Mahalanobis Distance Research Articles

Extended Hellwig's Method Utilizing Entropy-Based Weights and Mahalanobis Distance: Applications in Evaluating Sustainable Development in the Education Area.

One of the crucial steps in the multi-criteria decision analysis involves establishing the importance of criteria and determining the relationship between them. This paper proposes an extended Hellwig's method (H_EM) that utilizes entropy-based weights and Mahalanobis distance to address this issue. By incorporating the concept of entropy, weights are determined based on their information content represented by the matrix data. The Mahalanobis distance is employed to address interdependencies among criteria, contributing to the improved performance of the proposed framework. To illustrate the relevance and effectiveness of the extended H_EM method, this study utilizes it to assess the progress toward achieving Sustainable Development Goal 4 of the 2030 Agenda within the European Union countries for education in the year 2021. Performance comparison is conducted between results obtained by the extended Hellwig's method and its other variants. The results reveal a significant impact on the ranking of the EU countries in the education area, depending on the choice of distance measure (Euclidean or Mahalanobis) and the system of weights (equal or entropy-based). Overall, this study highlights the potential of the proposed method in addressing complex decision-making scenarios with interdependent criteria.

Obtaining morphometric standards of drone wings of separate populations of honey bees (Apis mellifera) in Ukraine

Today, there are no systematic studies on the wing phenotypes of drone populations of the honeybee widespread in Ukraine. Considering that drone genomes are haploid, this allows one to establish the correspondence between the phenotype and the drone genome, thereby roughly determining the queen's genome in the part responsible for the wing phenotype. This partially compensates for the lack of resources among domestic scientists to conduct genetic research on bees. The aim of the study was to examine the wings of drones from several apiaries in the Kharkiv, Sumy, Poltava, and Zhytomyr regions, identify typical phenotypes, and attempt their taxonomic identification. Using discriminant analysis, 4640 drone wings were classified into three clusters. A two-step scheme for forming significantly different phenotype clusters of wings was proposed. Initially, based on the similarity of Euclidean distances and Mahalanobis distances (<2.6) between clusters, three groups were obtained, which, for refinement, underwent a second classification. As a result, average values and confidence intervals of eight morphometric traits were established: Ci, Dbi, Disc.sh, Pci, Ri, Ci.3, Ci.2.1, Ci.2.2 for the three wing groups. It is suggested to accept the trait values of these groups as reference data: one as a local population of the A. m. carnica subspecies, and the other two as regional standards for Ukrainian bees. Based on the obtained standards, a significant presence of A. m. carnica subspecies bees was established in all studied apiaries, except for the apiary with the status of a breeding ground for Ukrainian steppe bees (Kuzemin village, Sumy region), where such presence is minimal. This fact indicates the need for special measures to reproduce and expand the ranges of existence of local populations of Ukrainian steppe bees. The example of creating local and regional morphometric standards provided in this work is specifically designed to address this issue.

Methadone Flexi Dispensing (MFlex) Intelligence System utilizing the Mahalanobis-Taguchi System

Methadone Flexi Dispensing (MFlex) Intelligence System utilizing the Mahalanobis-Taguchi System

The influence of parental involvement on students’ non-cognitive abilities in rural ethnic regions of northwest China

The development of children’s non-cognitive abilities is crucial for both individuals and society as a whole. In this study, using a follow-up survey on 5369 primary students in rural ethnic regions of northwest China, we aim to examine the levels of parental involvement in rural ethnic regions and investigate its effect on students’ non-cognitive abilities. Our results show the following: first, parental involvement in rural ethnic regions of northwest China is quite low. Parents pay more attention to their children’s academic performance than to their non-cognitive abilities and the personal involvement is seriously lacking. Second, students from families with more favorable economic status, high parental education levels, non-migrant parents, and primary caregivers who are parents experience higher levels of parental involvement. Though Han students generally have higher maternal involvement and lower paternal involvement than minorities, the ethnic differences are reduced after controlling the covariates. Third, using the value-added model, after controlling for individual, family, class, county and baseline variables, we find that maternal behavioral and personal involvement and paternal cognitive and behavioral involvement have significant positive effects on children’s non-cognitive abilities. We use causal identification methods including propensity score matching and Mahalanobis distance matching to do the robustness test.

