Geometric median and its application in the identification of multiple outliers

Das, Keya Rani; Imon, A. H. M. Rahmatullah

doi:10.1080/02664763.2013.856385

Cited by 6 publications

(5 citation statements)

References 12 publications

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“…Thus, GM gave an appropriate mean of the data set by neglecting the factors that provided values in negative and zero and obstructed the mean data. In the case of a skewed distribution of the data, by GM, the symmetry of data was made by log transformation [ 55 ]. The GM provides values less than the actual arithmetic mean, as the arithmetic mean gives a sum of the total number of values and is sensitive to outliers, while the effect of outliers on the geometric mean is mild [ 55 ].…”

Section: Resultsmentioning

confidence: 99%

“…In the case of a skewed distribution of the data, by GM, the symmetry of data was made by log transformation [ 55 ]. The GM provides values less than the actual arithmetic mean, as the arithmetic mean gives a sum of the total number of values and is sensitive to outliers, while the effect of outliers on the geometric mean is mild [ 55 ]. Thus, in the case of a nonparametric test, the exact mean was obtained by GM.…”

Section: Resultsmentioning

confidence: 99%

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Effects of Muscle Energy Technique and Joint Manipulation on Pulmonary Functions, Mobility, Disease Exacerbations, and Health-Related Quality of Life in Chronic Obstructive Pulmonary Disease Patients: A Quasiexperimental Study

Bains

Chahal

Shaphe

et al. 2022

BioMed Research International

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Chronic obstructive pulmonary disease (COPD) is primarily a disease of the lungs; however, extrapulmonary comorbidities like rib cage stiffness, decreased thoracic spine mobility, postural changes, and skeletal muscle dysfunctions also coexist. Muscle energy technique (MET) and joint manipulation (JM) may help alleviate these musculoskeletal problems. This study was aimed at evaluating the effectiveness of MET and JM on pulmonary functions, dyspnea, chest wall mobility, disease exacerbations, and health-related quality of life in COPD patients. A total of 16 patients (7 women and 9 men) suffering from COPD between the ages of 35 and 65 years participated in the study. Pretest-posttest quasiexperimental design was used. MET was applied to the sternocleidomastoid, anterior scalene, pectoralis major muscles, and at the C4-C6 level of the cervical spine. Maitland JM was performed in the thoracic region at the intervertebral, costovertebral, and costotransverse joints. The treatment intervention lasted for 3 weeks. FEV1/FVC, maximum inspiratory pressure (MIP), SpO2, modified Borg dyspnea scale (MBDS), COPD assessment test (CAT), mMRC dyspnea scale, BODE index, right and left hemidiaphragm excursion, and chest wall expansion at T4 and T10 levels were the outcome measures. Significant improvement ( p < 0.05 ) was observed in FEV1/FVC, MIP, SpO2, MBDS, CAT, mMRC dyspnea scale, BODE index, and chest expansion at T4 and T10 levels. Only for the hemidiaphragm excursion, no significant ( p > 0.05 ) improvement was observed. Combined application of MET to accessory respiratory muscles and cervical spine and JM to thoracic spine improved pulmonary functions, chest wall mobility, and health-related quality of life and reduced dyspnea and disease exacerbations in patients with mild to moderate COPD.

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Effects of Muscle Energy Technique and Joint Manipulation on Pulmonary Functions, Mobility, Disease Exacerbations, and Health-Related Quality of Life in Chronic Obstructive Pulmonary Disease Patients: A Quasiexperimental Study

Bains

Chahal

Shaphe

et al. 2022

BioMed Research International

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“…By Equation ( 16), the occupancy probability of each accessible grid cell m i a will asymptotically tend to the geometric mean of [ ū1 a • • • ūN R a ] T if the proportionality constant < P m a [0] > gm is 1, which also occurs if we initialize P m i j (0) = 1 for each robot R i . Since the occupancy probability P m i j of each grid cell m i j ultimately converges to the geometric mean of occupancy probabilities computed by every robot, and the effect of outliers in the data is greatly dampened in the geometric mean [44], the resulting P m i j reasonably represents the true occupancy of the grid cell, even if a few robots record highly noisy or inaccurate measurements.…”

Section: Proof See Appendix Bmentioning

confidence: 99%

Information correlated Levy walk exploration and distributed mapping using a swarm of robots

Ramachandran,

Kakish,

Berman

2019

Preprint

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In this work, we present a novel distributed method for constructing an occupancy grid map of an unknown environment using a swarm of robots with global localization capabilities and limited inter-robot communication. The robots explore the domain by performing Lévy walks in which their headings are defined by maximizing the mutual information between the robot's estimate of its environment in the form of an occupancy grid map and the distance measurements that it is likely to obtain when it moves in that direction. Each robot is equipped with laser range sensors, and it builds its occupancy grid map by repeatedly combining its own distance measurements with map information that is broadcast by neighboring robots. Using results on average consensus over time-varying graph topologies, we prove that all robots' maps will eventually converge to the actual map of the environment. In addition, we demonstrate that a technique based on topological data analysis, developed in our previous work for generating topological maps, can be readily extended for adaptive thresholding of occupancy grid maps. We validate the effectiveness of our distributed exploration and mapping strategy through a series of 2D simulations and multi-robot experiments.

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“…Geometric median (Gmed) is a robust estimator of centrality in Euclidean spaces [16]. Gmed of a dataset is the data minimizing the sum of distances to the sample dataset.…”

Section: Estimation Methods For Missing Rainfall Valuesmentioning

confidence: 99%

Normal Ratio in Multiple Imputation Based on Bootstrapped Sample for Rainfall Data With Mis Singness

Burhanuddin

Deni²,

Ramli

2017

GEOMATE

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ABSTRACT:The existence of missing values in rainfall data series is inevitably affects the quality of the data. This problem will influence the results of analysis and subsequently provide imprecise information to the hydrological and meteorological management. A practical and reliable approach is needed in developing estimation methods to impute the missing values. Single imputation is the most commonly used approach for missing values, but, it encounters with the limitation of not considering the uncertainty and natural variability in missing data imputation. Thus, this study has proposed multiple imputation approach based on bootstrap samples in order to overcome the limitation of single imputation approach. Three normal ratio estimation methods are implemented using the proposed approach. The performances of the estimation methods are evaluated at six different levels of missingness. Complete 40 years daily rainfall data from four meteorology stations were considered for the analysis purpose with Johor Bahru station was selected as the target station. The results of the proposed approach were compared to the results obtained from single imputation approach and the widely known built in software for multiple imputation, Amelia II package, in assessing the performance of proposed approach. The results showed that all estimation methods that implemented using proposed approach provided the most accurate estimation results at all percentages of missingness. This proves the advantage of adaption of variability and uncertainty element in the proposed approach in estimating the missing rainfall data at the area of the current study.

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Geometric median and its application in the identification of multiple outliers

Cited by 6 publications

References 12 publications

Effects of Muscle Energy Technique and Joint Manipulation on Pulmonary Functions, Mobility, Disease Exacerbations, and Health-Related Quality of Life in Chronic Obstructive Pulmonary Disease Patients: A Quasiexperimental Study

Effects of Muscle Energy Technique and Joint Manipulation on Pulmonary Functions, Mobility, Disease Exacerbations, and Health-Related Quality of Life in Chronic Obstructive Pulmonary Disease Patients: A Quasiexperimental Study

Information correlated Levy walk exploration and distributed mapping using a swarm of robots

Normal Ratio in Multiple Imputation Based on Bootstrapped Sample for Rainfall Data With Mis Singness

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