Analysis Of Covariance Matrices Research Articles

An optimized and hybrid gating scheme for the suppression of very low-frequency radios in transient electromagnetic systems

Abstract. One of the most widely used approaches for measuring the earth's subsurface resistivity is the transient electromagnetic (TEM) method. However, noise and interference from different sources, e.g., radio communication, the instrument, the atmosphere, and power lines, severely taint these types of signals. In particular, radio transmission in the very low-frequency (VLF) range between 3 and 30 kHz is one of the most prominent sources of noise. Transient electromagnetic signals are normally gated to increase the signal-to-noise ratio. A precise selection of gate shapes is required to suppress undesired noise while allowing the TEM signal to pass unaltered. We employ the multi-objective particle swarm optimization technique to choose optimal gate shapes and placements by minimizing an objective function composed of standard error bars, the covariance between gates, and the distortion of the gated signal. The proposed method is applied to both fully sampled synthetic TEM data and to boxcar-gated field data. The best output from the search space of gate shapes was found to be a hybrid combination of boxcar and Hamming gates. The effectiveness of hybrid gating over traditional boxcar and semi-tapered gating is confirmed by an analysis of covariance matrices and error bars. The results show that the developed method effectively suppresses VLF noise in the middle gates, which are gates with center times spanning 30 to 200 µs , and in the late gates, which are gates with center times spanning 200 to 1130 µs. The analysis shows that the average improvement in standard errors obtained for the hybrid gating scheme over boxcar gating is 1.719 and 1.717 for synthetic and field data, respectively.

Features of Fluorescence Profiles and Species Composition of Phytoplankton in the Black Sea and the Sea of Azov

The aim of this work was to study the properties of vertical fluorescence intensity (FI) profiles of phytoplankton pigments (chlorophyll-a, phycocyanin, phycoerythrin, and beta-carotene) using data on the phytoplankton species composition obtained during the cruise 114 of the R/V ‘Professor Vodyanitsky’. The analysis of covariance matrices of phytoplankton pigment FI profiles in the upper 50-meter layer of the Black Sea indicates that the pigment composition of phytoplankton changes with depth, which may be associated with changes in its species composition. At the same time, 80 % variability of phytoplankton pigment FI profiles in the upper 20-meter layer is described by the first eigenvector. It agrees well with direct observations of the phytoplankton species composition, indicating the dominance of one phytoplankton division in the 20-meter layer. In addition, there are regional peculiarities: for example, the average FI values of the phytoplankton pigments in the Sea of Azov are significantly higher than those in the Black Sea, which is associated with a higher concentration of phytoplankton in the Sea of Azov.

Navigation complex of impact unmanned aerial vehicle

The navigation complex of a promising impact unmanned vehicle is studied. With respect to the features of navigation systems are determined the composition of the navigation complex. An adaptive estimation algorithm is chosen to correct the inertial navigation system. The structure of the navigation complex, which provides the best choice of the working contour and is distinguished by ease of implementation on board an unmanned aerial vehicle is developed. The choice of a navigation information sensor external to the inertial system based on the analysis of covariance matrices of estimation errors is carried out. Keywords impact unmanned aerial vehicle, navigation system, estimation algorithm, inertial navigation system, Kalman filter, estimation error covariance matrix

PBBFMM3D: A parallel black-box algorithm for kernel matrix-vector multiplication

Kernel matrix-vector product is ubiquitous in many science and engineering applications. However, a naive method requires O(N2) operations, which becomes prohibitive for large-scale problems. To reduce the computation cost, we introduce a parallel method that provably requires O(N) operations and delivers an approximate result within a prescribed tolerance. The distinct feature of our method is that it requires only the ability to evaluate the kernel function, offering a black-box interface to users. Our parallel approach targets multi-core shared-memory machines and is implemented using OpenMP. Numerical results demonstrate up to 19× speedup on 32 cores. We also present a real-world application in geo-statistics, where our parallel method was used to deliver fast principle component analysis of covariance matrices.