Using craniofacial fluctuating asymmetry to examine the effects of sex, socioeconomic status, and early life experiences on adult age at death in industrial England.

Historical evidence from 18th- and 19th-century England suggests that industrialization's impacts on health were largely negative, especially among marginalized groups. However, available documentary evidence is often biased toward adult men and rarely sheds light on the experiences of other members of the population, such as women and children. Craniofacial fluctuating asymmetry (FA) can serve as a proxy measurement of developmental instability and stress during development. This study examines the associations among age, sex, socioeconomic status (SES), and FA in skeletal samples from industrial-era England. The sample for this study comes from four industrial-era cemeteries from England (A.D. 1711-1857). Geometric morphometric analyses of three-dimensional landmark coordinate data were used to generate a measure of FA for each individual (Mahalanobis distance). A three-way ANOVA was used to evaluate the impacts of sex, SES, and FA scores on adult age at death (n = 168). Significant associations existed between age at death and SES (p = 0.004) and FA scores (p = 0.094). Comparisons of the estimated means indicated that age at death was consistently higher among high SES individuals and individuals with FA scores less than one standard deviation from the mean. This study supports findings from previous studies that have suggested that the differences in resource access and environmental buffering generated by socioeconomic inequality can impact longevity and patterns of mortality among socioeconomic status groups. Likewise, stress in early life-evinced by craniofacial fluctuating asymmetry-can influence observed patterns of longevity in adults decades later.

Semantic-driven dimension reduction for wireless internet of things

In recent years, mobile communication and artificial intelligence technologies have been widely used in the construction of wireless networks, bringing about a dramatic increase in data size. Existing wireless networks usually consist of a large number of nodes, with the potential risk of the curse of dimensionality. High dimensionality plays a negative role in learning effectiveness and efficiency, which should have been studied in depth but is neglected in existing wireless network research. In order to generate effective semantic-driven efficiency, this paper focuses on semantic-driven dimensionality reduction for wireless Internet of Things. Specifically, this paper introduces a series of feature selection techniques centered on Mahalanobis distance for dimensionality reduction, which helps to select discriminative features by measuring the effectiveness of semantic preferences and semantic-driven efficiency through Mahalanobis distance. Experiments on a set of wireless sensor data and various high-dimensional microarray data validate the superior performance of the proposed method.

Advancing (U-Th)/He Zircon Dating: Novel Approaches in Sample Preparation and Uncertainty Reduction

Abstract The laser microprobe (U-Th)/He dating method is a new and efficient technique that utilizes an interoperable and integrated suite of instruments, including the excimer laser system, quadrupole helium mass spectrometer, and quadrupole inductively coupled plasma mass spectrometer. To demonstrate the applicability of this new method, we applied both the conventional and laser microprobe techniques to the Sri Lanka zircon (LGC-1). We obtained twenty-two (U-Th)/He ages on nine shards using the laser microprobe method, showing an average (U-Th)/He age of 471.1 ± 16.6 Ma (1σ). This result is generally consistent with the mean conventional age (484.1 ± 9.6 Ma) for twenty-two zircon fragments. Both are nearly equal to the age value (~476 Ma) predicted by the He diffusion model and the thermal history model of Sri Lanka highland. The variations in the laser microprobe-derived ages are most likely caused by the uncertainties in volume measurements, which is also common in other studies. We used the Mahalanobis distance technique to reduce the volume measurement bias by identifying and eliminating abnormal data.

Forest Canopy Height Estimation by Integrating Structural Equation Modeling and Multiple Weighted Regression

