Least Median Of Squares Research Articles

Robust Image Stitching and Reconstruction of Rolling Stocks Using a Novel Kalman Filter With a Multiple-Hypothesis Measurement Model

This work introduces a novel algorithm for the reconstruction of rolling stocks from a sequence of images. The research aims at producing an accurate and wide image model that can be used as a Digital Twin (DT) for diagnosis, fault prediction, maintenance, and other monitoring operations. When observing large surfaces with nearly constant textures, metallic reflections, and repetitive patterns, motion estimation algorithms based on whole image error minimization and feature pairing with Random Sampling and Consensus(RANSAC) or Least Median of Squares (LMedS) fail to provide appropriate associations. To overcome such an issue, we propose a custom Kalman Filter (KF) modified by adding multiple input-noise sources represented as a Gaussian mixture distribution (GM), and specific algorithms to select appropriate data and variance to use for state prediction and correction. The proposed algorithm has been tested on images of train vessels, having a high number of windows, and large metallic paintings with constant or repetitive patterns. The approach here presented showed to be robust in the presence of high environmental disturbances and a reduced number of features. A large set of rolling stocks has been collected during a six months campaign. The set was employed to demonstrate the validity of the proposed algorithm by comparing the reconstructed twin versus known data. The system showed an overall accuracy in length estimation above 99%.

LMedS-Based Power Regression: An Optimal and Automatic Method of Radiometric Intercalibration for DMSP-OLS NTL Imagery

The further scientific applications of DMSP-OLS night-time light (NTL) imagery have been being limited by the accuracy, automation, and speed of radiometric intercalibration. In order to solve the aforementioned problems, this article is the first to propose a new least-median-of-squares (LMedS)-based power regression (LBPR) for automatically radiometric intercalibration and investigate the reasons for the optimal model of radiometric intercalibration, especially those based on the Taylor expansion and probability principle. NTL data in six regions all over the world, from 1994 and 1997 to 2007, were used as the test datasets. When the five kinds of LMedS-based radiometric intercalibration models (i.e., linear, quadratic, power, exponential, and logarithmic regression) are synthetically compared in absolute accuracy (adjusted RMSE) and running speed, it is concluded that the LBPR, which has the highest accuracy and preferable running speed, is recommended as the optimal method, which can also be used as a reference for other types of imagery preprocessing.

Estimate The Parameters in Presence of Multicollinearity And Outliers Using Bisquare Weighted Ridge Least Median Squares Regression (wrlms)

The presence of multicollinearity and outliers are classical problems of data within the linear regression framework. We are going to present a proposal of a new method which can be a potential candidate for robust ridge regression as well as a robust detection of multicollinearity. This proposal arises as a logical combination of principles used in the ridge regression and the Bisquare weighted function. The technique of the Least Median of Squares (LMS) is used for the sake of overcoming the resulting regression problems. This paper investigates the non-resistance of Ordinary Least Square (OLS) to multicollinearity and outliers and proposes the utilization of robust regression for instance, Least Median Squares LMS to detect non-normality of residuals, the use of robust methods yields more reliable trend estimations and outlier detection. LMS is introduced as a robust regression technique and through medical application its effect on regression is discussed. The numerical example and simulation study shows that the outcome of the Weighted Ridge Least Median Squares (WRLMS) is better than other estimators in terms of its efficiency. This has been done by utilizing both Standard Error (SE) and the Root Mean Squared Error criterion for the numerical example and simulation study, respectively as far as a lot of combinations of error distribution and degree of multicollinearity are concerned.

Iteratively reweighted total least squares for PEIV model

The weighted total least-squares (WTLS) estimate for the partial EIV (PEIV) model is very susceptible to outliers. In view of outliers in observations and coefficient matrix, a robust estimate of WTLS which makes using of iteratively reweighted technique (IRTLS) for the PEIV model is developed by combining a new two-step iterated algorithm of the WTLS estimate with the sensitivity-analysis based on the robust M-estimation. The uniformly most powerful test statistics are constructed to determine the down-weighting factor and the variance of unit weight is estimated by least median squares (LMS) method possessing high break-down point. Depended on the PEIV model, two different down-weighting schemes are presented. In the first scheme down-weighting is only implemented for the coefficient matrix and not for observations when the elements of the coefficient matrix are estimated, and the second scheme is contrary. The most attractive aspect is that the suggested computational formulae are the same with the traditional robust least-squares (LS) methods. The two-dimensional affine transformation and liner fitting example are analyzed, and some comparisons are performed with different available weight functions. The proposed approach (Scheme 1) proves to be a powerful tool in detecting outliers for the PEIV model.