Performance measurement using linear additive directional distance function and PCA based directions

In this paper, the performance of a firm vis-à-vis its rivals is measured with a reoriented form of the Linear Directional Distance Function and setting the Directions obtained from the Principal Component Analysis of non-central covariance matrices. Eigenvectors thus obtained will have a connection with the variance explained and Competitive Intensity. In this context, two types of covariance matrices are analysed within two alternative models prescribed here. The former one investigates the position of a firm in comparison to others and prescribes a path of effective utilization of resources to generate outputs using the extant technology by the firms. The second approach is centred on comparing the weighted sum of input-output vectors of all rivals with the concerned Decision-Making Unit. This matrix is akin to the Multi-Dimensional Herfindahl Hirschman Indices (input and output-based) to symbolise the market concentration when the current firm (as if) is assumed to be a new entrant. The paper finds the Second approach superior to the former one for two major reasons. Firstly, a typical non-central covariance matrix obtained from the former may fail to provide a legitimate direction vector. Secondly, even if one is found then also it may not be pointing towards the direction of the highest variation to clarify the large extent of competitive intensity. However, the later method overcomes all these issues.

Faults detection and classification in a centrifugal pump from vibration data using markov parameters

One of the strategies to detect and classify faults in mechanical systems is to use a time domain family of techniques known as output-only methods. Those methods are based on the analysis of sample covariance matrices, which are estimated from vibration data extracted from mechanical systems under unmeasured natural excitation. Using the stochastic realization theory, it is possible to derive Markov parameters from sample covariance matrices. Those parameters contain only the significant spectral components from data. In this paper, a novel output-only method based on the Markov parameters is proposed to diagnose faults. The idea is to use the Markov parameters estimated from vibration data as features in classification algorithms based on convex optimization. The method was applied to diagnose incipient cavitation failures in a water supply network centrifugal pump. A low-cost triaxial vibration sensor developed by one of the authors was used to register the vibration data. The proposed method was compared to the analysis based on sample covariance matrices demonstrating the advantages related to the use of the Markov parameters.

A multivariate view of parallel evolution

A growing number of empirical studies have quantified the degree to which evolution is geometrically parallel by estimating and interpreting pairwise angles between multiple replicate lineages' evolutionary change vectors in multivariate trait space. Similar comparisons, of distance in trait space, are used to assess the degree of convergence. These approaches amount to element-by-element interpretation of distance matrices, typically testing for differences among replicate evolutionary vectors, compared to a null hypothesis of perfect parallelism. We suggest a complimentary set of approaches, co-opted from evolutionary quantitative genetics, involving eigen analysis and comparison of among-lineage covariance matrices. Such approaches allow one to identify multiple major axes of evolutionary change (e.g., alternative adaptive solutions), and also allow for the definition of biologically tenable null hypotheses, such as drift, against which empirical patterns can be tested. Reanalysis of a dataset of multivariate evolution across a replicated lake/stream gradient in threespine stickleback reveals that most of the variation in the direction of evolutionary change can be captured in just a few dimensions, indicating a greater extent of parallelism than previously appreciated. We suggest that applying such multivariate approaches may often be necessary to fully understand the extent and form of parallel and convergent evolution.

Phase I analysis of high-dimensional covariance matrices based on sparse leading eigenvalues

In statistical process control (SPC), a proper Phase I analysis is essential to the success of Phase II monitoring. With recent advances in sensing technology and data acquisition systems, Phase I analysis of high-dimensional data is increasingly encountered. However, the high dimensionality presents a new challenge to the traditional Phase I techniques. A literature review reveals nearly no Phase I techniques in existence for analyzing high-dimensional process variability. Motivated by this, this paper develops a sparse-leading-eigenvalue-driven control chart for retrospectively monitoring high-dimensional covariance matrices in Phase I, denoted as the SLED control chart. The key idea of it is to track changes in the sparse leading eigenvalue between two covariance matrices. Compared to the L 2-type and -type methods, the proposed method can extract stronger signal with less noise. It is shown that the proposed method can gain high detection power, especially when the shift is weak and is not very dense, which is often the case in practical applications.

