Mahalanobis Distance Research Articles

Minimum Regularized Covariance Trace Estimator and Outlier Detection for Functional Data

We propose the Minimum Regularized Covariance Trace (MRCT) estimator, a novel method for robust covariance estimation and functional outlier detection designed primarily for dense functional data. The MRCT estimator employs a subset-based approach that prioritizes subsets exhibiting greater centrality based on the generalization of the Mahalanobis distance, resulting in a fast-MCD type algorithm. Notably, the MRCT estimator handles high-dimensional datasets without the need for preprocessing or dimension reduction techniques, due to the internal smoothening whose amount is determined by the regularization parameter α > 0 . The selection of α is automated. An extensive simulation study demonstrates the efficacy of the MRCT estimator in terms of robust covariance estimation and automated outlier detection, emphasizing the balance between noise exclusion and signal preservation achieved through appropriate selection of α. The method converges fast in practice and performs favorably when compared to other functional outlier detection methods.

An Adaptive Robust EKF Based on Mahalanobis Distance and Non-Holonomic Constraints for Enhancing Vehicle Positioning Accuracy

An Adaptive Robust EKF Based on Mahalanobis Distance and Non-Holonomic Constraints for Enhancing Vehicle Positioning Accuracy

Appropriate indicator of modeling error for threshold-based model selection in statistics-based ultrasound tissue characterization

Analysis of the envelope statistics of ultrasound echo signals contributes to quantitative tissue characterization in medical ultrasound. Many probability distribution model functions have been studied, and the model function that should be used for tissue characterization depends on the type of disease, even in the same organ. Thus, an appropriate model selection is important for an accurate diagnosis. In this study, we aimed to select a model using threshold processing for modeling errors instead of a simple selection by minimizing the modeling error. For this purpose, we compared several indicators of modeling errors using random number simulations, ultrasonic simulation, and phantom experiment. The results validated that the Mahalanobis distance of moments is an appropriate indicator because it enables the use of a constant threshold value, regardless of the type of model function and data length.

Intrinsic Information-Theoretic Models

With this follow-up paper, we continue developing a mathematical framework based on information geometry for representing physical objects. The long-term goal is to lay down informational foundations for physics, especially quantum physics. We assume that we can now model information sources as univariate normal probability distributions N (μ, σ0), as before, but with a constant σ0 not necessarily equal to 1. Then, we also relaxed the independence condition when modeling m sources of information. Now, we model m sources with a multivariate normal probability distribution Nm(μ,Σ0) with a constant variance–covariance matrix Σ0 not necessarily diagonal, i.e., with covariance values different to 0, which leads to the concept of modes rather than sources. Invoking Schrödinger’s equation, we can still break the information into m quantum harmonic oscillators, one for each mode, and with energy levels independent of the values of σ0, altogether leading to the concept of “intrinsic”. Similarly, as in our previous work with the estimator’s variance, we found that the expectation of the quadratic Mahalanobis distance to the sample mean equals the energy levels of the quantum harmonic oscillator, being the minimum quadratic Mahalanobis distance at the minimum energy level of the oscillator and reaching the “intrinsic” Cramér–Rao lower bound at the lowest energy level. Also, we demonstrate that the global probability density function of the collective mode of a set of m quantum harmonic oscillators at the lowest energy level still equals the posterior probability distribution calculated using Bayes’ theorem from the sources of information for all data values, taking as a prior the Riemannian volume of the informative metric. While these new assumptions certainly add complexity to the mathematical framework, the results proven are invariant under transformations, leading to the concept of “intrinsic” information-theoretic models, which are essential for developing physics.

Learning in Deep Radial Basis Function Networks

Learning in neural networks with locally-tuned neuron models such as radial Basis Function (RBF) networks is often seen as instable, in particular when multi-layered architectures are used. Furthermore, universal approximation theorems for single-layered RBF networks are very well established; therefore, deeper architectures are theoretically not required. Consequently, RBFs are mostly used in a single-layered manner. However, deep neural networks have proven their effectiveness on many different tasks. In this paper, we show that deeper RBF architectures with multiple radial basis function layers can be designed together with efficient learning schemes. We introduce an initialization scheme for deep RBF networks based on k-means clustering and covariance estimation. We further show how to make use of convolutions to speed up the calculation of the Mahalanobis distance in a partially connected way, which is similar to the convolutional neural networks (CNNs). Finally, we evaluate our approach on image classification as well as speech emotion recognition tasks. Our results show that deep RBF networks perform very well, with comparable results to other deep neural network types, such as CNNs.

