlier resting-state fMRI studies revealed an age-associated weakening of intra-system functional connectivity (FC) and age-associated strengthening of inter-system FC. However, the majority of such FC studies did not investigate the relationship between age and network amplitude, without which correlation-based measures of FC can be challenging to interpret. Consequently, the main aim of this study was to investigate how three primary measures of resting-state fMRI signal-network amplitude, network topography, and inter-network FC-are affected by healthy cognitive aging. We acquired resting-state fMRI data on a 4.7T scanner for 105 healthy participants representing the entire adult lifespan (18-85years of age). To study age differences in network structure, we combined ICA-based network decomposition with sparse graphical models. Older adults displayed lower blood-oxygen-level-dependent (BOLD) signal amplitude in all functional systems, with sensorimotor networks showing the largest age differences. Our age comparisons of network topography and inter-network FC demonstrated a substantial amount of age invariance in the brain's functional architecture. Despite architecture similarities, old adults displayed a loss of communication efficiency in our inter-network FC comparisons, driven primarily by theFC reduction in frontal and parietal association cortices. Together, our results provide a comprehensive overview of age effects on fMRI-based FC.

Assessing the significance of directed and multivariate measures of linear dependence between time series

Inferring linear dependence between time series is central to our understanding of natural and artificial systems. Unfortunately, the hypothesis tests that are used to determine statistically significant directed or multivariate relationships from time-series data often yield spurious associations (Type I errors) or omit causal relationships (Type II errors). This is due to the autocorrelation present in the analysed time series -- a property that is ubiquitous across diverse applications, from brain dynamics to climate change. Here we show that, for limited data, this issue cannot be mediated by fitting a time-series model alone (e.g., in Granger causality or prewhitening approaches), and instead that the degrees of freedom in statistical tests should be altered to account for the effective sample size induced by cross-correlations in the observations. This insight enabled us to derive modified hypothesis tests for any multivariate correlation-based measures of linear dependence between covariance-stationary time series, including Granger causality and mutual information with Gaussian marginals. We use both numerical simulations (generated by autoregressive models and digital filtering) as well as recorded fMRI-neuroimaging data to show that our tests are unbiased for a variety of stationary time series. Our experiments demonstrate that the commonly used $F$- and $\chi^2$-tests can induce significant false-positive rates of up to $100\%$ for both measures, with and without prewhitening of the signals. These findings suggest that many dependencies reported in the scientific literature may have been, and may continue to be, spuriously reported or missed if modified hypothesis tests are not used when analysing time series.

Multivariate Correlation Measures Reveal Structure and Strength of Brain-Body Physiological Networks at Rest and During Mental Stress.

In this work, we extend to the multivariate case the classical correlation analysis used in the field of network physiology to probe dynamic interactions between organ systems in the human body. To this end, we define different correlation-based measures of the multivariate interaction (MI) within and between the brain and body subnetworks of the human physiological network, represented, respectively, by the time series of δ, θ, α, and β electroencephalographic (EEG) wave amplitudes, and of heart rate, respiration amplitude, and pulse arrival time (PAT) variability (η, ρ, π). MI is computed: (i) considering all variables in the two subnetworks to evaluate overall brain–body interactions; (ii) focusing on a single target variable and dissecting its global interaction with all other variables into contributions arising from the same subnetwork and from the other subnetwork; and (iii) considering two variables conditioned to all the others to infer the network topology. The framework is applied to the time series measured from the EEG, electrocardiographic (ECG), respiration, and blood volume pulse (BVP) signals recorded synchronously via wearable sensors in a group of healthy subjects monitored at rest and during mental arithmetic and sustained attention tasks. We find that the human physiological network is highly connected, with predominance of the links internal of each subnetwork (mainly η−ρ and δ−θ, θ−α, α−β), but also statistically significant interactions between the two subnetworks (mainly η−β and η−δ). MI values are often spatially heterogeneous across the scalp and are modulated by the physiological state, as indicated by the decrease of cardiorespiratory interactions during sustained attention and by the increase of brain–heart interactions and of brain–brain interactions at the frontal scalp regions during mental arithmetic. These findings illustrate the complex and multi-faceted structure of interactions manifested within and between different physiological systems and subsystems across different levels of mental stress.