As an important component of forest parameters, forest canopy height is of great significance to the study of forest carbon stocks and carbon cycle status. There is an increasing interest in obtaining large-scale forest canopy height quickly and accurately. Therefore, many studies have aimed to address this issue by proposing machine learning models that accurately invert forest canopy height. However, most of the these approaches feature PolSAR observations from a data-driven viewpoint in the feature selection part of the machine learning model, without taking into account the intrinsic mechanisms of PolSAR polarization observation variables. In this work, we evaluated the correlations between eight polarization observation variables, namely, T11, T22, T33, total backscattered power (SPAN), radar vegetation index (RVI), the surface scattering component (Ps), dihedral angle scattering component (Pd), and body scattering component (Pv) of Freeman-Durden three-component decomposition, and the height of the forest canopy. On this basis, a weighted inversion method for determining forest canopy height under the view of structural equation modeling was proposed. In this study, the direct and indirect contributions of the above eight polarization observation variables to the forest canopy height inversion task were estimated based on structural equation modeling. Among them, the indirect contributions were generated by the interactions between the variables and ultimately had an impact on the forest canopy height inversion. In this study, the covariance matrix between polarization variables and forest canopy height was calculated based on structural equation modeling, the weights of the variables were calculated by combining with the Mahalanobis distance, and the weighted inversion of forest canopy height was carried out using PSO-SVR. In this study, some experiments were carried out using three Gaofen-3 satellite (GF-3) images and ICESat-2 forest canopy height data for some forest areas of Gaofeng Ridge, Baisha Lizu Autonomous County, Hainan Province, China. The results showed that T11, T33, and total backscattered power (SPAN) are highly correlated with forest canopy height. In addition, this study showed that determining the weights of different polarization observation variables contributes positively to the accurate estimation of forest canopy height. The forest canopy height-weighted inversion method proposed in this paper was shown to be superior to the multiple regression model, with a 26% improvement in r and a 0.88 m reduction in the root-mean-square error (RMSE).

Predicting lodging severity in dry peas using UAS-mounted RGB, LIDAR, and multispectral sensors

This study investigated the feasibility of using data collected by sensors mounted onto unmanned aerial systems (UASs) and traditional classification methods (Maximum Likelihood, Mahalanobis Distance, Minimum Distance, and Adaptive Coherence Estimator) and four machine learning models (Random Forest [RF], Support Vector Machine [SVM], K-Nearest Neighbor [KNN], and Extreme Gradient Boosting [XGBOOST]) to predict the severity of dry pea lodging. Data were collected in two environments in North Dakota during the 2022 crop season, where lodging was visually estimated at the plot level using a lodging scale range of 0 to 9. Aerial images were collected using two UASs (DJI Matrice 200 and 300) during early, mid, and late stages of growth. Synthetic Minority Oversampling Technique combined with Edited Nearest Neighbors (SMOTE-ENN) was used to balance the imbalanced dataset. Different feature selection models (recursive feature elimination, lasso regression, principal component analysis, and correlation-based methods) were used and compared to identify the most important features in the dataset. Our study found that similar channels can be used interchangeably for analyzing lodging without compromising accuracy, simplifying data acquisition, and saving time and resources. The maximum plant height values obtained from LiDAR and RGB sensors showed a strong correlation with actual values. Recursive feature elimination was the most effective feature selection method for handling high-dimensional datasets. The XGBOOST model outperformed all traditional and machine learning classification models, with the lowest variation in precision values. RF showed the most pronounced overfitting among the machine learning models, while Mahalanobis distance showed the least overfitting among all traditional classification models. Overall, the study demonstrated the potential of UAS and machine learning models for predicting lodging severity in dry peas, with XGBOOST being the best-performing model.

Discriminant canonical analysis as a tool for genotype traceability testing based on turkey meat and carcass traits.

The present study aims to develop a statistical tool for turkey breed traceability testing based on meat and carcass quality characteristics. To this end, a comprehensive meta-analysis was performed, collecting data from a total of 75 studies approaching meat and carcass attributes of 37 turkey strains and landraces since the late 1960s. A total of 22 meat and carcass traits were considered variables, grouped in the following clusters: carcass dressing traits, muscle fiber properties, pH, colorimetry, water-capacity traits, texture-related attributes, and nutritional composition of the meat. Once the multicollinearity analysis allowed the deletion of redundant variables, cold carcass weight, slaughter weight, muscle fiber diameter, sex-female, carcass/piece weight, meat redness, ashes, pH24, meat lightness, moisture, fat, and water-holding capacity showed explanatory properties in the discriminating analysis (p < 0.05). In addition, strong positive and negative correlations were found among those variables studied. Carcass traits were positively associated, particularly slaughter weight and cold carcass weight (+0.561). Among meat physical traits, pH showed positive correlations with drip loss (+0.490) and pH24 (+0.327), and water-holding capacity was positively associated with cholesterol (+0.434) and negatively associated with collagen (-0.398). According to nutritional traits, fat and ash showed a strong correlation (+0.595), and both were negatively associated with moisture (-0.375 and -0.498, respectively). Strong negative correlations were found as well between meat protein and fat (-0.460) and between collagen and cholesterol (-0.654). Finally, the Mahalanobis distance suggested a clustering pattern based on meat and carcass characteristics that report information about interbreeding and variety proximity. This study establishes a departure point in the development of a tool for breed traceability guaranteeing aimed at enhancing distinguished, local breed-based turkey meat.

