Least Median Of Squares Research Articles

Dynamics of Shoreline Changes Along the Coast of Subarnarekha and Budhabalanga River Estuary, North Eastern Coast of India Using DSAS Technique: A Geospatial Technology Approach

ABSTRACTThe coastal regions represent one of the most significant environmental and economic resources, offering critical ecosystems that support biodiversity. Shoreline change analysis offers critical insights into coastal dynamics, providing trends in erosion and accretion, enabling effective coastal management and hazard mitigation. In the current study, shoreline change is assessed utilizing the Digital Shoreline Analysis System (DSAS) model for Subarnarekha and Budhabalanga river estuaries in Baleswar district, Odisha, India. The shoreline was extracted using multitemporal satellite images like Landsat‐5 and Landsat‐7 for the years 1991, 2000, and 2011. Similarly Sentinel‐2 and Landsat‐8 satellite imagery were used for the year 2022. The satellite data from 1991 to 2022 were processed using Envi, ArcGIS softwares and the shoreline is extracted for each year using band ratioing methods to demarcate shoreline. In the current research, the net accretion and erosion along the coast were analyzed using the GIS (geographic information systems) technique and the DSAS model. The four important statistical parameters of the DSAS model utilized in the study area are end point rate (EPR), net shoreline movement (NSM), linear regression rate (LRR), and least median of squares (LMS). The shoreline change analysis for the coast of Subarnarekha and Budhabalanga river estuary area from 1991 to 2022 reveals that 44% of the coast is under accretion, 7% is under stable coast, and 23% is under erosion. According to the findings, the coastal area of the recent study is both progressive and regressive in nature. For the study area, the average rates of shoreline accretion and erosion are 1.05 m and 0.45 m per year, respectively. The study gives information on erosion and accretion near the Subarnarekha and Budhabalanga river estuaries, which will aid in the development of an adaptive shoreline management strategy and coastal vulnerability assessment.

Robust Liu Estimator Used to Combat Some Challenges in Partially Linear Regression Model by Improving LTS Algorithm Using Semidefinite Programming

Outliers are a common problem in applied statistics, together with multicollinearity. In this paper, robust Liu estimators are introduced into a partially linear model to combat the presence of multicollinearity and outlier challenges when the error terms are not independent and some linear constraints are assumed to hold in the parameter space. The Liu estimator is used to address the multicollinearity, while robust methods are used to handle the outlier problem. In the literature on the Liu methodology, obtaining the best value for the biased parameter plays an important role in model prediction and is still an unsolved problem. In this regard, some robust estimators of the biased parameter are proposed based on the least trimmed squares (LTS) technique and its extensions using a semidefinite programming approach. Based on a set of observations with a sample size of n, and the integer trimming parameter h ≤ n, the LTS estimator computes the hyperplane that minimizes the sum of the lowest h squared residuals. Even though the LTS estimator is statistically more effective than the widely used least median squares (LMS) estimate, it is less complicated computationally than LMS. It is shown that the proposed robust extended Liu estimators perform better than classical estimators. As part of our proposal, using Monte Carlo simulation schemes and a real data example, the performance of robust Liu estimators is compared with that of classical ones in restricted partially linear models.

Robust regression modelling for inflation factor in the Indonesian economy development

Inflation is a general and continuous increase in the prices of goods and services over a while. Inflation is measured by the Consumer Price Index (CPI) indicator to calculate the average price change of a package of goods and services households consume over time. Inflation in Indonesia is not in a precarious condition. However, it also states that inflation in Indonesia could rise. This rise can affect the sustainable development goals (SDGs). Therefore, Indonesia needs to have inflation data scrutinized every year. This study aims to examine and show the factors that affect inflation. Robust regression is an important method to analyze data contaminated by outliers and provide more flexible results. So that it can produce robust regression models and determine what factors significantly affect inflation in Indonesia by the research objectives, this study’s research type is experimental research with literature studies. The variable used is Inflation in Indonesia, which is the dependent variable of the study, and the other four independent variables are export value, interest rate, money supply, and exchange rate. After that, a robust regression model with maximum likelihood type (M) estimation, scale (S) estimation, and least median of squares (LMS) estimation will be obtained, and the best model will be selected. The results show that the least median of squares (LMS) estimation is the best with the acquisition of an Akaike information criteria value of -390.1363. Furthermore, the high and low inflation in 20182022 is influenced by interest rates, money supply and export value.