Attrition from Jail Reentry Program Increases Recidivism

AbstractReentry programs represent an increasingly popular method to reduce recidivism for individuals exiting prison and jail systems throughout the United States. Most evaluations tend to focus on recidivism as the primary outcome of interest. Attrition, however, can function an important supplementary measure that complements recidivism outcomes. To demonstrate, we analyze a jail reentry program built around peer navigators serving as staff members that refer participants to necessary support services while also serving as a mentor to participants exiting jail. We use a combination of general linear models (GLMs), Mahalanobis distance matching (MDM), and panel regression to both predict attrition and compare recidivism outcomes between three attrition groups: program completers, program quitters, and matched controls. Participants that successfully completed the program did not avoid new convictions or reincarceration significantly more or less than matched controls. Participants that quit the program, however, saw significantly higher conviction and reincarceration rates compared to matched controls. The nuance added to our program evaluation by adding attrition as a differential factor is worth consideration by other reentry programs who may not be realizing the full picture of their results by presenting recidivism outcomes alone.

Clustering-Based Classification of Polygonal Wheels in a Railway Freight Vehicle Using a Wayside System

Polygonal wheels are one of the most common defects in train wheels, causing a reduction in comfort levels for passengers and a higher degradation of vehicle and track components. With the aim of contributing to the safety and reliability of railway transport, this paper presents the development of an innovative methodology for classifying polygonal wheels based on a wayside system. To achieve that, a numerical train-track interaction model was adopted to simulate the passage of a freight train over a virtual wayside monitoring system composed of a set of accelerometers installed on the rails. Then, the acquired acceleration time series was transformed to a frequency domain using a Fast Fourier transform (FFT), and on this data, damage-sensitive features were extracted. The features based on Principal Component Analysis (PCA) showed great sensitivity to the harmonic order, while the ones based on Continuous Wavelet Transform (CWT) model showed great sensitivity to the defect amplitude. One step further, all features are merged using the Mahalanobis distance in order to obtain a damage index strongly correlated with the polygonal defect. Finally, a cluster analysis allowed the automatic classification of polygonal wheels, according to the harmonic order (harmonic-based) and defect amplitude (amplitude-based). The proposed methodology demonstrated high efficiency in identifying different types of polygonal wheels using a minimum layout of two sensors.

Predicting shear strength in UHPC beams through an innovative neural network with SHAP interpretation

Ultra-High performance concrete (UHPC) has garnered considerable attention in the construction industry due to its exceptional mechanical properties and durability. In the design of UHPC beams, accurately predicting shear strength is crucial. Inspired by the dense blocks in DenseNet, this paper proposes a novel neural network for predicting the shear strength of UHPC beams. A comprehensive database of UHPC beams was initially established through extensive literature data collection, amassing 619 experimental data samples. Preprocessing was subsequently conducted using mahalanobis distance (DM) to eliminate outliers. Subsequently, the database underwent detailed parameter analysis. In practical testing, the novel neural network model exhibited superior accuracy in predicting the shear strength of UHPC beams, surpassing traditional machine learning (ML) models and empirical formulas. Furthermore, it demonstrated excellent generalization capabilities, achieving an R2 value of 0.988 in the training set and 0.964 in the test set. The study introduced the shapley additive explanations (SHAP) method to conduct global and local interpretability analysis of the network model, demonstrating the contributions of each input parameter to the model predictions. Finally, based on this network model, a graphical user interface (GUI) was developed for researchers engaged in UHPC beam design, enabling users to easily input relevant parameters and obtain shear strength predictions. The findings of this study are expected to promote the application of ML models in predicting the complex nonlinear behavior of UHPC structures, providing strong support for engineering practice.

Leaf functional traits and ecological niche of Fagus grandifolia and Oreomunnea mexicana in natural forests and plantings as a proxy of climate change.