A fusion algorithm for HRG output errors based on improved support function and MDTW

To improve the accuracy of hemispherical resonator gyro (HRG) output errors, a novel fusion algorithm is proposed based on improved support function and multi-dimensional dynamic time warping. By analyzing the temperature characteristics and big data characteristics of HRG, the eigenvectors are initially selected, and the correlation and redundancy are later removed by Kernel principal component analysis. To obtain potential relationships between different time series, an improved support function based on grey incidence analysis theory is brought in to reduce the computational complexity, and the genetic algorithm is introduced to identify the optimal parameters rather than manually setting them. To accurately quantify how similar or different a time series is compared with another, multi-dimensional dynamic time warping which utilizes Mahalanobis distance is introduced instead of dynamic time warping. Experiment results show that the proposed algorithm performs better in both accuracy and universality compared with the other three comparative methods.

Some new invariant sum tests and MAD tests for the assessment of Benford’s law

AbstractThe Benford law is used world-wide for detecting non-conformance or data fraud of numerical data. It says that the significand of a data set from the universe is not uniformly, but logarithmically distributed. Especially, the first non-zero digit is One with an approximate probability of 0.3. There are several tests available for testing Benford, the best known are Pearson’s $$\chi ^2$$ χ 2 -test, the Kolmogorov–Smirnov test and a modified version of the MAD-test. In the present paper we propose some tests, three of the four invariant sum tests are new and they are motivated by the sum invariance property of the Benford law. Two distance measures are investigated, Euclidean and Mahalanobis distance of the standardized sums to the orign. We use the significands corresponding to the first significant digit as well as the second significant digit, respectively. Moreover, we suggest inproved versions of the MAD-test and obtain critical values that are independent of the sample sizes. For illustration the tests are applied to specifically selected data sets where prior knowledge is available about being or not being Benford. Furthermore we discuss the role of truncation of distributions.

Underwater terrain-matching algorithm based on improved iterative closest contour point algorithm

Although an autonomous underwater vehicle (AUV) is noted for its good autonomy, concealment and anti-interference ability, errors in its inertial navigation system (INS) inevitably increase over time, leading to positional failure during long-term voyages. Terrain-assisted navigation can help the INS to correct its position. The traditional iterative closest contour point (ICCP) achieves high matching accuracy when the initial position error of the INS is small, but is prone to mismatching when the initial error is large. This study combines ICCP with particle swarm optimization (PSO) to overcome this problem. First, the global optimization ability of PSO is improved by changing the acceleration factor and introducing an artificial bee colony (ABC) onlooker bee greedy search (ABC- ωAPSO). Second, the Euclidean distance of ICCP is replaced by the Mahalanobis distance to abate the influence of system error on the matching accuracy. Finally, the initial position error is reduced by rough matching using the ABC- ωAPSO, which has global optimization capability. Next, fine matching is performed by ICCP. This two-step process resolves the sensitivity problem of ICCP to the initial position error. The experimental results revealed a good matching effect after the double-matching procedure. When the initial INS errors were 0.55′ to the east and 0.55′ to the north, the matching error was reduced to 89.3 m, suggesting that the approach can realize autonomous passive navigation of AUVs.

Method for Estimating Road Impulse Ahead of Vehicles in Urban Environment with Microelectromechanical System Three-Dimensional Sensor.