Modelling Tap Water Consumer Ratio

Increasing population and the rising air temperatures are known as factors that cause water depletion in the watersheds. Therefore, it is important to accurately predict the future ratios of tap water consumers using the same watershed to the population living in the specified area, to produce better water policies and to take the necessary measures. Predictions can be made by a growth curve model (GCM). Parameter estimations of the GCM are usually based on the ordinary least square (OLS) estimator. However, the outlier presence affects the estimations and the predictions, which are obtained by using the estimated model. The present article attempts to construct first- and third-order GCMs with robust least median square (LMS) and M estimators to make short-term predictions of ratios of tap water consumers. According to the findings, parameter estimations of the models, the outliers, and the predictions vary with respect to the estimators. The M estimator for short-term predictions is suggested for use, due to its robustness against outlier points.

Analysis of Efficiency of Least Trimmed Square and Least Median Square Methods in The Estimation of Robust Regression Parameters

<span lang="EN">Robust regression is a regression method used when the remainder's distribution is not reasonable, or there is an outreach to observational data that affects the model. One method for estimating regression parameters is the Least Squares Method (MKT). The method is easily affected by the presence of outliers. Therefore we need an alternative method that is robust to the presence of outliers, namely robust regression. Methods for estimating robust regression parameters include Least Trimmed Square (LTS) and Least Median Square (LMS). These methods are estimators with high breakdown points for outlier observational data and have more efficient algorithms than other estimation methods. This study aims to compare the regression models formed from the LTS and LMS methods, determine the efficiency of the model formed, and determine the factors that influence the production of community oil palm in Langkat District in 2018. The results showed that in testing, the estimated model of the regression parameters showed the same results. Compared to the efficiency estimator and the error square value, it was concluded that the LTS method was more efficient. Variable land area and productivity influence the production of palm oil smallholders in Langkat District in 2018. as well as the comparison of the efficiency estimator and the error square value, it was concluded that the LTS method was more efficient. Variable land area and productivity are factors that influence the production of palm oil smallholders in Langkat District in 2018. as well as the comparison of the efficiency estimator and the error square value, it was concluded that the LTS method was more efficient. Variable land area and productivity are factors that influence the production of palm oil smallholders in Langkat District in 2018</span>

Effect of outliers on the coefficient of determination in multiple regression analysis with the application on the GPA for student

The study aims to solve the problem of contradiction between the statistical significance and real significance of regression parameters , when using multiple linear regression analysis . In this regard, an algorithm was presented based on the simple and multiple of determination coefficient , and the sum of averages to estimate multiple outliers, when outliers are real . Regression analysis was applied to a phenomenon, whose results are known in advance (The relationship between Semester average and Cumulative average). The results were misleading and we cannot firmly stand on analysis results. Also the regression model did not improve much, when increase sample size more than doubled , so the study presents an algorithm for finding a solution to this contradiction. After checking Ordinary Least Squares (OLS) assumptions, outliers were identified, based on Cook's distance because it was the best. The proposed algorithm was compared with some robust regression methods, [Weighted Least Squares , Fully Modified Least Squares and Least Median of Squares]. The results proved that the proposed method is a robust solution for outliers’ estimation, therefore, it is recommended to using the proposed algorithm to estimate multiple outliers on others similar phenomena, (E.g. The algorithm can be applied to a credit card transaction control system in a bank). And also doing designing software Packages statistical for proposed algorithm. Also the novelty of this study can be observed by investigating testing the significance of outliers as most of the previous researchers were interested diagnosis the outliers, without checking its significance.

On the total least median of squares adjustment for the pattern recognition in point clouds

Robust estimation techniques are an important tool in the adjustment of geodetic data, as even a single undetected gross error can render parameters estimates meaningless. In this contribution, the total least median of squares (TLMS) adjustment is investigated. Unlike typical least median of squares (LMS) criterion, which operates on observation errors, the TLMS strategy focuses on equation errors, which is expressed as a linear combination of the observation vector and the columns of the design matrix. TLMS is numerically implemented by the combinatorial strategy, and can speed up by the Monte Carlo acceleration for any large data set. Finally, we demonstrate that the proposed method resists multiple outliers for the pattern recognition in point clouds, even in the presence of cluster and collinear outliers, and the comparison to other methods and the statistical assessment are also presented.

