Algorithms and statistical analysis for linear structured weighted total least squares problem

Weighted total least squares(WTLS)have been regarded as the standard tool for the errors-in-variables(EIV)model in which all the elements in the observation vector and the coefficient matrix are contaminated with random errors.However,in many geodetic applications,some elements are error-free and some random observations appear repeatedly in different positions in the augmented coefficient matrix.It is called the linear structured EIV(LSEIV)model.Two kinds of methods are proposed for the LSEIV model from functional and stochastic modifications.On the one hand,the functional part of the LSEIV model is modified into the errors-in-observations(EIO)model.On the other hand,the stochastic model is modified by applying the Moore-Penrose inverse of the cofactor matrix.The algorithms are derived through the Lagrange multipliers method and linear approximation.The estimation principles and iterative formula of the parameters are proven to be consistent.The first-order approximate variance-covariance matrix(VCM)of the parameters is also derived.A numerical example is given to compare the performances of our proposed three algorithms with the STLS approach.Afterwards,the least squares(LS),total least squares(TLS)and linear structured weighted total least squares(LSWTLS)solutions are compared and the accuracy evaluation formula is proven to be feasible and effective.Finally,the LSWTLS is applied to the field of deformation analysis,which yields a better result than the traditional LS and TLS estimations.

Geographically and Temporally Weighted Regression in Assessing Dengue Fever Spread Factors in Yunnan Border Regions

Objective This study employs the Geographically and Temporally Weighted Regression(GTWR)model to assess the impact of meteorological elements and imported cases on dengue fever outbreaks,emphasizing the spatial-temporal variability of these factors in border regions.Methods We conducted a descriptive analysis of dengue fever’s temporal-spatial distribution in Yunnan border areas.Utilizing annual data from 2013 to 2019,with each county in the Yunnan border serving as a spatial unit,we constructed a GTWR model to investigate the determinants of dengue fever and their spatio-temporal heterogeneity in this region.Results The GTWR model,proving more effective than Ordinary Least Squares(OLS)analysis,identified significant spatial and temporal heterogeneity in factors influencing dengue fever’s spread along the Yunnan border.Notably,the GTWR model revealed a substantial variation in the relationship between indigenous dengue fever incidence,meteorological variables,and imported cases across different counties.Conclusion In the Yunnan border areas,local dengue incidence is affected by temperature,humidity,precipitation,wind speed,and imported cases,with these factors’influence exhibiting notable spatial and temporal variation.

Operational optimization of copper flotation process based on the weighted Gaussian process regression and index-oriented adaptive differential evolution algorithm

Concentrate copper grade(CCG)is one of the important production indicators of copper flotation processes,and keeping the CCG at the set value is of great significance to the economic benefit of copper flotation industrial processes.This paper addresses the fluctuation problem of CCG through an operational optimization method.Firstly,a density-based affinity propagationalgorithm is proposed so that more ideal working condition categories can be obtained for the complex raw ore properties.Next,a Bayesian network(BN)is applied to explore the relationship between the operational variables and the CCG.Based on the analysis results of BN,a weighted Gaussian process regression model is constructed to predict the CCG that a higher prediction accuracy can be obtained.To ensure the predicted CCG is close to the set value with a smaller magnitude of the operation adjustments and a smaller uncertainty of the prediction results,an index-oriented adaptive differential evolution(IOADE)algorithm is proposed,and the convergence performance of IOADE is superior to the traditional differential evolution and adaptive differential evolution methods.Finally,the effectiveness and feasibility of the proposed methods are verified by the experiments on a copper flotation industrial process.

