Covariance Criterion Research Articles

An active noise control algorithm based on fractional lower order covariance with on-line characteristics estimation

Active impulsive noise control (AINC) is a specific research interest for improving the performance of traditional algorithms against impulsive environments. By studying existing algorithms, this paper employs a fractional lower order covariance criterion and proposes a filtered-x fractional lower order covariance (FxFLOC) algorithm. After that, the FxFLOC algorithm is equipped with an on-line estimation method using a sampled characteristic function to overcome the dependency on prior knowledge of α-stable distribution. Furthermore, the convergence condition and the influence of hyperparameters are discussed. Extensive simulations are carried out to suggest that the proposed algorithms enhance the stability and accelerate the convergence speed compared with prior algorithms. Also, experiments are conducted to verify the performance of the proposed algorithms. The results show that the proposed algorithms are practical on symmetric α-stable (SαS) impulsive noise attenuation.

Robust Frequency Estimation Under Additive Mixture Noise

In many applications such as multiuser radar communications and astrophysical imaging processing, the encountered noise is usually described by the finite sum of -stable variables. In this paper, a new parameter estimator is developed, in the presence of this new heavy-tailed noise. Since the closed-form PDF of the -stable variable does not exist except and , we take the sum of the Cauchy () and Gaussian () noise as an example, namely, additive Cauchy-Gaussian (ACG) noise. The probability density function (PDF) of the mixed random variable, can be calculated by the convolution of the Cauchy's PDF and Gaussian's PDF. Because of the complicated integral in the PDF expression of the ACG noise, traditional estimators, e.g., maximum likelihood, are analytically not tractable. To obtain the optimal estimates, a new robust frequency estimator is devised by employing the Metropolis-Hastings (M-H) algorithm. Meanwhile, to guarantee the fast convergence of the M-H chain, a new proposal covariance criterion is also devised, where the batch of previous samples are utilized to iteratively update the proposal covariance in each sampling process. Computer simulations are carried out to indicate the superiority of the developed scheme, when compared with several conventional estimators and the Cramér-Rao lower bound.

Hybrid cooperative localization based on robot-sensor networks

For cooperative localization in robot-sensor networks (RSNs), efficient utilization of multiple measurements produced by heterogeneous nodes is the key to improving their positioning accuracy. The existing approaches usually focus on the measurement of pseudo-anchor cooperation (PAC) or non-anchor cooperation (NAC), which is often adopted in wireless sensor networks and robotics separately. Therefore, the case where the two types of cooperations are involved cannot be handled reasonably. In view of this, the new concept of a temporary pseudo-anchor (TPA) has been introduced in this work. Owing to the dynamic switching mechanism of TPA, a hybrid range-based node switchable cooperative localization (NSCL) approach can be easily derived, in which the effective PAC and NAC can be realized simultaneously. Furthermore, to extract valuable information from redundant measurements, the TPA selection strategies based on minimum covariance criterion (MCC) and maximum entropy change (MEC) have also been deduced, inspired by the information theory. Benefiting from their different optimization objectives, the two strategies can be employed depending on the requirements of the practical applications. Experimental results indicate that the MCC- and MEC-based NSCL exhibit higher positioning accuracy as compared to the existing PAC and NAC approaches. More importantly, they can still work well even with the only anchor, which exhibits robustness and adaptability to the complex environment.

A Novel Experimental Strategy for In situ SR-CT Mechanical Loading Test

In synchrotron radiation computed tomography (SR-CT) of mechanical loading process, accurate reconstruction of finite angle projection information shielded by mechanical loading devices is a bottleneck problem. For accurate characterization, an experimental strategy for in situ SR-CT mechanical loading test was proposed in this manuscript, which was called "finite angle CT reconstruction method based on tilted sampling information recovery" or TSIR-CT. Effectively recovering the information lost in finite angle CT is a fundamental solution. From the new perspective of the frequency domain, the tilt sampled projection information was utilized to recover the missing angle information. A series of numerical reconstruction experiments were carried out to verify the new method. It was indicated that the reconstruction results of TSIR-CT method have been improved quantitatively comparing with filtered back projection (FBP) and algebraic reconstruction technique (ART) method. For the 506th layer from top end of the 3D test model, the standardized covariance criterion for evaluating similarity was increased from 0.8400 of FBP and 0.9148 of ART to 0.9357, respectively. Finally, this new method was validated using actual SR-CT data and demonstrated effective improvement of reconstruction quality. This new method is suitable for in situ SR-CT mechanical loading test.