Spatiotemporal shoreline change in Boushehr Province coasts, Iran

Since coastal areas have highly dynamic nature and are one of the most beneficial regions of civilizations, it is of great significance to understand their characteristics and behavior. Changes in shorelines in the form of accretion and erosion can leave devastating effects on businesses and cities located along the shore. In this study, we statistically calculated the tendency of shoreline changes by processing and analyzing historical satellite images of Boushehr Province, Iran. Results show that these shores have experienced both sedimentation and erosion in the past 30 years. Net shoreline movement presents more than 350 m of erosion and 650 m of accretion, which are corresponded to change rates of almost 12 and 22 m/a, respectively. Statistics of shoreline changes are calculated from regression methods including end point rate, linear regression rate, weighted linear regression, and least median of squares. The best-performed method is applied to predict the shoreline position in 2050 and 2100. Potential locations of excessive changes are identified for the predicted shorelines, which should be dealt with properly.

On the automatic parameter selection for permutation entropy.

Permutation Entropy (PE) is a cost effective tool for summarizing the complexity of a time series. It has been used in many applications including damage detection, disease forecasting, detection of dynamical changes, and financial volatility analysis. However, to successfully use PE, an accurate selection of two parameters is needed: the permutation dimension n and embedding delay τ. These parameters are often suggested by experts based on a heuristic or by a trial and error approach. Both of these methods can be time-consuming and lead to inaccurate results. In this work, we investigate multiple schemes for automatically selecting these parameters with only the corresponding time series as the input. Specifically, we develop a frequency-domain approach based on the least median of squares and the Fourier spectrum, as well as extend two existing methods: Permutation Auto-Mutual Information Function and Multi-scale Permutation Entropy (MPE) for determining τ. We then compare our methods as well as current methods in the literature for obtaining both τ and n against expert-suggested values in published works. We show that the success of any method in automatically generating the correct PE parameters depends on the category of the studied system. Specifically, for the delay parameter τ, we show that our frequency approach provides accurate suggestions for periodic systems, nonlinear difference equations, and electrocardiogram/electroencephalogram data, while the mutual information function computed using adaptive partitions provides the most accurate results for chaotic differential equations. For the permutation dimension n, both False Nearest Neighbors and MPE provide accurate values for n for most of the systems with a value of n=5 being suitable in most cases.

KAJIAN REGRESI KEKAR MENGGUNAKAN METODE PENDUGA-MM DAN KUADRAT MEDIAN TERKECIL

Regression is a statistical method that is used to obtain a pattern of relations between two or more variables presented in the regression line equation. This line equation is derived from estimation using ordinary least squares (OLS). However, OLS has limitations that are highly dependent on outliers data. One solution to the outliers problem in regression analysis is to use the robust regression method. This study used the least median squares (LMS) and multi-stage method (MM) robust regression for analysis of data containing outliers. Data analysis was carried out on generation data simulation and actual data. The simulation results of regression analysis in various scenarios are concluded that the LMS and MM methods have better performance compared to the OLS on data containing outliers. MM method has the lowest average parameter estimation bias, followed by the LMS, then OLS. The LMS has the smallest average root mean squares error (RMSE) and the highest average R2 is followed by the MM then the OLS. The results of the regression analysis comparison of the three methods on Indonesian rice production data in 2017 which contains 10% outliers were concluded that the LMS is the best method. The LMS produces the smallest RMSE of 4.44 and the highest R2 that is 98%. MM's method is in the second-best position with RMSE of 6.78 and R2 of 96%. OLS method produces the largest RMSE and lowest R2 that is 23.15 and 58% respectively.

