Improvement of the prediction accuracy of polar motion using empirical mode decomposition

Previous studies revealed that the error of pole coordinate prediction will significantly increase for a prediction period longer than 100 days, and this is mainly caused by short period oscillations. Empirical mode decomposition （EMD）, which is increasingly popular and has advantages over classical wavelet decomposition, can be used to remove short period variations from observed time series of pole co- ordinates. A hybrid model combing EMD and extreme learning machine （ELM）, where high frequency signals are removed and processed time series is then modeled and predicted, is summarized in this paper. The prediction performance of the hybrid model is compared with that of the ELM-only method created from original time series. The results show that the proposed hybrid model outperforms the pure ELM method for both short-term and long-term prediction of pole coordinates. The improvement of prediction accuracy up to 360 days in the future is found to be 24.91% and 26.79% on average in terms of mean absolute error （MAE） for the xp and yp components of pole coordinates, respectively.

ON SEVERAL NEW METHODS TO POLAR DECOMPOSITION COMPUTATION

In this paper, the polar decomposition of a deformation gradient tensor is analyzed in detail. The four new methods for polar decompositioncomputation are given: (1) the iterated method, (2) the principal invariant's method, (3) the principal rotation axis' s method, (4) the coordinate transformation's method. The iterated method makes it possible to establish the nonlinear finite element method based on polar decomposition. Furthermore, the material time derivatives of the stretch tensor and the rotation tensor are obtained by explicit and simple expressions.

On Polar Decomposition of Tensors with Einstein Product and a Novel Iterative Parametric Method

This study aims to investigate the polar decomposition of tensors with the Einstein product for thefirst time.The polar decomposition of tensors can be computed using the singular value decomposition of the tensors with the Einstein product.In the following,some iterative methods forfinding the polar decomposi-tion of matrices have been developed into iterative methods to compute the polar decomposition of tensors.Then,we propose a novel parametric iterative method tofind the polar decomposition of tensors.Under the obtained conditions,we prove that the proposed parametric method has the order of convergence four.In every iteration of the proposed method,only four Einstein products are required,while other iterative methods need to calculate multiple Einstein products and one tensor inversion in each iteration.Thus,the new method is superior in terms of efficiency index.Finally,the numerical comparisons performed among several well-known methods,show that the proposed method is remarkably efficient and accurate.

Polar Decomposition-based Algorithms on the Product of Stiefel Manifolds with Applications in Tensor Approximation

In this paper,we propose a general algorithmic framework to solve a class of optimization problems on the product of complex Stiefel manifolds based on the matrix polar decomposition.We establish the weak convergence,global convergence and linear convergence properties,respectively,of this general algorithmic approach using theŁojasiewicz gradient inequality and the Morse–Bott property.This general algorithmic approach and its convergence results are applied to the simultaneous approximate tensor diagonalization problem and the simultaneous approximate tensor compression problem,which include as special cases the low rank orthogonal approximation,best rank-1 approximation and low multilinear rank approximation for higher order complex tensors.We also present a variant of this general algorithmic framework to solve a symmetric version of this class of optimization models,which essentially optimizes over a single Stiefel manifold.We establish its weak convergence,global convergence and linear convergence properties in a similar way.This symmetric variant and its convergence results are applied to the simultaneous approximate symmetric tensor diagonalization,which includes as special cases the low rank symmetric orthogonal approximation and best symmetric rank-1 approximation for higher order complex symmetric tensors.It turns out that well-known algorithms such as LROAT,S-LROAT,HOPM and S-HOPM are all special cases of this general algorithmic framework and its symmetric variant,and our convergence results subsume the results found in the literature designed for those special cases.All the algorithms and convergence results in this paper are straightforwardly applicable to the real case.

Forest type identification by random forest classification combined with SPOT and multitemporal SAR data

We developed a forest type classification technology for the Daxing＇an Mountains of northeast China using multisource remote sensing data.A SPOT-5 image and two temporal images of RADARSAT-2 full-polarization SAR were used to identify forest types in the Pangu Forest Farm of the Daxing＇an Mountains.Forest types were identified using random forest（RF） classification with the following data combination types： SPOT-5 alone,SPOT-5 and SAR images in August or November,and SPOT-5 and two temporal SAR images.We identified many forest types using a combination of multitemporal SAR and SPOT-5 images,including Betula platyphylla,Larix gmelinii,Pinus sylvestris and Picea koraiensis forests.The accuracy of classification exceeded 88% and improved by 12% when compared to the classification results obtained using SPOT data alone.RF classification using a combination of multisource remote sensing data improved classification accuracy compared to that achieved using single-source remote sensing data.

Weighted Polar Decomposition

In this paper,a new matrix decomposition called the weighted polar decomposition is considered.Two uniqueness theorems of weighted polar decomposition are presented,and the best approximation property of weighted unitary polar factor and perturbation bounds for weighted polar decomposition are also studied.

APPLICATION OF TWO OPERATORS TRANSFORM FROM CLASS A OPERATOR TO THE CLASS OF HYPONORMAL OPERATOR

In this article, we give an operator transform T （＊） from class A operator to the class of hyponormal operators. It is different from the operator transform T defined by M. Ch and T. Yamazaki. Then, we show that σ（T ） = σ（ T （＊）） and σa（T ）／{0} = σa（ T （＊））／{0}, in case T belongs to class A. Next, we obtain some relations between T and T （9）.