Mathematical structure and physical content of composite gravity in weak-field approximation

The natural constraints for the weak-field approximation to composite gravity, which is obtained by expressing the gauge vector fields of the Yang-Mills theory based on the Lorentz group in terms of tetrad variables and their derivatives, are analyzed in detail within a canonical Hamiltonian approach. Although this higher derivative theory involves a large number of fields, only few degrees of freedom are left, which are recognized as selected stable solutions of the underlying Yang-Mills theory. The constraint structure suggests a consistent double coupling of matter to both Yang-Mills and tetrad fields, which results in a selection among the solutions of the Yang-Mills theory in the presence of properly chosen conserved currents. Scalar and tensorial coupling mechanisms are proposed, where the latter mechanism essentially reproduces linearized general relativity. In the weak-field approximation, geodesic particle motion in static isotropic gravitational fields is found for both coupling mechanisms. An important issue is the proper Lorentz covariant criterion for choosing a background Minkowski system for the composite theory of gravity.

Entanglement between total intensity and polarization for pairs of coherent states

We examine entanglement between number and polarization, or between number and relative phase, for pairs of coherent states and two-mode squeezed vacuum via linear entropy and covariance criteria. We consider the embedding of the two-mode Hilbert space in a larger space to get a well-defined factorization of the number-phase variables. This can be regarded as a kind of proto-entanglement that can be extracted and converted into real particle entanglement via feasible experimental procedures. In particular this reveals interesting entanglement properties of pairs of coherent states.

In situ investigation on rapid microstructure evolution in extreme complex environment by developing a new AFBP-TVM sparse tomography algorithm from original CS-XPCMT

A new sparse tomography method for observing the rapid internal microstructure evolution of material, called the Algebraic Filtered-Back-Projection and Total Variation Minimization (AFBP-TVM) iteration sparse reconstruction algorithm, was proposed in this paper. The new algorithm was developed by combining the two techniques of the Algebraic Reconstruction Technique (ART) and the Filtered-Back-Projection (FBP) on the basis of analysis in linear space. A series of numerical reconstruction experiments were conducted to validate the new algorithm. The results indicated the new algorithm can obtain satisfactory reconstruction images from 1/6 of the projections that were used in traditional algorithms. So the time spent on projection acquisition process can be reduced to 1/6 of that in traditional tomography method. The quality of images reconstructed by new algorithm was better than other algorithms, which was evaluated by three quantitative parameters. The normalized average absolute distance criterion and the normalized mean square criterion, which were used to evaluate the relative error of the reconstruction results (smaller value means better quality of reconstruction), decreased from 0.3758 to 0.1272 and from 0.1832 to 0.0894 respectively. The standardized covariance criterion, which was used to evaluate the similarity level (greater value means higher accuracy of reconstruction), increased from 92.72% to 99.30%. Finally, the new algorithm was validated under actual experimental conditions. The results indicated that the AFBP-TVM algorithm obtained better reconstruction quality than other algorithms. It meant that the AFBP-TVM algorithm may be a suitable method for in situ investigation on material's rapid internal microstructure evolution in extreme complex environment.

Quasi Closed Phase Glottal Inverse Filtering Analysis With Weighted Linear Prediction

This study presents a new glottal inverse filtering (GIF) technique based on closed phase analysis over multiple fundamental periods. The proposed quasi closed phase (QCP) analysis method utilizes weighted linear prediction (WLP) with a specific attenuated main excitation (AME) weight function that attenuates the contribution of the glottal source in the linear prediction model optimization. This enables the use of the autocorrelation criterion in linear prediction in contrast to the covariance criterion used in conventional closed phase analysis. The QCP method was compared to previously developed methods by using synthetic vowels produced with the conventional source-filter model as well as with a physical modeling approach. The obtained objective measures show that the QCP method improves the GIF performance in terms of errors in typical glottal source parametrizations for both low- and high-pitched vowels. Additionally, QCP was tested in a physiologically oriented vocoder, where the analysis/synthesis quality was evaluated with a subjective listening test indicating improved perceived quality for normal speaking style.

