Least Median Of Squares Research Articles

Shoreline changes along the Kutubdia Island, south east Bangladesh using digital shoreline analysis system

A ~65 km coastal stretch has been analyzed to estimate the change dynamics of Kutubdia Island with the help of digital shoreline analysis system (DSAS). This study investigated the reliability of medium resolution satellite imagery for mapping shoreline positions and for estimating historic rates of changes. Nine shoreline positions were extracted on 1972, 1976, 1980, 1989, 1999, 2004, 2009, 2011 and 2014 covering a long term of 42 years period. Rates of shoreline changes were estimated by four statistical methods namely, end point rate (EPR), linear regression rate (LRR), weighted linear regression (WLR) and least median of squares (LMS) by using DSAS and subsequently all the methods were verified with the correlation coefficient (R).The scrutiny of shoreline changes shows that the erosion during the last 42 years has affected the island, with some exception, at the north and west segment where minor accretion has been documented. The average rates of changes estimated for north, south, east and west segment using WLR, LMS, EPR and LRR are Ñ4.0 m/yr, Ñ33.7 m/yr Ñ2.6 m/yr and Ñ5.6 m/yr, respectively. The outcome of this particular analysis might be useful for proper planning and management of Kutubida Island. However, this may also be used in statistical modeling for forecasting the future shoreline position.Bangladesh J. Sci. Res. 27(1): 99-108, June-2014

Robust surface normal estimation via greedy sparse regression

Photometric stereo (PST) is a widely used technique of estimating surface normals from an image set. However, it often produces inaccurate results for non-Lambertian surface reflectance. In this study, PST is reformulated as a sparse recovery problem where non-Lambertian errors are explicitly identified and corrected. We show that such a problem can be accurately solved via a greedy algorithm called orthogonal matching pursuit (OMP). The performance of OMP is evaluated on synthesized and real-world datasets: we found that the greedy algorithm is overall more robust to non-Lambertian errors than other state-of-the-art sparse approaches with little loss of efficiency. Along with providing an overview of current methods, novel contributions in this paper are as follows: we propose an alternative sparse formulation for PST; in previous PST studies (Wu et al., Robust photometric stereo via low-rank matrix completion and recovery, 2010), (S. Ikehata et al., Robust photometric stereo using sparse regression, 2012), the surface normal vector and the error vector are treated as two entities and are solved independently. In this study, we convert their formulation into a new canonical form of the sparse recovery problem by combining the two vectors into one large vector in a new “stacked” formulation in this domain. This allows for a large repertoire of existing sparse recovery algorithms to be more straightforwardly applied to the PST problem. In our application of the OMP greedy algorithm, we show that greedy solvers can indeed be applied, with this study supplying the first of such attempt at employing greedy approaches to estimate surface normals within the framework of PST. We numerically compare the performance of several normal vector recovery methods. Most notably, this is the first detailed test on complex images of the normal estimation accuracy of our previously proposed method, least median of squares (LMS).

TraIL: Pinpoint Trajectory for Indoor Localization

Indoor localization on smartphones is an enabler for a number of ubiquitous and mobile computing applications attracting worldwide attentions. Many location-based services rely on WiFi fingerprinting approaches to achieve a reasonable accuracy. However, there is still room for improvement due to the prevalent-existing errors (e.g., 8∼12 m). In this study, we devise and implement a high-accuracy indoor localization solution leveraging the WiFi-based method and pedestrian mobility provided by smartphones. Our basic idea is that WiFi-only localization can generate rough but absolute positions, while user motion is able to bring accurate but relative locations. Taking both sides into account simultaneously, we design techniques to refine the raw WiFi positions in the process of laying the precise local trajectory appropriately down to the absolute coordinate using a novel least median of squares (LMS) fit algorithm. We develop a prototype system, named TraIL, and conduct comprehensive experiments in a building along different shaped routes. The evaluation results show that TraIL can achieve 80% improvement on average error with respect to WiFi-only indoor localization.

Robust regression with CUDA and its application to plasma reflectometry.

In many applications, especially those involving scientific instrumentation data with a large experimental error, it is often necessary to carry out linear regression in the presence of severe outliers which may adversely affect the results. Robust regression methods do exist, but they are much more computationally intensive, making it difficult to apply them in real-time scenarios. In this work, we resort to graphics processing unit (GPU)-based computing to carry out robust regression in a time-sensitive application. We illustrate the results and the performance gains obtained by parallelizing one of the most common robust regression methods, namely, least median of squares. Although the method has a complexity of O(n(3)logn), with GPU computing, it is possible to accelerate it to the point that it becomes usable within the required time frame. In our experiments, the input data come from a plasma diagnostic system installed at Joint European Torus, the largest fusion experiment in Europe, but the approach can be easily transferred to other applications.