Optimising network modelling methods for fMRI

A major goal of neuroimaging studies is to develop predictive models to analyze the relationship between whole brain functional connectivity patterns and behavioural traits. However, there is no single widely-accepted standard pipeline for analyzing functional connectivity. The common procedure for designing functional connectivity based predictive models entails three main steps: parcellating the brain, estimating the interaction between defined parcels, and lastly, using these integrated associations between brain parcels as features fed to a classifier for predicting non-imaging variables e.g., behavioural traits, demographics, emotional measures, etc. There are also additional considerations when using correlation-based measures of functional connectivity, resulting in three supplementary steps: utilising Riemannian geometry tangent space parameterization to preserve the geometry of functional connectivity; penalizing the connectivity estimates with shrinkage approaches to handle challenges related to short time-series (and noisy) data; and removing confounding variables from brain-behaviour data. These six steps are contingent on each-other, and to optimise a general framework one should ideally examine these various methods simultaneously. In this paper, we investigated strengths and short-comings, both independently and jointly, of the following measures: parcellation techniques of four kinds (categorized further depending upon number of parcels), five measures of functional connectivity, the decision of staying in the ambient space of connectivity matrices or in tangent space, the choice of applying shrinkage estimators, six alternative techniques for handling confounds and finally four novel classifiers/predictors. For performance evaluation, we have selected two of the largest datasets, UK Biobank and the Human Connectome Project resting state fMRI data, and have run more than 9000 different pipeline variants on a total of ∼14000 individuals to determine the optimum pipeline. For independent performance validation, we have run some best-performing pipeline variants on ABIDE and ACPI datasets (∼1000 subjects) to evaluate the generalisability of proposed network modelling methods.

Real-Time Tracking of Selective Auditory Attention From M/EEG: A Bayesian Filtering Approach.

Humans are able to identify and track a target speaker amid a cacophony of acoustic interference, an ability which is often referred to as the cocktail party phenomenon. Results from several decades of studying this phenomenon have culminated in recent years in various promising attempts to decode the attentional state of a listener in a competing-speaker environment from non-invasive neuroimaging recordings such as magnetoencephalography (MEG) and electroencephalography (EEG). To this end, most existing approaches compute correlation-based measures by either regressing the features of each speech stream to the M/EEG channels (the decoding approach) or vice versa (the encoding approach). To produce robust results, these procedures require multiple trials for training purposes. Also, their decoding accuracy drops significantly when operating at high temporal resolutions. Thus, they are not well-suited for emerging real-time applications such as smart hearing aid devices or brain-computer interface systems, where training data might be limited and high temporal resolutions are desired. In this paper, we close this gap by developing an algorithmic pipeline for real-time decoding of the attentional state. Our proposed framework consists of three main modules: (1) Real-time and robust estimation of encoding or decoding coefficients, achieved by sparse adaptive filtering, (2) Extracting reliable markers of the attentional state, and thereby generalizing the widely-used correlation-based measures thereof, and (3) Devising a near real-time state-space estimator that translates the noisy and variable attention markers to robust and statistically interpretable estimates of the attentional state with minimal delay. Our proposed algorithms integrate various techniques including forgetting factor-based adaptive filtering, ℓ1-regularization, forward-backward splitting algorithms, fixed-lag smoothing, and Expectation Maximization. We validate the performance of our proposed framework using comprehensive simulations as well as application to experimentally acquired M/EEG data. Our results reveal that the proposed real-time algorithms perform nearly as accurately as the existing state-of-the-art offline techniques, while providing a significant degree of adaptivity, statistical robustness, and computational savings.

Inequivalence of correlation-based measures of non-Markovianity

We conclusively show that the entanglement- and the mutual information-based measures of quantum non-Markovianity are inequivalent. To this aim, we first analytically solve the optimization problem in the definition of the entanglement-based measure for a two-level system. We demonstrate that the optimal initial bipartite state of the open system and the ancillary is always given by one of the Bell states for any one qubit dynamics. On top of this result, we present an explicit example dynamics where memory effects emerge according to the mutual information-based measure, even though the time evolution remains memoryless with respect to the entanglement-based measure. Finally, we explain this disagreement between the two measures in terms of the information dynamics of the open system, exploring the accessible and inaccessible parts of information.