THEME‐SEER: a multidimensional exploratory technique to analyze a structural model using an extended covariance criterion

In this work, we present a new approach to path modeling based on an extended multiple covariance criterion: system extended multiple covariance (SEMC). SEMC is suitable to measure the quality of any structural equations system. We show why SEMC may be preferred to criteria based on usual covariance of components and also to criteria based on residual sums of squares. We give a pursuit algorithm ensuring that SEMC increases and converges. When one wishes to extract more than one component per variable group, a problem arises of component hierarchy. To solve it, we define a local nesting principle of component models that makes the role of each component statistically clear. We then embed the pursuit algorithm in a more general algorithm that extracts sequences of locally nested models. We finally provide a component backward selection strategy. The technique is applied to cigarette data to model the generation of chemical compounds in smoke through tobacco combustion. Copyright © 2012 John Wiley & Sons, Ltd.

Diffractive optical elements with porous silicon layers

We investigate the basic chromatic properties of dispersive surface relief diffractive optical elements with porous silicon (PSi) layers. Rigorous and scalar wavelength-dependent diffraction efficiencies are juxtaposed and compared to reflection coefficients of uniform silicon and PSi layers. The application of the device as an enhanced sensor is discussed. A spectral covariance criterion for efficient evaluation of the spectral changes induced by analyte filling the pores is presented. Experimental results for the device reveal an increased spectral selectivity of the diffractively structured PSi layers compared to uniform PSi layers.

Exploring a physico-chemical multi-array explanatory model with a new multiple covariance-based technique: Structural equation exploratory regression

In this work, we consider chemical and physical variable groups describing a common set of observations (cigarettes). One of the groups, minor smoke compounds ( minSC), is assumed to depend on the others ( minSC predictors). PLS regression (PLSR) of m inSC on the set of all predictors appears not to lead to a satisfactory analytic model, because it does not take into account the expert’s knowledge. PLS path modeling (PLSPM) does not use the multidimensional structure of predictor groups. Indeed, the expert needs to separate the influence of several pre-designed predictor groups on minSC, in order to see what dimensions this influence involves. To meet these needs, we consider a multi-group component-regression model, and propose a method to extract from each group several strong uncorrelated components that fit the model. Estimation is based on a global multiple covariance criterion, used in combination with an appropriate nesting approach. Compared to PLSR and PLSPM, the structural equation exploratory regression (SEER) we propose fully uses predictor group complementarity, both conceptually and statistically, to predict the dependent group.

A covariant theory of negative phase velocity propagation

We develop a covariant criterion for negative phase velocity propagation, one that is robust to coordinate transformations in both space and spacetime, and can be applied to moving media. Conversely, the criterion used widely for static media, namely ( 1 / 2 ) R e ( E × H ∗ ) ⋅ k < 0 , is not covariant and can be satisfied by viewing a simple medium (characterized by rest-frame constitutive parameters ϵ , μ > 0 ) in a frame that moves faster than ( ϵ μ ) − 1 / 2 , the speed of light in the medium’s rest frame. Our covariant criterion also confirms that in the geometric optics limit negative refraction cannot occur in curved vacuum.

Author's reply to ‘Response to “On negative refraction in classical vacuum” ’

The ‘subregional frames’ considered by Mackay and Lakhtakia (ML) in their comment [Mackay, T.G.; Lakhtakia, A. J. Mod. Opt. 2007, 55, 323–328] to be noninertial within the ‘global perspective of curved spacetime’, are actually isomorphic to flat, inertial, Minkowski spacetime. Their claims of gravitationally induced vacuum negative refraction originate from the non-covariance of the criterion they used. When a covariant criterion is applied (as in [McCall, M.W. J. Mod. Opt., 2007, 54, 119–128; Phys. Rev. Lett. 2007, 98, 091102]) vacuum NPV does not occur. This argument is unaffected by noting that the sign changes of the metric eigenvalues were incorrectly stated in [McCall, M.W. J. Mod. Opt., 2007, 54, 119–128].

The significant digit law: a paradigm of statistical scale symmetries

In many different topics, the most significant digits of data series display a non-uniform distribution which points to an equiprobability of logarithms. This surprising ubiquitous property, known as the significant digit law, is shown here to follow from two similar, albeit different, scale symmetries: the scale-invariance and the scale-ratio invariance. After having legitimized these symmetries in the present context, the corresponding symmetric distributions are determined by implementing a covariance criterion. The logarithmic distribution is identified as the only distribution satisfying both symmetries. Attraction of other distributions to this most symmetric distribution by dilation, stretching and merging is investigated and clarified. The natures of both the scale-invariance and the scale-ratio invariance are further analyzed by determining the structure of the sets composed by the corresponding symmetric distributions. Altogether, these results provide new insights into the meaning and the role of scale symmetries in statistics.