Spectral analysis of molecular dynamics simulations on PDZ: MD sectors

The idea of protein “sectors” posits that sparse subsets of amino acid residues form cooperative networks that are key elements of protein stability, ligand binding, and allosterism. To date, protein sectors have been calculated by the statistical coupling analysis (SCA) method of Ranganathan and co-workers via the spectral analysis of conservation-weighted evolutionary covariance matrices obtained from a multiple sequence alignments of homologous families of proteins. SCA sectors, a knowledge-based protocol, have been indentified with functional properties and allosterism for a number of systems. In this study, we investigate the utility of the sector idea for the analysis of physics-based molecular dynamics (MD) trajectories of proteins. Our test case for this procedure is PSD95- PDZ3, one of the smallest proteins for which allosterism has been observed. It has served previously as a model system for a number of prediction algorithms, and is well characterized by X-ray crystallography, NMR spectroscopy and site specific mutagenisis. All-atom MD simulations were performed for a total of 500 nanoseconds using AMBER, and MD-calculated covariance matrices for the fluctuations of residue displacements and non-bonded interaction energies were subjected to spectral analysis in a manner analogous to that of SCA. The composition of MD sectors was compared with results from SCA, site specific mutagenesis, and allosterism. The concordance indicates that MD sectors are a viable protocol for analyzing MD trajectories and provide insight into the physical origin of the phenomenon.Communicated by Ramaswamy H. Sarma

Spectral analysis of high-dimensional sample covariance matrices with missing observations

We study high-dimensional sample covariance matrices based on independent random vectors with missing coordinates. The presence of missing observations is common in modern applications such as climate studies or gene expression micro-arrays. A weak approximation on the spectral distribution in the “large dimension $d$ and large sample size $n$” asymptotics is derived for possibly different observation probabilities in the coordinates. The spectral distribution turns out to be strongly influenced by the missingness mechanism. In the null case under the missing at random scenario where each component is observed with the same probability $p$, the limiting spectral distribution is a Marcenko–Pastur law shifted by $(1-p)/p$ to the left. As $d/n\rightarrow y\in(0,1)$, the almost sure convergence of the extremal eigenvalues to the respective boundary points of the support of the limiting spectral distribution is proved, which are explicitly given in terms of $y$ and $p$. Eventually, the sample covariance matrix is positive definite if $p$ is larger than \[1-(1-\sqrt{y})^{2},\] whereas this is not true any longer if $p$ is smaller than this quantity.

Kriging prediction for manifold-valued random fields

The statistical analysis of data belonging to Riemannian manifolds is becoming increasingly important in many applications, such as shape analysis, diffusion tensor imaging and the analysis of covariance matrices. In many cases, data are spatially distributed but it is not trivial to take into account spatial dependence in the analysis because of the non linear geometry of the manifold. This work proposes a solution to the problem of spatial prediction for manifold valued data, with a particular focus on the case of positive definite symmetric matrices. Under the hypothesis that the dispersion of the observations on the manifold is not too large, data can be projected on a suitably chosen tangent space, where an additive model can be used to describe the relationship between response variable and covariates. Thus, we generalize classical kriging prediction, dealing with the spatial dependence in this tangent space, where well established Euclidean methods can be used. The proposed kriging prediction is applied to the matrix field of covariances between temperature and precipitation in Quebec, Canada.

<b>Repeatability and phenotypic stabilization of <i>Panicum maximum</i> accessions

The experiment aimed at determining repeatability coefficients for four methods (analysis of variance, principal components-correlation and covariance matrices and structural analysis), number of harvests necessary to increase accuracy and phenotypic stability of yield characteristics of accessions of Panicum maximum. The experiment was conducted in a completely randomized design with 35 genotypes and three replications. Five cuts were made and material was weighed and dried to obtain total, stem, leaf and dead forage dry matter yields. The repeatability coefficients in the different methods, for the evaluated characteristics, ranged from 0.1867 and 0.6583. The estimates of repeatability coefficients obtained for the evaluated characteristics by analysis of variance were generally smaller than the ones obtained with the other methods. By the principal components (based on the covariance matrix), the estimates were usually larger than those for the other methods. Therefore, it is possible to recommend this method to estimate the coefficient of repeatability for traits evaluated in this study. Considering that levels of 80 or 90% of confidence in the evaluation of the relative superiority of the accessions for all the evaluated characteristics are satisfactory, five harvests are sufficient for the choice of the best accession.

Dissecting high-dimensional phenotypes with bayesian sparse factor analysis of genetic covariance matrices.