Computing the maximum violation of a Bell inequality is an NP-problem

The number of steps required in order to maximize a Bell inequality for arbitrary number of qubits is shown to grow exponentially with the number of parties involved. The proof that the optimization of such correlation measure is an NP-problem based on an operational perspective involving a Turing machine, which follows a general algorithm. The implications for the computability of the so-called nonlocality for any number of qubits is similar to recent results involving entanglement or similar quantum correlation-based measures.

A test of asymmetric comovement for state-dependent stock returns

I propose a test of asymmetric stock return comovement across states. The test can be viewed as a variation of Kendall's τ conditional on the state and has an asymptotic χ2-distribution. A refined version of the test is derived based on the Markov chain theory of regenerative cycles which substantially improves finite sample size and power properties. I show that the test has power against local alternatives, which is nonetheless compromised due to a finite sample convergence bound put on the implied local alternative data generating process. I evaluate the new test against traditional correlation-based measures and demonstrate power attrition of a state-free tail dependence test as parameter values are varied. Broad market-based ETFs and international indices are studied and in most cases there is no compelling evidence for asymmetric comovement across states. A list of related tests is given as an extension at the end.

Computer-aided unbalanced supersaturated designs involving interactions

Supersaturated designs (SSDs) are defined as fractional factorial designs whose experimental run size is smaller than the number of main effects to be estimated. While most of the literature on SSDs has focused only on main effects designs, the construction and analysis of such designs involving interactions has not been developed to a great extent. In this paper, we propose a backward elimination design-driven optimization (BEDDO) method, with one main goal in mind, to eliminate the factors which are identified to be fully aliased or highly partially aliased with each other in the design. Under the proposed BEDDO method, we implement and combine correlation-based statistical measures taken from classical test theory and design of experiments field, and we also present an optimality criterion which is a modified form of Cronbach's alpha coefficient. In this way, we provide a new class of computer-aided unbalanced SSDs involving interactions, that derive directly from BEDDO optimization.

Voxel-wise motion artifacts in population-level whole-brain connectivity analysis of resting-state FMRI.

Functional Magnetic Resonance Imaging (fMRI) based brain connectivity analysis maps the functional networks of the brain by estimating the degree of synchronous neuronal activity between brain regions. Recent studies have demonstrated that “resting-state” fMRI-based brain connectivity conclusions may be erroneous when motion artifacts have a differential effect on fMRI BOLD signals for between group comparisons. A potential explanation could be that in-scanner displacement, due to rotational components, is not spatially constant in the whole brain. However, this localized nature of motion artifacts is poorly understood and is rarely considered in brain connectivity studies. In this study, we initially demonstrate the local correspondence between head displacement and the changes in the resting-state fMRI BOLD signal. Than, we investigate how connectivity strength is affected by the population-level variation in the spatial pattern of regional displacement. We introduce Regional Displacement Interaction (RDI), a new covariate parameter set for second-level connectivity analysis and demonstrate its effectiveness in reducing motion related confounds in comparisons of groups with different voxel-vise displacement pattern and preprocessed using various nuisance regression methods. The effect of using RDI as second-level covariate is than demonstrated in autism-related group comparisons. The relationship between the proposed method and some of the prevailing subject-level nuisance regression techniques is evaluated. Our results show that, depending on experimental design, treating in-scanner head motion as a global confound may not be appropriate. The degree of displacement is highly variable among various brain regions, both within and between subjects. These regional differences bias correlation-based measures of brain connectivity. The inclusion of the proposed second-level covariate into the analysis successfully reduces artifactual motion-related group differences and preserves real neuronal differences, as demonstrated by the autism-related comparisons.

Quaternionic Signal Processing Techniques for <newline/>Automatic Evaluation of Dance Performances <newline/>From MoCap Data