THE WEIGHTED KATO SQUARE ROOT PROBLEMOF ELLIPTIC OPERATORS HAVING A BMOANTI-SYMMETRICPART

Let n≥2 and let L be a second-order elliptic operator of divergence form with coefficients consisting of both an elliptic symmetric part and a BMO anti-symmetric part in ℝ^(n).In this article,we consider the weighted Kato square root problem for L.More precisely,we prove that the square root L^(1/2)satisfies the weighted L^(p)estimates||L^(1/2)(f)||L_(ω)^p(R^(n))≤C||■f||L_(ω)^p(R^(n);R^(n))for any p∈(1,∞)andω∈Ap(ℝ^(n))(the class of Muckenhoupt weights),and that||■f||L_(ω)^p(R^(n);R^(n))≤C||L^(1/2)(f)||L_(ω)^p(R^(n))for any p∈(1,2+ε)andω∈Ap(ℝ^(n))∩RH_(2+ε/p),(R^(n))(the class of reverse Hölder weights),whereε∈(0,∞)is a constant depending only on n and the operator L,and where(2+ε/p)'denotes the Hölder conjugate exponent of 2+ε/p.Moreover,for any given q∈(2,∞),we give a sufficient condition to obtain that||■f||L_(ω)^p(R^(n);R^(n))≤C||L^(1/2)(f)||L_(ω)^p(R^(n))for any p∈(1,q)andω∈A_(p)(R^(n))∩pRH_(q/p),(R^(n)).As an application,we prove that when the coefficient matrix A that appears in L satisfies the small BMO condition,the Riesz transform∇L^(−1/2)is bounded on L_(ω)^(p)(ℝ^(n))for any given p∈(1,∞)andω∈Ap(ℝ^(n)).Furthermore,applications to the weighted L^(2)-regularity problem with the Dirichlet or the Neumann boundary condition are also given.

Exploring spatial non-stationarity of near-miss ship collisions from AIS data under the influence of sea fog using geographically weighted regression:A case study in the Bohai Sea,China

Sea fog is a disastrous weather phenomenon,posing a risk to the safety of maritime transportation.Dense sea fogs reduce visibility at sea and have frequently caused ship collisions.This study used a geographically weighted regression(GWR)model to explore the spatial non-stationarity of near-miss collision risk,as detected by a vessel conflict ranking operator(VCRO)model from automatic identification system(AIS)data under the influence of sea fog in the Bohai Sea.Sea fog was identified by a machine learning method that was derived from Himawari-8 satellite data.The spatial distributions of near-miss collision risk,sea fog,and the parameters of GWR were mapped.The results showed that sea fog and near-miss collision risk have specific spatial distribution patterns in the Bohai Sea,in which near-miss collision risk in the fog season is significantly higher than that outside the fog season,especially in the northeast(the sea area near Yingkou Port and Bayuquan Port)and the southeast(the sea area near Yantai Port).GWR outputs further indicated a significant correlation between near-miss collision risk and sea fog in fog season,with higher R-squared(0.890 in fog season,2018),than outside the fog season(0.723 in non-fog season,2018).GWR results revealed spatial non-stationarity in the relationships between-near miss collision risk and sea fog and that the significance of these relationships varied locally.Dividing the specific navigation area made it possible to verify that sea fog has a positive impact on near-miss collision risk.

Tricube Weighted Linear Regression and Interquartile for Cloud Infrastructural Resource Optimization

Cloud infrastructural resource optimization is the process of precisely selecting the allocating the correct resources either to a workload or application.When workload execution,accuracy,and cost are accurately stabilized in opposition to the best possible framework in real-time,efficiency is attained.In addition,every workload or application required for the framework is characteristic and these essentials change over time.But,the existing method was failed to ensure the high Quality of Service(QoS).In order to address this issue,a Tricube Weighted Linear Regression-based Inter Quartile(TWLR-IQ)for Cloud Infrastructural Resource Optimization is introduced.A Tricube Weighted Linear Regression is presented in the proposed method to estimate the resources(i.e.,CPU,RAM,and network bandwidth utilization)based on the usage history in each cloud server.Then,Inter Quartile Range is applied to efficiently predict the overload hosts for ensuring a smooth migration.Experimental results show that our proposed method is better than the approach in Cloudsim under various performance metrics.The results clearly showed that the proposed method can reduce the energy consumption and provide a high level of commitment with ensuring the minimum number of Virtual Machine(VM)Migrations as compared to the state-of-the-art methods.