Quantitative genetic studies that model complex, multivariate phenotypes are important for both evolutionary prediction and artificial selection. For example, changes in gene expression can provide insight into developmental and physiological mechanisms that link genotype and phenotype. However, classical analytical techniques are poorly suited to quantitative genetic studies of gene expression where the number of traits assayed per individual can reach many thousand. Here, we derive a Bayesian genetic sparse factor model for estimating the genetic covariance matrix (G-matrix) of high-dimensional traits, such as gene expression, in a mixed-effects model. The key idea of our model is that we need consider only G-matrices that are biologically plausible. An organism’s entire phenotype is the result of processes that are modular and have limited complexity. This implies that the G-matrix will be highly structured. In particular, we assume that a limited number of intermediate traits (or factors, e.g., variations in development or physiology) control the variation in the high-dimensional phenotype, and that each of these intermediate traits is sparse – affecting only a few observed traits. The advantages of this approach are twofold. First, sparse factors are interpretable and provide biological insight into mechanisms underlying the genetic architecture. Second, enforcing sparsity helps prevent sampling errors from swamping out the true signal in high-dimensional data. We demonstrate the advantages of our model on simulated data and in an analysis of a published Drosophila melanogaster gene expression data set.

Investigating the stratigraphy of an alluvial aquifer using crosswell seismic traveltime tomography

In this study, we investigate the use of crosswell P-wave seismic tomography to obtain spatially extensive information about subsurface sedimentary architecture and heterogeneity in alluvial aquifers. Our field site was a research wellfield in an unconfined aquifer near Boise, Idaho. The aquifer consists of a ∼ 20-m-thick sequence of alluvial cobble-and-sand deposits, which have been subdivided into five stratigraphic units based on neutron porosity logs, grain-size analysis, and radar reflection data. We collected crosswell and borehole-to-surface seismic data in wells [Formula: see text] apart. We carefully considered the impact of well deviation, data quality control, and the choice of inversion parameters. Our linearized inverse routine had a curved-ray forward model and used different grids for forward modeling and inversion. An analysis of the model covariance and resolution matrices showed that the velocity models had an uncertainty of [Formula: see text], a vertical resolution of [Formula: see text], and a horizontal resolution of [Formula: see text]. The velocity in the saturated zone varied between [Formula: see text] and [Formula: see text]. Inclusion of the borehole-to-surface data eliminated the X- shaped pattern that is a common artifact in crosswell tomography, and the increased angular coverage also improved the accuracy of the model near the top of the tomogram. The final velocity model is consistent with previous stratigraphic analyses of the site, although the locations of some of the unit boundaries differ by as much as [Formula: see text] in places. The results of this study demonstrate that seismic tomography can be used to image the sedimentary architecture of unconsolidated alluvial aquifers, even when the lithologic contrasts between units are subtle.

Degree of Polarization Filter for Frequency-Dependent Signal Enhancement Through Noise Suppression

We construct and examine a new frequency-dependent polarization filter to attenuate less polarized signals and noise in single and multichannel seismic data. The filter uses a degree of polarization measure which is defined as a measure of the variations of an arbitrary instantaneous polarization through the course of the signal. Small variations indicate a high degree of polarization. The frequency-dependent degree of polarization is based on the eigen analysis of the data covariance matrices and is used to weight the decomposed time series in the time-frequency domain. This approach permits the frequency-dependent detection of polarized signals and their enhancement through less polarized signal and noise suppression. Further, interfering signals with different frequency contents can be separated. With densely spaced data the degree of polarization can be averaged locally to include the wave-field directivity. This procedure is important since, through the averaging, isolated polarized noise can be removed, but isolated unpolarized signals are not suppressed. In contrast to waveform stacks or stacks of data covariance matrices our approach does not punish signals with spatially changing characteristics, such as happens in the transition from precritical to postcritical reflections. Our data adaptive filter is analyzed with theoretical test data before it is applied to a complex wide-angle record section from the West Pyrenees.