Non‐linear partial least squares. Estimation of the weight vector

AbstractA key issue in non‐linear partial least squares (PLS) is the calculation of the weight vectors. The weight vector can be derived in a number of ways; for example, as in linear PLS, through an optimization routine as in error‐based non‐linear PLS, or through the covariance criterion as in Spline‐PLS. An alternative approach to the estimation of the weight vector in non‐linear PLS is proposed based on the theory of the weighted average, the reciprocal variance criterion. Unlike the covariance‐based criterion that gives equal consideration to both the response and the process variables in the calculation of the weight vector, the proposed approach gives emphasis to the response variables. The new weighting criterion performs well where the variability in the response variables can be captured by a few underlying phenomena. The methodology is illustrated through its application to simulated spectral data and an industrial NIR data set. It is shown that for the case studies the proposed approach outperforms the covariance criteria of PLS in terms of performance on a validation data set. Copyright © 2002 John Wiley &amp; Sons, Ltd.

Combining information for prediction in linear regression

This article deals with the prediction problem in linear regression where the measurements are obtained using k different devices or collected from k different independent sources. For the case of k=2, a Graybill-Deal type combined estimtor for the regression parameters is shown to dominate the individual least squares estimators under the covariance criterion. Two predictors ŷ c and ŷ p are proposed. ŷ c is based on a combined estimator of the regression coefficient vector, and ŷ p is obtained by combining the individual predictors from different models. Prediction mean square errors of both predictors are derived. It is shown that the predictor ŷ p is better than the individual predictors for k≥2 and the predictor ŷ c is better than the individual predictors for k=2. Numerical comparison between ŷ c and ŷ p shows that the former is superior to the latter for the case k=2.

Cherenkov radiation in a gravitational-wavebackground

A covariant criterion for the emission of Cherenkovradiation in the field of a nonlinear gravitational waveis considered within the framework of exact integrablemodels of particle dynamics and electromagnetic wavepropagation. It is shown that a vacuum interacting withcurvature can give rise to Cherenkov radiation. Theconically shaped spatial distribution of radiation isderived and its basic properties are discussed.

Multivariate co-inertia analysis for qualitative data by partial least squares

In this paper we propose a new strategy to study a dependence problem among qualitative variables, based upon 1) a generalization of the covariance criterion (Tucker, 1958), 2) a monotone regression in order to preserve the original ordering of categories on the axis of maximal covariance, and 3) the Partial Least Squares (PLS) approach (Wold, 1966) to compute the remaining axes. From a practical point of view, the use of a complete ordering of predictors can be considered as a way to extract more interpretable information Under the completer order constraint of the scores, different techniques have been proposed in literature, specifically within the context of optimal scaling (Nishisato, 1980; Nishisato and Arri, 1975).

Fast initialization for cascade-correlation learning

Weight initialization in the cascade-correlation learning is considered. Most of the previous studies use the so called candidate training to deal with the initialization problem in the cascade-correlation learning. There several candidate hidden units are first trained, and then the one yielding the best value for the covariance criterion is installed to the network. In case there are many candidate units to be trained, the total computational cost of the training can become very large. Here we consider a new approach for weight initialization in the cascade-correlation learning. The proposed method is based on the concept of stepwise regression. Empirical simulations show that the new method can significantly speed-up the cascade-correlation learning compared to the case where the candidate training is used. Moreover, the overall performance remained similar or was even better than with the candidate training.

SIMPLS: An alternative approach to partial least squares regression

De Jong, S., 1993. SIMPLS: an alternative approach to partial least squares regression. Chemometrics and Intelligent Laboratory Systems, 18: 251–263. A novel algorithm for partial least squares (PLS) regression, SIMPLS, is proposed which calculates the PLS factors directly as linear combinations of the original variables. The PLS factors are determined such as to maximize a covariance criterion, while obeying certain orthogonality and normalization restrictions. This approach follows that of other traditional multivariate methods. The construction of deflated data matrices as in the nonlinear iterative partial least squares (NIPALS)-PLS algorithm is avoided. For univariate y SIMPLS is equivalent to PLS1 and closely related to existing bidiagonalization algorithms. This follows from an analysis of PLS1 regression in terms of Krylov sequences. For multivariate Y there is a slight difference between the SIMPLS approach and NIPALS-PLS2. In practice the SIMPLS algorithm appears to be fast and easy to interpret as it does not involve a breakdown of the data sets.