Functional traits reflect species' responses to environmental variation and the breadth of their ecological niches. Fagus grandifolia and Oreomunnea mexicana have restricted distribution in upper montane cloud forests (1700-2000 m a.s.l.) in Mexico. These species were introduced into plantings at lower elevations (1200-1600 m a.s.l.) that have climates predicted for montane forests in 2050 and 2070. The aim was to relate morphological leaf traits to the ecological niche structure of each species. Leaf functional traits (leaf area, specific leaf area [SLA], thickness, and toughness) were analyzed in forests and plantings. Atmospheric circulation models and representative concentration pathways (RCPs: 2.6, 4.5, 8.5) were used to assess future climate conditions. Trait-niche relationships were analyzed by measuring the Mahalanobis distance (MD) from the forests and the plantings to the ecological niche centroid (ENC). For both species, leaf area and SLA were higher and toughness lower in plantings at lower elevation relative to those in higher-elevation forests, and thickness was similar. Leaf traits varied with distance from sites to the ENC. Forests and plantings have different environmental locations regarding the ENC, but forests are closer (MD 0.34-0.58) than plantings (MD 0.50-0.70) for both species. Elevation as a proxy for expected future climate conditions influenced the functional traits of both species, and trait patterns related to the structure of their ecological niches were consistent. The use of distances to the ENC is a promising approach to explore variability in species' functional traits and phenotypic responses in optimal versus marginal environmental conditions.

Fuzzy SVM With Mahalanobis Distance for Situational Awareness-Based Recognition of Public Health Emergencies

In public health emergencies, situational awareness is crucial for swift responses by governments and rescue organizations. In this manuscript, a novel framework is proposed to identify and classify event-specific information, aiming to comprehend concepts, characteristics, and classifications associated with situational awareness in social media emergencies. First, a statistical approach is employed to extract a set of standard features. Second, a category-based latent dirichlet allocation to vector (LDA2vec) model is leveraged to extract topic-based features to enhance accuracy, particularly for unbalanced datasets. Finally, a fuzzy support vector machine (FSVM) classifier utilizing the Mahalanobis distance kernel is introduced to improve the detection accuracy of event-specific information. The framework's effectiveness is evaluated using the social media public health dataset, achieving superior filtering capabilities for non-informative data with a precision of 89% and an F1-Score of 91%, surpassing other standard methods.

A randomized permutation whole-model test heuristic for Self-Validated Ensemble Models (SVEM)

We introduce a heuristic to test the significance of fit of Self-Validated Ensemble Models (SVEM) against the null hypothesis of a constant response. A SVEM model averages predictions from nBoot fits of a model, applied to fractionally weighted bootstraps of the target dataset. It tunes each fit on a validation copy of the training data, utilizing anti-correlated weights for training and validation. The proposed test computes SVEM predictions centered by the response column mean and normalized by the ensemble variability at each of nPoint points spaced throughout the factor space. A reference distribution is constructed by refitting the SVEM model to nPerm randomized permutations of the response column and recording the corresponding standardized predictions at the nPoint points. A reduced-rank singular value decomposition applied to the centered and scaled nPerm×nPoint reference matrix is used to calculate the Mahalanobis distance for each of the nPerm permutation results as well as the jackknife (holdout) Mahalanobis distance of the original response column. The process is repeated independently for each response in the experiment, producing a joint graphical summary. We present a simulation driven power analysis and discuss limitations of the test relating to model flexibility and design adequacy. The test maintains the nominal Type I error rate even when the base SVEM model contains more parameters than observations.

Remaining useful life prediction of rolling bearings based on performance evaluation and multifractional generalized Cauchy model with adaptive drift

The proposed Remaining Useful Life (RUL) prediction framework utilizes several advanced techniques to accurately estimate the remaining service life of rolling bearings. The framework includes early failure assessment, adaptive failure threshold (FT) determination, and a multifractional generalized Cauchy model (MfGC). The early failure assessment is enabled by establishing early FTs and health indicator (HI) curves generated by the Mahalanobis distance cumulative sum (MD-CUSUM) technique. The proposed dynamic fault threshold update method uses the BOX-COX transformation and Chebyshev inequality to determine confidence intervals for evaluating the fault threshold time. The multifractional nature of the MfGC process is characterized by independent, time-varying Hurst indices and fractional dimensions, and the long-range dependence (LRD) characteristics and stochasticity of the process are explained by the diffusion terms generated from the MfGC differential time series. The MfGC model with adaptive drift is constructed for various degenerate trajectories, and a method for estimating the model’s parameters is proposed. The effectiveness of the proposed RUL prediction method is demonstrated using the XJTU-SY bearing dataset.