In this paper, the problem of automatic dance performance evaluation from human Motion Capture (MoCap) data is addressed. A novel framework is presented, using data captured by Kinect-based human skeleton tracking, where the evaluation of user's performance is achieved against a gold-standard performance of a teacher. The framework addresses several technical challenges, including global and local temporal synchronization, spatial alignment and comparison of two “dance motion signals.” Towards the solution of these technical challenges, a set of appropriate quaternionic vector-signal processing methodologies is proposed, where the 4D (spatiotemporal) human motion data are represented as sequences of pure quaternions. Such a quaternionic representation offers several advantages, including the facts that joint angles and rotations are inherently encoded in the phase of quaternions and the three coordinates variables ( X,Y,Z) are treated jointly, with their intra-correlations being taken into account. Based on the theory of quaternions, a number of advantageous algorithms are formulated. Initially, global temporal synchronization of dance MoCap data is achieved by the use of quaternionic cross-correlations, which are invariant to rigid spatial transformations between the users. Secondly, a quaternions-based algorithm is proposed for the fast spatial alignment of dance MoCap data. Thirdly, the MoCap data can be temporally synchronized in a local fashion, using Dynamic Time Warping techniques adapted to the specific problem. Finally, a set of quaternionic correlation-based measures (scores) are proposed for evaluating and ranking the performance of a dancer. These quaternions-based scores are invariant to rigid transformations, as proved and demonstrated. A total score metric, through a weighted combination of three different metrics is proposed, where the weights are optimized using Particle Swarm Optimization (PSO). The presented experimental results using the Huawei/3DLife/EMC 2 dataset are promising and verify the effectiveness of the proposed methods.

DTW4Omics: Comparing Patterns in Biological Time Series

When studying time courses of biological measurements and comparing these to other measurements eg. gene expression and phenotypic endpoints, the analysis is complicated by the fact that although the associated elements may show the same patterns of behaviour, the changes do not occur simultaneously. In these cases standard correlation-based measures of similarity will fail to find significant associations. Dynamic time warping (DTW) is a technique which can be used in these situations to find the optimal match between two time courses, which may then be assessed for its significance. We implement DTW4Omics, a tool for performing DTW in R. This tool extends existing R scripts for DTW making them applicable for “omics” datasets where thousands entities may need to be compared with a range of markers and endpoints. It includes facilities to estimate the significance of the matches between the supplied data, and provides a set of plots to enable the user to easily visualise the output. We illustrate the utility of this approach using a dataset linking the exposure of the colon carcinoma Caco-2 cell line to oxidative stress by hydrogen peroxide (H2O2) and menadione across 9 timepoints and show that on average 85% of the genes found are not obtained from a standard correlation analysis between the genes and the measured phenotypic endpoints. We then show that when we analyse the genes identified by DTW4Omics as significantly associated with a marker for oxidative DNA damage (8-oxodG), through over-representation, an Oxidative Stress pathway is identified as the most over-represented pathway demonstrating that the genes found by DTW4Omics are biologically relevant. In contrast, when the positively correlated genes were similarly analysed, no pathways were found. The tool is implemented as an R Package and is available, along with a user guide from http://web.tgx.unimaas.nl/svn/public/dtw/.

REGISTRATION OF OPTICAL DATA WITH HIGH-RESOLUTION SAR DATA: A NEW IMAGE REGISTRATION SOLUTION

Abstract. Accurate image-to-image registration is critical for many image processing workflows, including georeferencing, change detection, data fusion, image mosaicking, DEM extraction and 3D modeling. Users need a solution to generate tie points accurately and geometrically align the images automatically. To solve these requirements we developed the Hybrid Powered Auto-Registration Engine (HyPARE). HyPARE combines all available spatial reference information with a number of image registration approaches to improve the accuracy, performance, and automation of tie point generation and image registration. We demonstrate this approach by the registration of a Pléiades-1a image with a TerraSAR-X SpotLight image of Hannover, Germany. Registering images with different modalities is a known challenging problem; e.g. manual tie point collection is prone to error. The registration engine allows to generate tie points automatically, using an optimized mutual information-based matching method. It produces more accurate results than traditional correlation-based measures. In this example the resulting tie points are well distributed across the overlapping areas, even as the images have significant local feature differences.

다중선택 시험에서 부정행위자 발견을 위한 새로운 통계적 측도

It is important to construct a firm basis for accusing potential violators of academic integrity in order to avoid spurious accusations and false convictions. Educational researchers have developed many statistical methods that can either uncover or confirm cases of cheating on tests. However, most of them rely on simple correlation-based measures, and often fail to account for patterns in responses or answers. In this paper, we propose a new statistical index denoted by a Standardized Signed Entropy Similarity Score to resolve this difficulty. In addition, we apply the proposed method to analyze a real data set and compare the results to other existing methods.