Bayesian inference using least median of squares and least trimmed squares in models with independent or correlated errors and outliers

We provide Bayesian inference in the context of Least Median of Squares and Least Trimmed Squares, two well-known techniques that are highly robust to outliers. We apply the new Bayesian techniques to linear models whose errors are independent or AR and ARMA. Model comparison is performed using posterior model probabilities, and the new techniques are examined using Monte Carlo experiments as well as an application to four portfolios of asset returns.

Predicting and validating the load-settlement behavior of large-scale geosynthetic-reinforced soil abutments using hybrid intelligent modeling

Settlement prediction of geosynthetic-reinforced soil (GRS) abutments under service loading conditions is an arduous and challenging task for practicing geotechnical/civil engineers. Hence, in this paper, a novel hybrid artificial intelligence (AI)-based model was developed by the combination of artificial neural network (ANN) and Harris hawks’ optimisation (HHO), that is, ANN-HHO, to predict the settlement of the GRS abutments. Five other robust intelligent models such as support vector regression (SVR), Gaussian process regression (GPR), relevance vector machine (RVM), sequential minimal optimisation regression (SMOR), and least-median square regression (LMSR) were constructed and compared to the ANN-HHO model. The predictive strength, relalibility and robustness of the model were evaluated based on rigorous statistical testing, ranking criteria, multi-criteria approach, uncertainity analysis and sensitivity analysis (SA). Moreover, the predictive veracity of the model was also substantiated against several large-scale independent experimental studies on GRS abutments reported in the scientific literature. The acquired findings demonstrated that the ANN-HHO model predicted the settlement of GRS abutments with reasonable accuracy and yielded superior performance in comparison to counterpart models. Therefore, it becomes one of predictive tools employed by geotechnical/civil engineers in preliminary decision-making when investigating the in-service performance of GRS abutments. Finally, the model has been converted into a simple mathematical formulation for easy hand calculations, and it is proved cost-effective and less time-consuming in comparison to experimental tests and numerical simulations.

A Combined Safety Monitoring Model for High Concrete Dams

When applying reliability analysis to the monitoring of structural health, it is very important that gross errors–which affect prediction accuracy–are included within the monitoring information. An approach using gross errors identification and a dam safety monitoring model for deformation monitoring data of concrete dams is proposed in this paper. It can solve the problems of strong nonlinearity and the difficulty of identifying and eliminating gross errors in deformation monitoring data in concrete dams. This new method combines the advantages of an incremental extreme learning machine (I-ELM) method to seek an optimal network structure, the Least Median Squares (LMS) method with strong robustness to multiple failure points, the robust estimation IGG method with the good robustness to outliers (gross errors) and extreme learning machine (ELM) method with high prediction efficiency and handling of nonlinear problems. The proposed method can eliminate gross errors and be utilized to predict the behavior of concrete dams. The deformation monitoring data of an existing 305 m-high concrete arch dam is acquired by combining remote sensing technology with other monitoring methods. The LMS-IGG-ELM method is utilized to eliminate outliers from the dam monitoring sequence and is compared with the processing result from a DBSCAN clustering algorithm, Romanovsky criterion and the 3σ method. The results show that the proposed method has the highest gross errors identification rate, the strongest generalization ability and the best prediction effect.