Revisiting Akaike’s Final Prediction Error and the Generalized Cross Validation Criteria in Regression from the Same Perspective: From Least Squares to Ridge Regression and Smoothing Splines

In regression, despite being both aimed at estimating the Mean Squared Prediction Error (MSPE), Akaike’s Final Prediction Error (FPE) and the Generalized Cross Validation (GCV) selection criteria are usually derived from two quite different perspectives. Here, settling on the most commonly accepted definition of the MSPE as the expectation of the squared prediction error loss, we provide theoretical expressions for it, valid for any linear model (LM) fitter, be it under random or non random designs. Specializing these MSPE expressions for each of them, we are able to derive closed formulas of the MSPE for some of the most popular LM fitters: Ordinary Least Squares (OLS), with or without a full column rank design matrix;Ordinary and Generalized Ridge regression, the latter embedding smoothing splines fitting. For each of these LM fitters, we then deduce a computable estimate of the MSPE which turns out to coincide with Akaike’s FPE. Using a slight variation, we similarly get a class of MSPE estimates coinciding with the classical GCV formula for those same LM fitters.

Weighted Maximum Likelihood Technique for Logistic Regression

In this paper, a weighted maximum likelihood technique (WMLT) for the logistic regression model is presented. This method depended on a weight function that is continuously adaptable using Mahalanobis distances for predictor variables. Under the model, the asymptotic consistency of the suggested estimator is demonstrated and properties of finite-sample are also investigated via simulation. In simulation studies and real data sets, it is observed that the newly proposed technique demonstrated the greatest performance among all estimators compared.

Prediction of earth rotation parameters based on improved weighted least squares and autoregressive model

In this paper, an improved weighted least squares （WLS）, together with autoregressive （AR） model, is proposed to improve prediction accuracy of earth rotation parameters（ERP）. Four weighting schemes are developed and the optimal power e for determination of the weight elements is studied. The results show that the improved WLS-AR model can improve the ERP prediction accuracy effectively, and for different prediction intervals of ERP, different weight scheme should be chosen.

Discrimination of Transgenic Rice Based on Near Infrared Reflectance Spectroscopy and Partial Least Squares Regression Discriminant Analysis

Near infrared reflectance spectroscopy （NIRS）, a non-destructive measurement technique, was combined with partial least squares regression discrimiant analysis （PLS-DA） to discriminate the transgenic （TCTP and mi166） and wild type （Zhonghua 11） rice. Furthermore, rice lines transformed with protein gene （OsTCTP） and regulation gene （Osmi166） were also discriminated by the NIRS method. The performances of PLS-DA in spectral ranges of 4 000-8 000 cm-1 and 4 000-10 000 cm-1 were compared to obtain the optimal spectral range. As a result, the transgenic and wild type rice were distinguished from each other in the range of 4 000-10 000 cm-1, and the correct classification rate was 100.0% in the validation test. The transgenic rice TCTP and mi166 were also distinguished from each other in the range of 4 000-10 000 cm-1, and the correct classification rate was also 100.0%. In conclusion, NIRS combined with PLS-DA can be used for the discrimination of transgenic rice.

Estimating Wheat Grain Protein Content Using Multi-Temporal Remote Sensing Data Based on Partial Least Squares Regression

Estimating wheat grain protein content by remote sensing is important for assessing wheat quality at maturity and making grains harvest and purchase policies. However, spatial variability of soil condition, temperature, and precipitation will affect grain protein contents and these factors usually cannot be monitored accurately by remote sensing data from single image. In this research, the relationships between wheat protein content at maturity and wheat agronomic parameters at different growing stages were analyzed and multi-temporal images of Landsat TM were used to estimate grain protein content by partial least squares regression. Experiment data were acquired in the suburb of Beijing during a 2-yr experiment in the period from 2003 to 2004. Determination coefficient, average deviation of self-modeling, and deviation of cross- validation were employed to assess the estimation accuracy of wheat grain protein content. Their values were 0.88, 1.30%, 3.81% and 0.72, 5.22%, 12.36% for 2003 and 2004, respectively. The research laid an agronomic foundation for GPC （grain protein content） estimation by multi-temporal remote sensing. The results showed that it is feasible to estimate GPC of wheat from multi-temporal remote sensing data in large area.