A spatial discrepancy measure between voxel sets in brain imaging

Functional Magnetic Resonance Imaging serves to identify networks and regions in the brain engaged in various mental activities, represented as a set of voxels in the 3D image. It is important to be able to measure how similar two selected voxel sets are. The major flaw of the currently used correlation-based and overlap-based measures is that they disregard the spatial proximity of the selected voxel sets. Here, we propose a measure for comparing two voxel sets, called Spatial Discrepancy, based upon the average Hausdorff distance. We demonstrate that Spatial Discrepancy can detect genuine similarities and differences where other commonly used measures fail to do so. A simulation experiment was carried out where distorted copies of the same voxel sets were compared, varying the level of distortion. The experiment revealed that the proposed measure correlates better with the level of distortion than any of the other measures. Data from a 10-subject experiment were used to demonstrate the advantages of the Spatial Discrepancy measure in multi-subject studies.

Financial Contagion and Systemic Risk: From Theory to Applicable Macroeconomic Model

This draft working paper is to summarize theoretical contributions in the field of measuring systemic risk and contagion of financial systems. Broad theoretical framework is analyzed and empiric approach to a macroeconomic model of global banking system systemic risk and contagion is offered. The model is to use BIS locational statistics as well as national consolidated balance sheets of banking systems to provide some insight into the vulnerability of modern banking system. As to theoretical contributions, three branches of literature are analyzed: correlation-based measures, network-based measures and various systemic risk measures.

Inhibitory coherence in a heterogeneous population of subthreshold and suprathreshold type-I neurons

We study inhibitory coherence (i.e. collective coherence by synaptic inhibition) in a population of globally coupled type-I neurons, which can fire at arbitrarily low frequency. No inhibitory coherence is observed in a homogeneous population composed of only subthreshold neurons, which exhibit noise-induced firings. In addition to subthreshold neurons, there exist spontaneously firing suprathreshold neurons in a noisy environment of a real brain. To take into consideration the effect of suprathreshold neurons on inhibitory coherence, we consider a heterogeneous population of subthreshold and suprathreshold neurons and investigate the inhibitory coherence by increasing the fraction of suprathreshold neurons Psupra. As Psupra passes a threshold P*supra, suprathreshold neurons begin to synchronize and play the role of coherent inhibitors for the emergence of inhibitory coherence. Thus, regularly oscillating population-averaged global potential appears for Psupra > P*supra. For this coherent case, suprathreshold neurons exhibit sparse spike synchronization (i.e. individual potentials of suprathreshold neurons consist of coherent sparse spikings and coherent subthreshold small-amplitude hoppings). By virtue of their coherent inhibition, sparsely synchronized suprathreshold neurons suppress the noisy activity of subthreshold neurons. Thus, subthreshold neurons exhibit hopping synchronization (i.e. only coherent subthreshold hopping oscillations without spikings appear in the individual potentials of subthreshold neurons). We also characterize the inhibitory coherence in terms of the ‘statistical-mechanical’ spike-based and correlation-based measures, which quantify the average contributions of the microscopic individual spikes and individual potentials to the macroscopic global potential. Finally, the effect of sparse randomness of synaptic connectivity on the inhibitory coherence is briefly discussed.

Incremental Mutual Information: A New Method for Characterizing the Strength and Dynamics of Connections in Neuronal Circuits

Understanding the computations performed by neuronal circuits requires characterizing the strength and dynamics of the connections between individual neurons. This characterization is typically achieved by measuring the correlation in the activity of two neurons. We have developed a new measure for studying connectivity in neuronal circuits based on information theory, the incremental mutual information (IMI). By conditioning out the temporal dependencies in the responses of individual neurons before measuring the dependency between them, IMI improves on standard correlation-based measures in several important ways: 1) it has the potential to disambiguate statistical dependencies that reflect the connection between neurons from those caused by other sources (e.g. shared inputs or intrinsic cellular or network mechanisms) provided that the dependencies have appropriate timescales, 2) for the study of early sensory systems, it does not require responses to repeated trials of identical stimulation, and 3) it does not assume that the connection between neurons is linear. We describe the theory and implementation of IMI in detail and demonstrate its utility on experimental recordings from the primate visual system.