Most automated vehicles (AVs) are equipped with abundant sensors, which enable AVs to improve ride comfort by sensing road elevation, such as speed bumps. This paper proposes a method for estimating the road impulse features ahead of vehicles in urban environments with microelectromechanical system (MEMS) light detection and ranging (LiDAR). The proposed method deploys a real-time estimation of the vehicle pose to solve the problem of sparse sampling of the LiDAR. Considering the LiDAR error model, the proposed method builds the grid height measurement model by maximum likelihood estimation. Moreover, it incorporates height measurements with the LiDAR error model by the Kalman filter and introduces motion uncertainty to form an elevation weight method by confidence eclipse. In addition, a gate strategy based on the Mahalanobis distance is integrated to handle the sharp changes in elevation. The proposed method is tested in the urban environment. The results demonstrate the effectiveness of our method.

Autonomous predictive maintenance of quadrotor UAV with multi-actuator degradation

Abstract With the wide application of quadrotor unmanned aerial vehicles (UAVs), the requirements for their safety and reliability are becoming increasingly stringent. In this paper, based on the feedback of airframe performance health perception information and the predictive function control strategy, the autonomous maintenance of a quadrotor UAV with multi-actuator degradation is realised. Autonomous maintenance architecture is constructed by the predictive maintenance (PdM) idea and the Laguerre function model predictive pontrol (LF-MPC) strategy. Using the two-stage Kalman filter (TSKF) method, based on the established UAV degradation model, the aircraft state and actuator degradation state are predicted simultaneously. For the predictive perception of system health, on the one hand, the system health degree (HD) based on Mahalanobis distance is defined by the degree of airframe state deviation from the expected state, and then the failure threshold of the UAV is obtained. On the other hand, according to the degradation state of each actuator, a comprehensive degradation variable fused with different weight coefficients of multiple actuators degradation is used to obtain the probability density function (PDF) of remaining useful life (RUL) prediction. For the autonomous maintenance of system health, the LF-MPC weight matrixes are adjusted adaptively in real-time based on the HD evaluation, to achieve a compromise balance between UAV performance and control effect, and greatly extend the working time of UAV. Simulation results verified the effectiveness of the proposed method.

Model-free measurement of case influence in structural equation modeling.

In the field of structural equation modeling (SEM), all commonly used case influence measures are model-based measures whose performance are affected by target-model-misspecification-error. This problem casts light on the need to come up with a model-free measure which avoids the misspecification problem. the main purpose of this study is to introduce a model-free case influence measure, the Deleted- One-Covariance-Residual (DOCR), and then evaluating its performance compared to that of Mahalanobis distance (MD) and generalized Cook's distance (gCD). The data of this study were simulated under three systematically manipulated conditions: the sample size, the proportion of target cases to non-target cases, and the type of model used to generate the data. The findings suggest that the DOCR measure generally performed better than MD and gCD in identifying the target cases across all simulated conditions. However, the performance of the DOCR measure under a small sample size was not satisfactory, and it raised a red flag about the sensitivity of this measure to small sample size. Therefore, researchers and practitioners should only use the DOCR measure with a sufficiently large sample size, but not larger than 600.

An Artificial Intelligence and Industrial Internet of Things-Based Framework for Sustainable Hydropower Plant Operations

Hydropower plays a crucial role in supplying electricity to developed nations and is projected to expand its capacity in various developing countries such as Sub-Saharan Africa, Argentina, Colombia, and Turkey. With the increasing demand for sustainable energy and the emphasis on reducing carbon emissions, the significance of hydropower plants is growing. Nevertheless, numerous challenges arise for these plants due to their aging infrastructure, impacting both their efficiency and structural stability. In order to tackle these issues, the present study has formulated a specialized real-time framework for identifying damage, with a particular focus on detecting corrosion in the conductors of generators within hydropower plants. It should be noted that corrosion processes can be highly complex and nonlinear, making it challenging to develop accurate physics-based models that capture all the nuances. Therefore, the proposed framework leverages autoencoder, an unsupervised, data-driven AI technology with the Mahalanobis distance, to capture the intricacies of corrosion and automate its detection. Rigorous testing shows that it can identify slight variations indicating conductor corrosion with over 80% sensitivity and a 5% false alarm rate for ‘medium’ to ‘high’ severity damage. By detecting and resolving corrosion early, the system reduces disruptions, streamlines maintenance, and mitigates unscheduled repairs’ negative effects on the environment. This enhances energy generation effectiveness, promotes hydroelectric facilities’ long-term viability, and fosters community prosperity.