On the study of efficiency of exponential‐type estimator of population mean using robust regression methods

AbstractThis study aimed at enhancing the efficiency of Zaman estimators using exponential transformation technique. A new class of estimators was obtained using the concept of Bahl and Tuteja. The bias and mean squared error (MSE) of the new class of suggested estimators was derived up to second degree approximation. The empirical study through simulations was conducted using Normal, exponential, gamma, chi‐square and beta distributions under robust regression methods (Huber‐M, Huber‐MM, LTS (least trimmed squares) and LMS (least median of squares)) and the results revealed that proposed estimators were more efficient.

Partial least median of squares regression

AbstractIn modern data analysis, there is an increasing availability of datasets with numerous variables. Linear models that deal with abundant predictor variables often have poor performance because they tend to produce large variances. As well known, partial least squares (PLS) regression standouts because it is serviceable even if the number of variables far exceeds the number of samples. However, PLS, at its core, is a least‐squares method based on latent space, which is spanned by the components extracted from the original predictors. Hence, it is sensitive to outliers. In this study, incorporating the idea of least median of squares, we propose a new robust PLS method, namely, partial least median of squares (PLMS) regression. Unlike most of the robust counterparts, we solve the PLMS problem via modern optimization rather than a heuristic process or a reweighting strategy. A classical PLS method and two of the most efficient robust PLS methods are compared with our method. Results on simulations and two real‐world data sets demonstrate the effectiveness and robustness of our approach.

Automatic Forest DBH Measurement Based on Structure from Motion Photogrammetry

Measuring diameter at breast height (DBH) is an essential but laborious task in the traditional forest inventory; it motivates people to develop alternative methods based on remote sensing technologies. In recent years, structure from motion (SfM) photogrammetry has drawn researchers’ attention in forest surveying for its economy and high precision as the light detection and ranging (LiDAR) methods are always expensive. This study explores an automatic DBH measurement method based on SfM. Firstly, we proposed a new image acquisition technique that could reduce the number of images for the high accuracy of DBH measurement. Secondly, we developed an automatic DBH estimation pipeline based on sample consensus (RANSAC) and cylinder fitting with the Least Median of Squares with impressive DBH estimation speed and high accuracy comparable to methods based on LiDAR. For the application of SfM on forest survey, a graphical interface software Auto-DBH integrated with SfM reconstruction and automatic DBH estimation pipeline was developed. We sampled four plots with different species to verify the performance of the proposed method. The result showed that the accuracy of the first two plots, where trees’ stems were of good roundness, was high with a root mean squared error (RMSE) of 1.41 cm and 1.118 cm and a mean relative error of 4.78% and 5.70%, respectively. The third plot’s damaged trunks and low roundness stems reduced the accuracy with an RMSE of 3.16 cm and a mean relative error of 10.74%. The average automatic detection rate of the trees in the four plots was 91%. Our automatic DBH estimation procedure is relatively fast and on average takes only 2 s to estimate the DBH of a tree, which is much more rapid than direct physical measurements of tree trunk diameters. The result proves that Auto-DBH could reach high accuracy, close to terrestrial laser scanning (TLS) in plot scale forest DBH measurement. Our successful application of automatic DBH measurement indicates that SfM is promising in forest inventory.

Vertical Ground Displacements and Its Impact on Erosion along the Karachi Coastline, Pakistan