Strategies for information injection for networks estimating emitter location

This paper considers the problem of emitter location in the presence of an adversary able to inject false information, where both the viewpoints of the adversary and locating network are considered. We begin by developing adversary strategies, which focus on degrading and redirecting the locating network. The locating network uses the time difference of arrival (TDOA) method and estimates the emitter location using both nonlinear least squares (LS) and the robust least median squares (LMS). Specifically, we determine the false sensor position the adversary should inject that maximally impacts the locating network by 1) minimizing the network’s accuracy, and 2) redirecting the network’s emitter location estimate. Similarly, we formulate a network’s strategy for detecting the adversary’s injection and develop a detector able to determine its presence under both adversary strategies. We present both theoretical and numerical results illustrating the effectiveness of the developed strategies.

ROBUST SPARSE MATCHING AND MOTION ESTIMATION USING GENETIC ALGORITHMS

Abstract. In this paper, we propose a robust technique using genetic algorithm for detecting inliers and estimating accurate motion parameters from putative correspondences containing any percentage of outliers. The proposed technique aims to increase computational efficiency and modelling accuracy in comparison with the state-of-the-art via the following contributions: i) guided generation of initial populations for both avoiding degenerate solutions and increasing the rate of useful hypotheses, ii) replacing random search with evolutionary search, iii) possibility of evaluating the individuals of every population by parallel computation, iv) being performable on images with unknown internal orientation parameters, iv) estimating the motion model via detecting a minimum, however more than enough, set of inliers, v) ensuring the robustness of the motion model against outliers, degeneracy and poorperspective camera models, vi) making no assumptions about the probability distribution of inliers and/or outliers residuals from the estimated motion model, vii) detecting all the inliers by setting the threshold on their residuals adaptively with regard to the uncertainty of the estimated motion model and the position of the matches. The proposed method was evaluated both on synthetic data and real images. The results were compared with the most popular techniques from the state-of-the-art, including RANSAC, MSAC, MLESAC, Least Trimmed Squares and Least Median of Squares. Experimental results proved that the proposed approach perform better than others in terms of accuracy of motion estimation, accuracy of inlier detection and the computational efficiency.

Extended least trimmed squares estimator in semiparametric regression models with correlated errors

Under a semiparametric regression model, a family of robust estimates for the regression parameter is proposed. The least trimmed squares (LTS) method is a statistical technique for fitting a regression model to a set of points. Given a set of n observations and the integer trimming parameter , the LTS estimator involves computing the hyperplane that minimizes the sum of the smallest h squared residuals. The LTS estimator is closely related to the well-known least median squares (LMS) estimator in which the objective is to minimize the median squared residual. Although LTS estimator has the advantage of being statistically more efficient than LMS estimator, the computational complexity of LTS is less understood than LMS. Here, we develop an algorithm for the LTS estimator. Through a Monte Carlo approach, performance of the robust estimates is compared with the classical ones in semiparametric regression models.

Least quantile regression via modern optimization

We address the Least Quantile of Squares (LQS) (and in particular the Least Median of Squares) regression problem using modern optimization methods. We propose a Mixed Integer Optimization (MIO) formulation of the LQS problem which allows us to find a provably global optimal solution for the LQS problem. Our MIO framework has the appealing characteristic that if we terminate the algorithm early, we obtain a solution with a guarantee on its sub-optimality. We also propose continuous optimization methods based on first-order subdifferential methods, sequential linear optimization and hybrid combinations of them to obtain near optimal solutions to the LQS problem. The MIO algorithm is found to benefit significantly from high quality solutions delivered by our continuous optimization based methods. We further show that the MIO approach leads to (a) an optimal solution for any dataset, where the data-points $(y_i,\mathbf{x}_i)$'s are not necessarily in general position, (b) a simple proof of the breakdown point of the LQS objective value that holds for any dataset and (c) an extension to situations where there are polyhedral constraints on the regression coefficient vector. We report computational results with both synthetic and real-world datasets showing that the MIO algorithm with warm starts from the continuous optimization methods solve small ($n=100$) and medium ($n=500$) size problems to provable optimality in under two hours, and outperform all publicly available methods for large-scale ($n={}$10,000) LQS problems.

Waist-to-height ratio percentiles and cutoffs for obesity: a cross-sectional study in brazilian adolescents.