Interpreting deformation results of geodetic network points using the strain models based on different estimation methods

Geodetic Networks designed as Deformation Networks or Continuous Networks are observed in different epochs/ sessions and evaluated as a function of time. Those can be design as global GNSS networks for aim monitoring active tectonic movements or as regional densification geodetic and deformation networks for monitoring local earthquakes and surface movements. The areas covered geodetic networks are assumed as any surface on ellipsoid or sphere. Characteristics of surfaces are analyzed with Geometric Strain Models using deformation data on surface points. In this case, effect rates on geodetic network area are determined from local surface movements or regional active earthquakes and interpreted as experimental. On the other hand, undetermined outliers by model hypothesis test affect coordinate unknowns separately. Outliers cause deformations in certain magnitude on networks points. Therefore, network points strain in different rates and directions. Query of maximum affects caused by these strain rates is a referenced reliability method called "Robustness Analysis in Geodetic Networks”. Mentioned strain rates are modelled by various estimation methods. Thus, deformation results could be interpreted together by the obtained strain components and deformation vector. In this paper, possible strain components belonging to network points are determined with methods of L1 Norm, Least Median Squares (LMS) and Least Squares Estimation (LSE). These estimation methods are tested on KOUSAGA (Kocaeli University Permanent GPS Network). Strain components are estimated by use polyhedrons covered by network points. Obtained results are compared and analyzed according to weakness and strengths of proposed estimation methods.

Three Decades of Coastal Changes in Sindh, Pakistan (1989–2018): A Geospatial Assessment

Coastal erosion endangers millions living near-shore and puts coastal infrastructure at risk, particularly in low-lying deltaic coasts of developing nations. This study focuses on morphological changes along the ~320-km-long Sindh coastline of Pakistan over past three decades. In this study, the Landsat images from 1989 to 2018 at an interval of 10 years are used to analyze the state of coastline erosion. For this purpose, well-known statistical approaches such as end point rate (EPR), least median of squares (LMS), and linear regression rate (LRR) are used to calculate the rates of coastline change. We analyze the erosion trend along with the underlying controlling variables of coastal change. Results show that most areas along the coastline have experienced noteworthy erosion during the study period. It is found that Karachi coastline experienced 2.43 ± 0.45 m/yr of erosion and 8.34 ± 0.45 m/yr of accretion, while erosion on the western and eastern sides of Indus River reached 12.5 ± 0.55 and 19.96 ± 0.65 m/yr on average, respectively. Coastal erosion is widespread along the entire coastline. However, the rate of erosion varies across the study area with a general trend of erosion increasing from west to east in the Indus Delta region (IDR), and the highest average erosion rate is 27.46 m/yr. The interdecadal change during 1989–1999, 1999–2009 and 2009–2018 periods depicted an increasing linear trend (R2 = 0.78) from Karachi to Indus River (IR) East zone. The spatial trend from west to east is positively correlated with mean sea level rise, which has increased from 1.1 to 1.9 mm/year, and negatively correlated with topographic slope, which is found to be decreasing eastward along the coastline. The findings necessitate appropriate actions and have important implications to better manage coastal areas in Pakistan in the wake of global climate change.

MENGATASI PENCILAN PADA PEMODELAN REGRESI LINEAR BERGANDA DENGAN METODE REGRESI ROBUST PENAKSIR LMS

Ordinary Least Squares (OLS) is frequent used method for estimating parameters. OLS estimator is not a robust regression procedure for the presence of outliers, so the estimate becomes inappropriate. Least Median of Squares (LMS) is one of a robust estimator for the presence of outliers and has a high breakdown value. LMS estimate parameters by minimizing the median of squared residuals. Least Median of Squares (LMS) The purpose of this study is geting a regression equation that better than the regression equation before using OLS for the data that having outlier. For the first step, checking if there is outlier at data and then searching regression equation with LMS method. In this study used data stackloss and from estimation parameter of this data, LMS estimator showed better results compared to the OLS estimator because the regression equation from LMS method have smaller value of Mean Absolute Percentage Error (MAPE).

Multiple Harmonic Source Location Using the Least Median of Squares Method with the Presence of Outliers in High Voltage Electric Power Systems

A static multipoint method to locate harmonic sources in high-voltage electric power systems based on the least median of squares approach is presented. Because of statistical robustness, the least median of squares method is used, even in the presence of multiple erroneous measurements. The special features of the method are described in this article. IEEE-30 bus test system with three harmonic sources and uniformly distributed erroneous measurements is solved with the least median of squares, Heydt’s and Euclidean norm methods. Several harmonic sources are correctly located with the least median of squares method. The least median of squares approach estimated harmonic bus voltages and currents is close to the actual values. With Heydt’s and the Euclidean norm methods the harmonic sources cannot be located in the presence of uniformly distributed erroneous measurements.