This study employed remote sensing (optical and synthetic aperture radar) and data analysis techniques to quantify vertical ground displacements and assess their contribution to coastline erosion. To provide evidence from Pakistan, we selected the coast of Karachi—a mega-city located along the dynamic coastline of the Indus River Delta—which has been experiencing severe coastal erosion during the last few decades. Observations from the C-band Envisat/ASAR and Sentinel-1A sensors over the 2004–2010 and 2014–2016 periods, respectively, enabled us to study vertical ground displacements in the study area, providing a long-term assessment during 2004–2016. Results suggest that some areas along the Karachi coastline are subsiding at comparable rates to or even much higher than the relative sea-level rise (SLR, ~1.9 mm/yr), which may amplify the rates of relative SLR in coming years, along with accelerating coastal erosion. Various parts of the study area along the coast are unstable and undergoing displacement. Landsat images from 1989 to 2018 (10-year temporal resolution) were further used to examine the state of coastline erosion using three statistical approaches (i.e., End Point Rate (EPR), Linear Regression Rate (LRR), and Least Median of Squares (LMS)). While the erosion underlaid the majority of the eastern sections of the study area, the ground displacements were spatially heterogeneous across the study area and along the coastline. Erosion rates of ~2.4 m/yr spatially corresponded with ground displacement rates of up to ~−1.4 cm/yr, but not all the coastline segments with high annual mean erosion rates were associated with local mean subsidence. The causes of ground displacements and coastline erosion were analyzed, and results were interpreted by integrating spatial ancillary information. Results indicate that rapid urbanization, construction on reclaimed land, coastline erosion favoring seawater intrusion, failed drainage/sewerage networks, and soil liquefaction are contributing to the site-specific variations in the land displacement in Karachi.

Stacking ensemble-based hybrid algorithms for discharge computation in sharp-crested labyrinth weirs

Labyrinth weirs are utilized to transport a greater discharge during floods in contrast to conventional weirs due to their increased weir crest length. Nevertheless, due to the increased geometric complexity of labyrinth weirs, determination of accurate discharge coefficients and accordingly, head-discharge ratings are quite essential issues in practical application. Hence, as a first step the present study proposes the following eight standalone algorithms: decision table (DT), Kstar, least median square (LMS), M5 prime (M5P), M5 rule (M5R), pace regression (PR), random forest (RF) and sequential minimal optimization (SMO). Then, applying the stacking (ST) algorithm, these standalone models were hybridized to predict the discharge coefficient (Cd) for sharp-crested labyrinth weirs. Potential/effective variables were constructed in the form of several independent dimensionless parameters (i.e., θ, h/W, L/B, L/h, Froude number (Fr), B/W and L/W) to predict Cd as an output. The accuracy of the developed models was examined in terms of different statistical visually based and quantitative-based error measurement criteria. The results illustrate that h/W and B/W parameters have the highest and lowest effect on the Cd prediction, respectively. According to NSE, all developed algorithms provided accurate performances, while ST-Kstar had the highest prediction power.

Study on Elimination Algorithms for Line Segment Mismatches

Image matching is a key step for remotely sensed image registration and digital elevation model (DEM) generation. Compared with point matching, few studies have focused on line matching for images, especially elimination algorithm of mismatched line segments. Therefore, this work systematically studies elimination algorithms of line segment mismatches by combining 2 transformation models (i.e., affine and homography) with 2 M-estimators or 2 sample consensus methods (i.e., random sample consensus, RANSAC, and least median of squares, LMedS). The main idea is as follows. After line segments are extracted and matched, the proposed algorithms can automatically remove mismatched line segments based on an error function of line segment. Aerial images with panchromatic bands and standard false color synthesis were selected for testing. Experiments were performed to compare different combinations of these models and methods and to quantitatively evaluate the performance of the algorithms in terms of accuracy and run time. The results show that the proposed algorithm can be effectively applied to automatically eliminate mismatched line segments, and among all combinations the homography model with LMedS performs the best. The algorithm can also ensure and control the quality of line segment matching from stereo pairs.

Data depth approach in fitting linear regression models

The data depth approach plays a vital role in regression and multivariate analysis. It is a recently emerging research topic in statistics. Regression techniques are mainly used for analysing and modelling multifactor data, it spans a large collection of applicative scenarios in many fields such as the developing discipline of data science which includes machine learning. This paper explores the idea of regression depth. The study is carried out the computational aspects of regression depth for a given dataset under classical and robust methods, like Least Squares (LS), Least Median Squares (LMS) and S-Estimator (S) along with Regression Depth Median (RDM) approach. Further, it is demonstrated the fitted models under various methods and their efficiencies have been studied under the regression depth approach. It is observed that regression depth under robust procedures outperforms the conventional regression procedure under with and without extreme observations in the data. It is concluded that researchers can apply the data depth procedure wherever the model fitting is required when the data contains extremes.