A normative modeling approach to quantify white matter changes and predict functional outcomes in stroke patients.

The diverse nature of stroke necessitates individualized assessment, presenting challenges to case-control neuroimaging studies. The normative model, measuring deviations from a normal distribution, provides a solution. We aim to evaluate stroke-induced white matter microstructural abnormalities at group and individual levels and identify potential prognostic biomarkers. Forty-six basal ganglia stroke patients and 46 healthy controls were recruited. Diffusion-weighted imaging and clinical assessment were performed within 7 days after stroke. We used automated fiber quantification to characterize intergroup alterations of segmental diffusion properties along 20 fiber tracts. Then each patient was compared to normative reference (46 healthy participants) by Mahalanobis distance tractometry for 7 significant fiber tracts. Mahalanobis distance-based deviation loads (MaDDLs) and fused MaDDLmulti were extracted to quantify individual deviations. We also conducted correlation and logistic regression analyses to explore relationships between MaDDL metrics and functional outcomes. Disrupted microstructural integrity was observed across the left corticospinal tract, bilateral inferior fronto-occipital fasciculus, left inferior longitudinal fasciculus, bilateral thalamic radiation, and right uncinate fasciculus. The correlation coefficients between MaDDL metrics and initial functional impairment ranged from 0.364 to 0.618 (p < 0.05), with the highest being MaDDLmulti. Furthermore, MaDDLmulti demonstrated a significant enhancement in predictive efficacy compared to MaDDL (integrated discrimination improvement [IDI] = 9.62%, p = 0.005) and FA (IDI = 34.04%, p < 0.001) of the left corticospinal tract. MaDDLmulti allows for assessing behavioral disorders and predicting prognosis, offering significant implications for personalized clinical decision-making and stroke recovery. Importantly, our method demonstrates prospects for widespread application in heterogeneous neurological diseases.

ICDM-GEHC: identifying cancer driver module based on graph embedding and hierarchical clustering

Due to the high heterogeneity of cancers, it is rather essential to explore driver modules with the help of gene mutation data as well as known interactions between genes/proteins. Unfortunately, latent false positive interactions are inevitable in the Protein-Protein Interaction (PPI) network. Hence in the presented method, a new weight evaluation index, based on the gene-microRNA network as well as somatic mutation profile, is introduced for weighting the PPI network first. Subsequently, the vertices in the weighted PPI network are hierarchically clustered by measuring the Mahalanobis distance of their feature vectors, extracted with the graph embedding method Node2vec. Finally, a heuristic process with dropping and extracting is conducted on the gene clusters to produce a group of gene modules. Numerous experiment results demonstrate that the proposed method exhibits superior performance to four cutting-edge identification methods in most cases regarding the capability of recognizing the acknowledged cancer-related genes, generating modules having relatively high coverage and mutual exclusivity, and are significantly enriched for specific types of cancers. The majority of the genes in the identified modules are involved in cancer-related signaling pathways, or have been reported to be carcinogenic in the literature. Furthermore, many cancer related genes detected by the proposed method are actually omitted by the four comparison methods, which has been verified in the experiments.

A Mahalanobis Distance-Based Approach for Dynamic Multiobjective Optimization With Stochastic Changes

In recent years, researchers have made significant progress in handling dynamic multi-objective optimization problems (DMOPs), particularly for environmental changes with predictable characteristics. However, little attention has been paid to DMOPs with stochastic changes. It may be difficult for existing dynamic multi-objective evolutionary algorithms (DMOEAs) to effectively handle this kind of DMOPs because most DMOEAs assume that environmental changes follow regular patterns and consecutive environments are similar. This paper presents a Mahalanobis Distance-based approach (MDA) to deal with DMOPs with stochastic changes. Specifically, we make an all-sided assessment of search environments via Mahalanobis distance on saved information to learn the relationship between the new environment and historical ones. Afterward, a change response strategy applies the learning to the new environment to accelerate the convergence and maintain the diversity of the population. Besides, the change degree is considered for all decision variables to alleviate the impact of stochastic changes on the evolving population. MDA has been tested on stochastic DMOPs with 2 to 4 objectives. The results show that MDA performs significantly better than the other latest algorithms in this paper, suggesting that MDA is effective for DMOPs with stochastic changes.