This study aimed to describe the distribution of waist-to-height ratio (WHtR) percentiles and cutoffs for obesity in Brazilian adolescents. A cross-sectional study including adolescents aged 10 to 15 years was conducted in the city of São Paulo, Brazil; anthropometric measurements (weight, height, and waist-circumference) were taken, and WHtRs were calculated and then divided into percentiles derived by using Least Median of Squares (LMS) regression. The receiver operating characteristic (ROC) curve was used in determining cutoffs for obesity (BMI ≥ 97th percentile) and Mann-Whitney and Kruskal-Wallis tests were used for comparing variables. The study included 8,019 adolescents from 43 schools, of whom 54.5% were female, and 74.8% attended public schools. Boys had higher mean WHtR than girls (0.45 ± 0.06 vs 0.44 ± 0.05; p=0.002) and higher WHtR at the 95th percentile (0.56 vs 0.54; p<0.05). The WHtR cutoffs according to the WHO criteria ranged from 0.467 to 0.506 and 0.463 to 0.496 among girls and boys respectively, with high sensitivity (82.8-95%) and specificity (84-95.5%). The WHtR was significantly associated with body adiposity measured by BMI. Its age-specific percentiles and cutoffs may be used as additional surrogate markers of central obesity and its co-morbidities.

Improved Least Median of Squares Localization for Non-Line-of-Sight Mitigation

Non-line-of-sight (NLOS) propagation is one of the major problems that cause errors in localization systems. There exist many algorithms to reduce NLOS caused errors. Most of these algorithms require ap rioriinformation about the NLOS links, which limits their application. The least median of squares (LMedS) method is an exception and is thus attractive for its simplicity. LMedS selects only a subset of the anchors with the smallest residue for location calculation, but it tends to discard more range measurements than necessary. Its performance can be improved significantly, particularly when the percentage of NLOS links is not high. In this paper, we present an improved LMedS method, which maximizes the subset of reliable anchors to be used. We show via simulation that, compared with the existing LMedS method, the proposed algorithm has significantly higher localization accuracy and is more stable. Index Terms—Least median of squares method (LMedS), local- ization, non-line-of-sight (NLOS) propagation.

Sci-Fri PM: Topics - 06: The influence of regional dose sensitivity on salivary loss and recovery in the parotid gland

Purpose: The Quantitative Analyses of Normal Tissue Effects in the Clinic (QUANTEC 2010) survey of radiation dose-volume effects on salivary gland function has called for improved understanding of intragland dose sensitivity and the effectiveness of partial sparing in salivary glands. Regional dose susceptibility of sagittally- and coronally-sub-segmented parotid gland has been studied. Specifically, we examine whether individual consideration of sub-segments leads to improved prediction of xerostomia compared with whole parotid mean dose. Methods: Data from 102 patients treated for head-and-neck cancers at the BC Cancer Agency were used in this study. Whole mouth stimulated saliva was collected before (baseline), three months, and one year after cessation of radiotherapy. Organ volumes were contoured using treatment planning CT images and sub-segmented into regional portions. Both non-parametric (local regression) and parametric (mean dose exponential fitting) methods were employed. A bootstrap technique was used for reliability estimation and cross-comparison. Results: Salivary loss is described well using non-parametric and mean dose models. Parametric fits suggest a significant distinction in dose response between medial-lateral and anterior-posterior aspects of the parotid (p<0.01). Least-squares and least-median squares estimates differ significantly (p<0.00001), indicating fits may be skewed by noise or outliers. Salivary recovery exhibits a weakly arched dose response: the highest recovery is seen at intermediate doses. Conclusions: Salivary function loss is strongly dose dependent. In contrast no useful dose dependence was observed for function recovery. Regional dose dependence was observed, but may have resulted from a bias in dose distributions.

Direct determination of antibacterial norfloxacin in urine by isopotential fluorimetry

A novel and simple method is presented for the determination of norfloxacin in human urine by matrix isopotential synchronous fluorescence spectrometry (MISF). This method is useful for the determination of compounds in samples with unknown background fluorescence, such as norfloxacin in urine, without the need for tedious sample pre-treatment. The method was performed in ethanol-water medium (10% v/v), at an apparent pH of 4.8 provided by adding sodium acetate-acetic acid buffer solution. In the determination of norfloxacin in urine the fluorescent intensity varied linearly with its concentration from 20 to 200 ng/mL. An exhaustive statistical analysis has been developed to all calibration graphs, this treatment includes robust regression such as least median of squares, which also detects outliers and leverage points. The overall least-squares regression has been applied to find the more exact straight line that fits the experimental data. The error propagation has been considered to calculate the detection limit and the repeatability of the method. The method shows very low detection limits with acceptable recoveries and precisions. The applicability of the proposed method was illustrated in the determination of norfloxacin in human urine sample without sample pre-treatment.