Robust restricted Liu estimator in censored semiparametric linear models

It is not unusual to have outliers and multicollinearity simultaneously in censored semiparametric linear models. In this paper for dealing with multicollinearity and outliers we introduce a family of robust censored Liu and non-Liu type of estimates for the regression parameter when some non-stochastic linear restrictions are imposed. The proposed robust estimators is based on least trimmed squares (LTS) method. The efficiency of LTS estimator statistically is more than the well-known least median squares (LMS) estimator. Unfortunately the computational complexity of LTS is less well understood than that of LMS in which the objective is to minimize the median squared residual. Here, we provide the robust estimators for linear and non-linear parts of the censored model based on robust shrinkage Liu estimators. The performance of proposed estimators compared to ordinary estimators numerically is evaluated by Monte Carlo simulation studies. We further illustrate the our procedures by an application.

Robust estimators for circular regression models

The problem of robust estimation in circular regression models has not been studied well. This paper considers the JS circular regression model due to its interesting properties and its sensitivity for existence and detection of outliers. We extend the robust estimators such as M-estimation, least-trimmed squares (LTS), and least-median squares (LMS) estimators, which have been successfully used in the linear regression models, to the JS circular regression model.The robustness of the proposed estimators are studied through its influence function, and via simulation study. The results show that the proposed robust circular M-estimation is effective in estimating circular models' parameters in the presence of vertical outliers. However, circular LTS and LMS are highly robust estimators in case of circular leverage points. An application of the proposed robust circular estimators is illustrated using a real eye data set.

Contour detection and salient feature line regularization for printed circuit board in point clouds based on geometric primitives

Effective extraction of the printed circuit board (PCB)’s key contour feature line is of great significance in the optoelectronic industry, especially for defect detection and accurate dimensional measurement. Here, we develop a method to convert the fold edge points into boundary points and then extract the salient contour feature lines of the PCB. The method is performed directly on the real PCB point cloud, and no image processing or 3D reconstruction is required. Our approach involves three key steps: point cloud preprocessing, feature point detection, and contour feature line regularization. Firstly, the PCB point cloud’s preprocessing is completed using the k-d tree and pass-through filtering algorithms. Secondly, through the least-median-of-squares (LMS) and the Euclidean-Clustering-Based-on-Gaussian-Mapping (ECGM), the fold edge points are converted into boundary points. Then, the contour feature points are identified by angle criterion between lines formed by the query point with respect to its neighboring points. Finally, the feature points are regularized by the self-pruning B-spline curve based on squared distance minimization (SDM). Compared with the other methods, our approach extracts more salient contour points and fewer redundant points. Experiments on real test data also suggest that this method has good potential in extracting feature lines, which ensures accuracy and strong applicability.

Stratified sampling in highly polluted data as an effective and reliable alternative to high breakdown point estimators

Observations on certain real-life cases include units that are incompatible with other data sets. Values that are extreme in nature do influence estimates obtained by conventional estimators. Robust estimators are therefore necessary for efficient estimation of parameters. This paper uses stratification with simple random sampling without replacement to optimize sample allocation in stratum for efficient parameter estimation as an alternative method of handling highly contaminated samples. Our proposed method stratifies the highly contaminated population into two non-overlapping sub-populations, and stratified samples of sizes 50, 200, and 500 was drawn. We estimate the model parameters form the contaminated sampled data using ordinary least squares under the proposed method, and using the two high breakdown point estimators; the Least Median of Squares and Least Trimmed Squares. Our findings shows that the proposed method did not perform well for low contamination levels (⩽ 30%) but outperformed Least Median of Squares and Least Trimmed Squares for higher contamination rates (⩾ 40%). This indicates that our proposed method compares well and compete favorably with the two high breakdown point estimators.