Tracking Registration Algorithm for Augmented Reality Based on Template Tracking

Tracking registration is a key issue in augmented reality applications, particularly where there are no artificial identifier placed manually. In this paper, an efficient markerless tracking registration algorithm which combines the detector and the tracker is presented for the augmented reality system. We capture the target images in real scenes as template images, use the random ferns classi- fier for target detection and solve the problem of reinitialization after tracking registration failures due to changes in ambient lighting or occlusion of targets. Once the target has been successfully detected, the pyramid Lucas-Kanade (LK) optical flow tracker is used to track the detected target in real time to solve the problem of slow speed. The least median of squares (LMedS) method is used to adaptively calculate the homography matrix, and then the three-dimensional pose is estimated and the virtual object is rendered and registered. Experimental results demonstrate that the algorithm is more accurate, faster and more robust.

Robust LMedS-Based WLS and Tukey-Based EKF Algorithms Under LOS/NLOS Mixture Conditions

In this paper, we present robust localization algorithms that use range measurements. The least median of squares (LMedS)-weighted least squares (WLS), LMedS-spherical simplex unscented transform (SSUT) based WLS and Tukey-based extended Kalman filter (EKF) algorithms are proposed for line-of-sight (LOS)/non-line-of-sight (NLOS) mixture environments. First, the LMedS solution is obtained, and then sensors are predicted to be LOS or LOS/NLOS mixture sensors. The range observation predicted as an outlier is replaced with the estimated distance obtained using the LMedS algorithm. Subsequently, the two-step WLS method is executed using these new distance measurements. In the Tukey-based EKF method, Tukey's risk function and the 3-σ edit rule are employed in the innovation step. Furthermore, the mean square error (MSE) analysis of the proposed algorithms is performed. We demonstrate that the positioning accuracy of the proposed methods is higher than that of conventional methods through extensive simulation.

Models Where the Least Trimmed Squares and Least Median of Squares Estimators Are Maximum Likelihood

The Least Trimmed Squares (LTS) and Least Median of Squares (LMS) estimators are popular robust regression estimators. The idea behind the estimators is to find, for a given h, a sub-sample of h 'good' observations among n observations and estimate the regression on that sub-sample. We find models, based on the normal or the uniform distribution respectively, in which these estimators are maximum likelihood. We provide an asymptotic theory for the location-scale case in those models. The LTS estimator is found to be h1/2 consistent and asymptotically standard normal. The LMS estimator is found to be h consistent and asymptotically Laplace.

SIMULASI PENANGANAN PENCILAN PADA ANALISIS REGRESI MENGGUNAKAN METODE LEAST MEDIAN SQUARE (LMS)

The simulation of handling of outliers on regression analysis used the method which was commonly used to predict the parameter in regression analysis, namely Least Median Square (LMS) due to the simple calculation it had. The data with outliers would result in unbiased parameter estimate. Hence, it was necessary to draw up the robust regression to overcome the outliers. The data used were simulation data of the number of data pairs ( X,Y) by 25 and 100 respectively. The result of the simulation was divided into 5 subsets of data cluster of parameter regression prediction by Ordinary Least Square (OLS) and Least Median Square (LMS) methods. The prediction result of the parameter of each method on each subset of data cluster was tested with both method to discover the which better one. Based on the research findings, it was found that The Least Median Square (LMS) method was known better than Ordinary Least Square (OLS) method in predicting the regression parameter on the data which had up to 3% of the percentage of the outlier.

Fast and accurate line detection with GPU-based least median of squares

We propose an accurate and efficient 2D line detection technique based on the standard Hough transform (SHT) and least median of squares (LMS). We prove our method to be very accurate and robust to noise and occlusions by comparing it with state-of-the-art line detection methods using both qualitative and quantitative experiments. LMS is known as being very robust but also as having high computation complexity. To make our method practical for real-time applications, we propose a parallel algorithm for LMS computation which is based on point-line duality. We also offer a very efficient implementation of this algorithm for GPU on CUDA architecture. Despite many years since LMS methods have first been described and the widespread use of GPU technology in computer vision and image-processing systems, we are unaware of previous work reporting the use of GPUs for LMS and line detection. We measure the computation time of our GPU-accelerated algorithm and prove it is suitable for real-time applications. Our accelerated LMS algorithm is up to 40 times faster than the fastest single-threaded CPU-based implementation of the state-of-the-art sequential algorithm.