Robust Estimation for Parameters of the Extended Burr Type III Distribution

We consider various robust estimators for the extended Burr Type III (EBIII) distribution for complete data with outliers. The considered robust estimators are M-estimators, least absolute deviations, Theil, Siegel's repeated median, least trimmed squares, and least median of squares. Before we perform the aforementioned estimators for the EBIII, we adapt the quantiles method to the estimation of the shape parameter k of the EBIII. The simulation results show that the considered robust estimators generally outperform the existing estimation approaches for data with upper outliers, with certain of them retaining a relatively high degree of efficiency for small sample sizes.

Efficient robust image interpolation and surface properties using polynomial texture mapping

Abstract Polynomial texture mapping (PTM) uses simple polynomial regression to interpolate and re-light image sets taken from a fixed camera but under different illumination directions. PTM is an extension of the classical photometric stereo (PST), replacing the simple Lambertian model employed by the latter with a polynomial one. The advantage and hence wide use of PTM is that it provides some effectiveness in interpolating appearance including more complex phenomena such as interreflections, specularities and shadowing. In addition, PTM provides estimates of surface properties, i.e., chromaticity, albedo and surface normals. The most accurate model to date utilizes multivariate Least Median of Squares (LMS) robust regression to generate a basic matte model, followed by radial basis function (RBF) interpolation to give accurate interpolants of appearance. However, robust multivariate modelling is slow. Here we show that the robust regression can find acceptably accurate inlier sets using a much less burdensome 1D LMS robust regression (or ‘mode-finder’). We also show that one can produce good quality appearance interpolants, plus accurate surface properties using PTM before the additional RBF stage, provided one increases the dimensionality beyond 6D and still uses robust regression. Moreover, we model luminance and chromaticity separately, with dimensions 16 and 9 respectively. It is this separation of colour channels that allows us to maintain a relatively low dimensionality for the modelling. Another observation we show here is that in contrast to current thinking, using the original idea of polynomial terms in the lighting direction outperforms the use of hemispherical harmonics (HSH) for matte appearance modelling. For the RBF stage, we use Tikhonov regularization, which makes a substantial difference in performance. The radial functions used here are Gaussians; however, to date the Gaussian dispersion width and the value of the Tikhonov parameter have been fixed. Here we show that one can extend a theorem from graphics that generates a very fast error measure for an otherwise difficult leave-one-out error analysis. Using our extension of the theorem, we can optimize on both the Gaussian width and the Tikhonov parameter.

Least median of squares regression and minimum volume ellipsoid estimator for outliers detection in housing appraisal

In the real estate sector, regression analysis is the most used method for interpretative and predictive purposes. However, the presence of outliers in the estimative sample can lead to ordinary last squared regression models that do not represent the investigated market phenomenon, with the consequence of producing unreliable assessments. In the present research, the issues of the identification and the removal of outliers are discussed. The outliers identified by the least median of squares (LMS) regression and the minimum volume ellipsoid (MVE) estimator are compared in order to test the coincidence or the diversity. A complete diagnosis of the data of the initial estimative sample is carried out, combining the robust residuals obtained with LMS and the robust distances obtained with MVE. The data are classified into regular observations, vertical outliers, good leverage points and bad leverage points, and cases to delete and those to keep in the sample are identified.

Subgroup and outlier detection analysis

Background High-dimensional biological data presents the opportunity to discover novel forms of biological heterogeneity, such as overexpression or suppression of expression of a particular gene in a subset of a cohort. This novel biological heterogeneity appears in the data as outliers or distinct subgroups. Here, we describe and evaluate three procedures for subgroup and outlier detection analysis (SODA): a leave-one-out (LOO) procedure that is widely used for outlier detection in the bioinformatics literature, the least median squares (LMS) procedure from the statistics literature, and the dip test (DT) from the statistics literature. We also propose and evaluate the max spacing test (MST) as a novel SODA method.

Implementation of robust estimation in GPS networks using the Artificial Bee Colony algorithm

Geodesy utilizes state of the art data collection techniques such as GPS (Global Positioning System) to acquire locations of points. Traditionally, the coordinates of these points are estimated using the Least Squares (LS) method. Nevertheless, Robust Estimation (RE) yields more accurate results than LS method in the presence of blunders (gross errors) among the data set. For example, the Least Trimmed Squares (LTS) method and the Least Median Squares (LMS) method can be used for this purpose. The first method aims to minimize the sum of the squared residuals by trimming away observations with large residuals. On the other hand, the second method involves the minimization of the median of the squared residuals. Both methods can be implemented using an optimization method, i.e., Artificial Bee Colony (ABC) algorithm. The ABC algorithm is a swarm intelligence (a branch of artificial intelligence) technique that can be used for the solution of minimization or maximization problems. In this paper, using the LTS and LMS methods for GPS data by employing the ABC, a new approach is put forward. Firstly, some discussions about the theoretical principals of RE and ABC are given. Then, a numerical example is used to demonstrate the validity of the proposed approach. Numerical results show that application of the robust estimation to GPS data can easily be carried out by ABC and this approach helps to enhance the reliability of geospatial data for any application of geodesy.