Robust detection of non-overlapping ellipses from points with applications to circular target extraction in images and cylinder detection in point clouds

Detection of non-overlapping ellipses from 2-dimensional (2D) edge points is an essential step towards solving typical photogrammetry problems pertaining to feature detection, calibration, and registration of optical instruments. For instance, circular and spherical black and white calibration and registration targets are represented as ellipses in images. Furthermore, the intersection of a cut plane with cylindrical point clouds generates 2D points following elliptic patterns. To this end, this study proposes a collection of new methods for the automatic and robust detection of non-overlapping ellipses from 2D points. These methods will first be applied to detect circular and spherical targets in images and, second, to detect cylinders in 3D point clouds. The method utilizes the Euclidian ellipticity and a new systematic and generalizable threshold to decide if a set of connected points follow an elliptic pattern. When connected points include outliers, the newly proposed robust Monte Carlo-based ellipse fitting method will be deployed. This method includes three new developments: (i) selecting initial subsamples using a bucketing strategy based on the polar angle of the points; (ii) detecting inlier points by reducing the robust ellipse fitting to a robust circle fitting problem; and (iii) choosing the best inlier set amongst all subsamples using adaptive, systematic, and generalizable selection criteria. A new process is presented to extract cylinders from a point cloud by detecting non-overlapping ellipses from the points projected onto an intersecting cut plane. The proposed methods were compared to established state-of-the-art methods, using simulated and real-world datasets, through the design of four sets of original experiments. The experiments include (i) comparisons of robust ellipse fitting; (ii) sensitivity analysis of the ellipse validation criteria; (iii) comparison of non-overlapping ellipse detection; and (iv) detection of pipes from terrestrial laser scanner point clouds. It was found that the proposed robust ellipse detection was superior to four reliable robust methods, including the popular least median of squares, in both simulated and real-world datasets. The proposed process for detecting non-overlapping ellipses achieved F-measure of 99.3% on real images, compared to 42.4%, 65.6%, and 59.2%, obtained using the methods of Fornaciari, Patraucean, and Panagiotakis, respectively. The proposed cylinder extraction method identified all detectable mechanical pipes in two real-world point clouds collected in laboratory and industrial construction site conditions. The results of this investigation show promise for the application of the proposed methods for automatic extraction of circular targets from images and pipes from point clouds.

Robust multi-stage method (MM) and least median square (LMS) evaluation on handling outlier for multiple regression

Outliers are observation with extreme values that are very different from most other data. The least squares method (OLS) is a method that is very sensitive to outliers because it can cause the modeling accuracy decrease. Throwing out outliers with the aim of improving the suitability of the regression equation cannot be done carelessly because it will provide imprecise estimation precision. This study examines the performance of robust method of the least median squares (LMS) and the multi-stage method (MM) compared to OLS in a regression analysis of data which contains outliers. Data analysis was performed on simulation data and oil palm production data. Based on the average parameter estimate bias value, MM method has the best performance in each scenario condition of data size and outlier percentage, while based on the average root mean squares error (RMSE), LMS has better performance than MM when the data size is 25. Analysis of Indonesian oil palm production data in 2018 which data size 25 and contains 44% outliers resulted the conclusion that LMS method produced smallest RMSE and highest R2, namely 38.81 and 99.78%, respectively. MM method is in the second best position, while OLS produces largest RMSE and highest R2.

Least quantile squares method for the detection of outliers

k-least quantile of squares (k-LQS) estimates are a generalization of least median of squares (LMS) estimates. They have not been used as much as LMS because their breakdown points become small as k increases. But if the size of outliers is assumed to be fixed LQS estimates yield a good fit to the majority of data and residuals calculated from LQS estimates can be a reliable tool to detect outliers. We propose to use LQS estimates for separating a clean set from the data in the context of outlyingness of the cases. Three procedures are suggested for the identification of outliers using LQS estimates. Examples are provided to illustrate the methods. A Monte Carlo study show that proposed methods are effective.