LEAST SQUARES ESTIMATION FOR ORNSTEIN-UHLENBECK PROCESSES DRIVEN BY THE WEIGHTED FRACTIONAL BROWNIAN MOTION

In this article, we study a least squares estimator （LSE） of θ for the Ornstein- Uhlenbeck process X0=0,dXt=θXtdt＋dBt^ab, t ≥ 0 driven by weighted fractional Brownian motion B^a,b with parameters a, b. We obtain the consistency and the asymptotic distribution of the LSE based on the observation {Xs, s∈[0,t]} as t tends to infinity.

Constrained Weighted Least Squares Location Algorithm Using Received Signal Strength Measurements

Determine the location of a target has gained considerable interest over the past few years. The Received Signal Strength(RSS) measurements and Differential RSS(DRSS) measurements can be converted to distance or distance ratio estimates for constructing a set of linear equations. Based on these linear equations, a constrained weighted least Squares(CWLS) algorithm for target localization is derived. In addition, an iterative technique based on Newton's method is utilized to give a solution. The covariance and bias of the CWLS algorithm is derived using perturbation analysis. Simulation shows that the proposed estimator achieves better performance than existing algorithms with reasonable complexity.

Improved adaptive pruning algorithm for least squares support vector regression

As the solutions of the least squares support vector regression machine （LS-SVRM） are not sparse, it leads to slow prediction speed and limits its applications. The defects of the ex- isting adaptive pruning algorithm for LS-SVRM are that the training speed is slow, and the generalization performance is not satis- factory, especially for large scale problems. Hence an improved algorithm is proposed. In order to accelerate the training speed, the pruned data point and fast leave-one-out error are employed to validate the temporary model obtained after decremental learning. The novel objective function in the termination condition which in- volves the whole constraints generated by all training data points and three pruning strategies are employed to improve the generali- zation performance. The effectiveness of the proposed algorithm is tested on six benchmark datasets. The sparse LS-SVRM model has a faster training speed and better generalization performance.

Spatial Downscaling of the Tropical Rainfall Measuring Mission Precipitation Using Geographically Weighted Regression Kriging over the Lancang River Basin, China

Satellite-based precipitation products have been widely used to estimate precipitation, especially over regions with sparse rain gauge networks. However, the low spatial resolution of these products has limited their application in localized regions and watersheds.This study investigated a spatial downscaling approach, Geographically Weighted Regression Kriging(GWRK), to downscale the Tropical Rainfall Measuring Mission(TRMM) 3 B43 Version 7 over the Lancang River Basin(LRB) for 2001–2015. Downscaling was performed based on the relationships between the TRMM precipitation and the Normalized Difference Vegetation Index(NDVI), the Land Surface Temperature(LST), and the Digital Elevation Model(DEM). Geographical ratio analysis(GRA) was used to calibrate the annual downscaled precipitation data, and the monthly fractions derived from the original TRMM data were used to disaggregate annual downscaled and calibrated precipitation to monthly precipitation at 1 km resolution. The final downscaled precipitation datasets were validated against station-based observed precipitation in 2001–2015. Results showed that: 1) The TRMM 3 B43 precipitation was highly accurate with slight overestimation at the basin scale(i.e., CC(correlation coefficient) = 0.91, Bias = 13.3%). Spatially, the accuracies of the upstream and downstream regions were higher than that of the midstream region. 2) The annual downscaled TRMM precipitation data at 1 km spatial resolution obtained by GWRK effectively captured the high spatial variability of precipitation over the LRB. 3) The annual downscaled TRMM precipitation with GRA calibration gave better accuracy compared with the original TRMM dataset. 4) The final downscaled and calibrated precipitation had significantly improved spatial resolution, and agreed well with data from the validated rain gauge stations, i.e., CC = 0.75, RMSE(root mean square error) = 182 mm, MAE(mean absolute error) = 142 mm, and Bias = 0.78%for annual precipitation and CC = 0.95, RMSE = 25 mm, MAE = 16 mm, and Bias = 0.67% for monthly precipitation.