Linear Fuzzy Clustering Techniques With Missing Values and Their Application to Local Principal Component Analysis

In this paper, we propose two methods for partitioning an incomplete data set with missing values into several linear fuzzy clusters by extracting local principal components. One is an extension of fuzzy c-varieties clustering that can be regarded as the algorithm for the local principal component analysis of fuzzy covariance matrices. The other is a simultaneous application of fuzzy clustering and principal component analysis of fuzzy correlation matrices. Both methods estimate prototypes ignoring only missing values and they need no preprocessing of data such as the elimination of samples with missing values or the imputation of missing elements. Numerical examples show that the methods provide useful tools for interpretation of the local structures of a database.

Three-mode analysis of multimode covariance matrices.

Multimode covariance matrices, such as multitrait-multimethod matrices, contain the covariances of subject scores on variables for different occasions or conditions. This paper presents a comparison of three-mode component analysis and three-mode factor analysis applied to such covariance matrices. The differences and similarities between the non-stochastic and stochastic approaches are demonstrated by two examples, one of which has a longitudinal design. The empirical comparison is facilitated by deriving, as a heuristic device, a statistic based on the maximum likelihood function for three-mode factor analysis and its associated degrees of freedom for the three-mode component models. Furthermore, within the present context a case is made for interpreting the core array as second-order components.

Estimates of Genetic Parameters for Single- and Multiple-Country Test-Day Models

Single- and multiple-country random regression models were applied to estimate genetic parameters for first-lactation test-day milk yield of cows from four countries: Australia, Canada, Italy, and New Zealand. Selected countries represented a wide range of production systems and environments. Milk production in Canada and Italy is based mainly on intensive management systems, while Australia and New Zealand are largely based on rotational grazing. Legendre polynomials with five coefficients were used to model genetic and environmental lactation curves. Covariance components of lactation curve coefficients within and across countries, and selected functions of those, were estimated by Bayesian methods with Gibbs sampling, on selected subsets of data. Countries differed in both phenotypic and genetic parameters of lactation curves between d 5 and 305 of lactation. Principal component analysis of single-trait genetic and environmental covariance matrices showed, however, that the pattern of variability in test-day milk yield was very similar between countries. General level of milk production in lactation and persistency components accounted for more than 90% of the total variance. Estimated genetic correlations between countries for total yield in lactation ranged from 0.65 (Italy and New Zealand) to 0.83 (Australia and New Zealand), indicating a possibility of genotype by environment interaction for some pairs of countries.

Bayesian analysis of covariance matrices and dynamic models for longitudinal data

Parsimonious modelling of the within‐subject covariance structure while heeding its positive‐definiteness is of great importance in the analysis of longitudinal data. Using the Cholesky decomposition and the ensuing unconstrained and statistically meaningful reparameterisation, we provide a convenient and intuitive framework for developing conditionally conjugate prior distributions for covariance matrices and show their connections with generalised inverse Wishart priors. Our priors offer many advantages with regard to elicitation, positive definiteness, computations using Gibbs sampling, shrinking covariances toward a particular structure with considerable flexibility, and modelling covariances using covariates. Bayesian estimation methods are developed and the results are compared using two simulation studies. These simulations suggest simpler and more suitable priors for the covariance structure of longitudinal data.

Influence of General and Crystallized Intelligence on Vocabulary Test Performance

Summary: Vocabulary tests, part of most test batteries of general intellectual ability, measure both verbal and general ability. Newly developed techniques for confirmatory factor analysis of dichotomous variables make it possible to analyze the influence of different abilities on the performance on each item. In the testing procedure of the Computerized Swedish Enlistment test battery, eight different subtests of a new vocabulary test were given randomly to subsamples of a representative sample of 18-year-old male conscripts (N = 9001). Three central dimensions of a hierarchical model of intellectual abilities, general (G), verbal (Gc'), and spatial ability (Gv') were estimated under different assumptions of the nature of the data. In addition to an ordinary analysis of covariance matrices, assuming linearity of relations, the item variables were treated as categorical variables in the Mplus program. All eight subtests fit the hierarchical model, and the items were found to load about equally on G and Gc'. The results also indicate that if nonlinearity is not taken into account, the G loadings for the easy items are underestimated. These items, moreover, appear to be better measures of G than the difficult ones. The practical utility of the outcome for item selection and the theoretical implications for the question of the origin of verbal ability are discussed.