ON THE CRITICAL POINTS OF THE MAP F_p:X→‖AXB-C‖_p^p

Suppose A,B and C are the bounded linear operators on a Hilbert space H, when A has a generalized inverse A - such that (AA -) *=AA - and B has a generalized inverse B - such that (B -B) *=B -B,the general characteristic forms for the critical points of the map F p:X→‖ A X B-C ‖ p p (1<p<∞), have been obtained, it is a generalization for P J Maher's result about p=2. Similarly, the same question has been discussed for several operators.

Further Extension of the Relations between Two Operator Inequalities

In this paper,we give out a further extension of the relations between two famous inequalities(B r 2 A p B r 2) r p+r≥B r and Ap≥(A p 2 B r A p 2) p p+r,which can yield the result of Yamazaki and Yanagida's.

Two Combinations of Unitary Operators and Frame Representations

In this paper, we prove that the norm closure of all linear combinations of two unitary operators is equal to the norm closure of all invertible operators in B(H). We apply the results to frame representations and give some simple and alternative proofis of the propositions in 'P. G. Casazza, Every frame is a sum of three (but not two) orthonormal bases-and other frame representations, J. Fourier Anal. Appl., 4(6)(1998), 727-732.'

On the classification of mixed floating pollutants on the Yellow Sea of China by using a quad-polarized SAR image

This study explored different methodologiesusing a C-band RADARSAT-2 quad-polarized SyntheticAperture Radar （SAR） image located over China＇s YellowSea to investigate polarization decomposition parametersfor identifying mixed floating pollutants from a complexocean background. It was found that solitary polarizationdecomposition did not meet the demand for detecting andclassifying multiple floating pollutants, even after applyinga polarized SAR image. Furthermore, considering thatYamaguchi decomposition is sensitive to vegetation andthe algal variety Enteromorpha prolifera, while H/A/alphadecomposition is sensitive to oil spills, a combination ofparameters which was deduced from these two decom-positions was proposed for marine environmental mon-itoring of mixed floating sea surface pollutants. Acombination of volume scattering, surface scattering, andscattering entropy was the best indicator for classifyingmixed floating pollutants from a complex ocean back-ground. The Kappa coefficients for Enteromorpha pro-lifera and oil spills were 0.7514 and 0.8470, respectively,evidence that the composite polarized parameters based onquad-polarized SAR imagery proposed in this research isan effective monitoring method for complex marinepollution.

Binormal Operator and *-Aluthge Transformation

Let T = U｜T｜ be the polar decomposition of a bounded linear operator T on a Hilbert space. The transformation T = ｜T｜^1/2 U｜T｜^1/2 is called the Aluthge transformation and Tn means the n-th Aluthge transformation. Similarly, the transformation T（＊）=｜T＊｜^1/2 U｜T＊｜＆1/2 is called the ＊-Aluthge transformation and Tn^（＊） means the n-th ＊-Aluthge transformation. In this paper, firstly, we show that T（＊） = UV｜T^（＊）｜ is the polar decomposition of T（＊）, where ｜T｜^1/2 ｜T^＊｜^1/2 = V｜｜T｜^1/2 ｜T^＊｜^1/2｜ is the polar decomposition. Secondly, we show that T（＊） = U｜T^（＊）｜ if and only if T is binormal, i.e., [｜T｜, ｜T^＊｜]=0, where [A, B] = AB - BA for any operator A and B. Lastly, we show that Tn^（＊） is binormal for all non-negative integer n if and only if T is centered, and so on.

Conversion algorithm for MPRM expansion

Conversion of the Reed–Muller（RM） expansion between two different polarities is an important step in the synthesis and optimization of RM circuits. By investigating XOR decomposition, a new conversion algorithm is proposed to convert MPRM expansion from one polarity to another. First, the relationship between XOR decomposition and mixed polarity is set up. Second, based on this, the operation relation of term coefficients between the two polarities is derived to realize MPRM expansion conversion. And finally, with the MCNC Benchmark, the resultsofouralgorithmshowthatitismoresuitablefordealingwithMPRMexpansionwithmoreterms.Compared to the previous tabular technique, the conversion efficiency is improved up to approximately 44.39%.

Spectral Animation Compression

This paper presents a spectral approach to compress dynamic animation consisting of a sequence of homeomorphic manifold meshes. Our new approach directly compresses the field of deformation gradient defined on the surface mesh, by decomposing it into rigid-body motion （rotation） and non-rigid-body deformation （stretching） through polar decomposition. It is known that the rotation group has the algebraic topology of 3D ring, which is different from other operations like stretching. Thus we compress these two groups separately, by using Manifold Harmonics Transform to drop out their high-frequency details. Our experimental result shows that the proposed method achieves a good balance between tile reconstruction quality and the compression ratio. We compare our results quantitatively with other existing approaches on animation compression, using standard measurement criteria.

A Note on the Perturbation Bound of Q-factors

In this note we present a perturbation bound of unitary polar factors.We add the orthogonalprojectors into the bound;as a result,a uniform perturbation bound of Q-factors is obtained,and the previousbounds are improved.