Travel Behaviours of Sharing Bicycles in the Central Urban Area Based on Geographically Weighted Regression: The Case of Guangzhou, China

Mobile information and communication technologies(MICTs) have fully penetrated everyday life in smart societies;this has greatly compressed time, space, and distance, and consequently, reshaped residents’ travel behaviour patterns. As a new mode of shared mobility, the sharing bicycle offers a variety of options for the daily travel of urban residents. Extant studies have mainly examined the travel characteristics and influencing factors of public bicycles with piles, while the travel patterns for sharing bicycles and their driving mechanisms have been largely ignored. Using one week’s travel data for Mobike, this study investigated the spatial and temporal distribution patterns of sharing bicycle travel behaviours in the central urban area of Guangzhou, China;furthermore, it identified the influences of built environment density factors on sharing bicycle travel behaviours based on the geographically weighted regression method. Obvious morning and evening peaks were observed in the sharing bicycle travel patterns for both weekdays and weekends. The old urban area, which had a high degree of mixed function, dense road networks, and cycling-friendly built environments, was the main travel area that attracted sharing bicycles on both weekdays and weekends. Furthermore, factors including the point of interest(POI) for the density of public transport stations, the functional mixing degree, and the density of residential POIs significantly affected residents’ travel behaviours. These findings could enrich discourse regarding shared mobility with a Chinese case characterised by rapidly developing MICTs and also provide references to local authorities for improving slow traffic environments.

ADAPTIVE FUSION ALGORITHMS BASED ON WEIGHTED LEAST SQUARE METHOD

Weighted fusion algorithms, which can be applied in the area of multi-sensor data fusion, are advanced based on weighted least square method. A weighted fusion algorithm, in which the relationship between weight coefficients and measurement noise is established, is proposed by giving attention to the correlation of measurement noise. Then a simplified weighted fusion algorithm is deduced on the assumption that measurement noise is uncorrelated. In addition, an algorithm, which can adjust the weight coefficients in the simplified algorithm by making estimations of measurement noise from measurements, is presented. It is proved by emulation and experiment that the precision performance of the multi-sensor system based on these algorithms is better than that of the multi-sensor system based on other algorithms.

Weak Type Estimates for Intrinsic Square Functions on Weighted Morrey Spaces

In this paper, we will obtain the weak type estimates of intrinsic square func- tions including the Lusin area integral, Littlewood-Paley g-function and g^-function on the weighted Morrey spaces L^1,k （w） for 0〈k〈 1 and w ∈ A1.

Novel passive localization algorithm based on weighted restricted total least square

A novel multi-observer passive localization algorithm based on the weighted restricted total least square （WRTLS） is proposed to solve the bearings-only localization problem in the presence of observer position errors. Firstly, the unknown matrix perturbation information is utilized to form the WRTLS problem. Then, the corresponding constrained optimization problem is transformed into an unconstrained one, which is a generalized Rayleigh quotient minimization problem. Thus, the solution can be got through the generalized eigenvalue decomposition and requires no initial state guess process. Simulation results indicate that the proposed algorithm can approach the Cramer-Rao lower bound （CRLB）, and the localization solution is asymptotically unbiased.

Preconditioned iterative methods for solving weighted linear least squares problems

A class of preconditioned iterative methods, i.e., preconditioned generalized accelerated overrelaxation （GAOR） methods, is proposed to solve linear systems based on a class of weighted linear least squares problems. The convergence and comparison results are obtained. The comparison results show that the convergence rate of the preconditioned iterative methods is better than that of the original methods. Furthermore, the effectiveness of the proposed methods is shown in the numerical experiment.