항공사진과 SPOT-5 위성영상을 이용한 낙동강 하구역 울타리섬들의 해안선 변화율

Shoreline data of the barrier islands in Nakdong River Estuary for the last three decades were assembled using six sets of aerial photographs and seven sets of satellite images. Canny Algorithm was applied to untreated data in order to obtain a wet-dry boundary as a proxy shoreline. Digital Shoreline Analysis System (DSAS 4.0) was used to estimate the rate of shoreline changes in terms of five statistical variables; SCE (Shoreline Change Envelope), NSM (Net Shoreline Movement), EPR(End Point Rate), LRR (Linear Regression Rate), and LMS (Least Median of Squares). The shoreline in Jinwoodo varied differently from one place to another during the last three decades; the west tail has advanced (i.e., seaward or southward), the west part has regressed, the south part has advanced, and the east part has regressed. After the 2000s, the rate of shoreline changes (-2.5~6.7 m/yr) increased and the east advanced. The shoreline in Shinjado shows a counterclockwise movement; the west part has advanced, but the east part has retreated. Since Shinjado was built in its present form, the west part became stable, but the east part has regressed faster. The rate of shoreline changes (-16.0~12.0 m/yr) in Shinjado is greater than that of Jinwoodo. The shoreline in Doyodeung has advanced at a rate of 31.5 m/yr. Since Doyodeung was built in its present form, the south part has regressed at the rate of -18.2 m/yr, but the east and west parts have advanced at the rate of 13.5~14.3 m/yr. Based on Digital Shoreline Analysis, shoreline changes in the barrier islands in the Nakdong River Estuary have varied both temporally and spatially, although the exact reason for the shoreline changes requires more investigation.

RELIABLE EXTERIOR ORIENTATION BY A ROBUST ANISOTROPIC ORTHOGONAL PROCRUSTES ALGORITHM

Abstract. The paper presents a robust version of a recent anisotropic orthogonal Procrustes algorithm that has been proposed to solve the socalled camera exterior orientation problem in computer vision and photogrammetry. In order to identify outliers, that are common in visual data, we propose an algorithm based on Least Median of Squares to detect a minimal outliers-free sample, and a Forward Search procedure, used to augment the inliers set one sample at a time. Experiments with synthetic data demonstrate that, when the percentage of outliers is greater than 30% or the data size is small, the proposed method is more accurate in detecting outliers than the customary detection based on median absolute deviation.

The Combined Effect of Applying Feature Selection and Parameter Optimization on Machine Learning Techniques for Solar Power Prediction

This paper empirically shows that the combined effect of applying the selected feature subsets and optimized parameters on machine learning techniques significantly improves the accuracy for solar power prediction. To provide evidence, experiments are carried on in two phases. For all the experiments the machine learning techniques namely Least Median Square (LMS), Multilayer Perceptron (MLP) and Support Vector Machine (SVM) are used. In the first phase five well-known wrapper feature selection methods are used to obtain the prediction accuracy of machine learning techniques with selected feature subsets and default parameter settings. The experiments from the first phase demonstrate that holding the default parameters, LMS, MLP and SVM provides better prediction accuracy (i.e. reduced MAE and MASE) with selected feature subsets rather than without selected feature subsets. After getting improved prediction accuracy from the first phase, the second phase continues the experiments to optimize machine learning parameters and the prediction accuracy of those machine learning techniques are re-evaluated through adopting both the optimized parameter settings and selected feature subsets. The comparison between the results of two phases clearly shows that the later phase (i.e. machine learning techniques with selected feature subsets and optimized parameters) provides substantial improvement in the accuracy for solar power prediction than the earlier phase (i.e. machine learning techniques with selected feature subsets and default parameters). Experiments are carried out using reliable and real life historical meteorological data. The machine learning accuracy of solar radiation prediction is justified in terms of statistical error measurement and validation metrics. Experimental results of this paper facilitate to make a concrete verdict that providing more attention and effort towards the feature subset selection and machine learning parameter optimization (e.g. combined effect of selected feature subsets and optimized parameters on prediction accuracy which is investigated in this paper) can significantly contribute to improve the accuracy of solar power prediction.