Machine learning insights to CO2-EOR and storage simulations through a five-spot pattern – a theoretical study

The utilization of CO2 flooding is a widely applied enhanced oil recovery (EOR) technique in mature onshore oil fields. As well as being able to increase oil production and recovery it offers the potential to provide long-term, geological storage for carbon in subsurface reservoirs, thereby contributing to the mitigation of carbon emissions originating from human activities. Substantial research efforts have provided some insight into the uncertainties associated with CO2-EOR projects, but further understanding and the development of more reliable methods are required to accurately predict the outcomes of the complex processes involved in CO2 reservoir flooding. In this study, four machine learning (ML) algorithms were developed to predict CO2 storage mass and cumulative oil production, using the CMG-GEM three-phase flow compositional reservoir simulator with nine reservoir input variables covering a range of uncertainties associated with oil zones. The Mahalanobis distance technique was applied for identifying and excluding outlier data points from the target variable distributions of training data groups. 520 and 439 data records were excluded from the CO2 storage quantity and cumulative oil production dataset, respectively, to generate more reliable predictions. Meticulous training and testing of the ML models revealed that, of the models evaluated, the LSSVM model generated the lowest prediction errors with the test dataset (RMSE = 0.7811 million mt for CO2 storage mass; RMSE = 10.1245 million barrels for cumulative oil production) demonstrating excellent generalization capabilities.

BoostTrack: boosting the similarity measure and detection confidence for improved multiple object tracking

Handling unreliable detections and avoiding identity switches are crucial for the success of multiple object tracking (MOT). Ideally, MOT algorithm should use true positive detections only, work in real-time and produce no identity switches. To approach the described ideal solution, we present the BoostTrack, a simple yet effective tracing-by-detection MOT method that utilizes several lightweight plug and play additions to improve MOT performance. We design a detection-tracklet confidence score and use it to scale the similarity measure and implicitly favour high detection confidence and high tracklet confidence pairs in one-stage association. To reduce the ambiguity arising from using intersection over union (IoU), we propose a novel Mahalanobis distance and shape similarity additions to boost the overall similarity measure. To utilize low-detection score bounding boxes in one-stage association, we propose to boost the confidence scores of two groups of detections: the detections we assume to correspond to the existing tracked object, and the detections we assume to correspond to a previously undetected object. The proposed additions are orthogonal to the existing approaches, and we combine them with interpolation and camera motion compensation to achieve results comparable to the standard benchmark solutions while retaining real-time execution speed. When combined with appearance similarity, our method outperforms all standard benchmark solutions on MOT17 and MOT20 datasets. It ranks first among online methods in HOTA metric in the MOT Challenge on MOT17 and MOT20 test sets. We make our code available at https://github.com/vukasin-stanojevic/BoostTrack.

Multidimensional credibility: A new approach based on joint distribution function

Abstract In the traditional multidimensional credibility models developed by Jewell ((1973) Operations Research Center, pp. 73–77.), the estimation of the hypothetical mean vector involves complex matrix manipulations, which can be challenging to implement in practice. Additionally, the estimation of hyperparameters becomes even more difficult in high-dimensional risk variable scenarios. To address these issues, this paper proposes a new multidimensional credibility model based on the conditional joint distribution function for predicting future premiums. First, we develop an estimator of the joint distribution function of a vector of claims using linear combinations of indicator functions based on past observations. By minimizing the integral of the expected quadratic distance function between the proposed estimator and the true joint distribution function, we obtain the optimal linear Bayesian estimator of the joint distribution function. Using the plug-in method, we obtain an explicit formula for the multidimensional credibility estimator of the hypothetical mean vector. In contrast to the traditional multidimensional credibility approach, our newly proposed estimator does not involve a matrix as the credibility factor, but rather a scalar. This scalar is composed of both population information and sample information, and it still maintains the essential property of increasingness with respect to the sample size. Furthermore, the new estimator based on the joint distribution function can be naturally extended and applied to estimate the process covariance matrix and risk premiums under various premium principles. We further illustrate the performance of the new estimator by comparing it with the traditional multidimensional credibility model using bivariate exponential-gamma and multivariate normal distributions. Finally, we present two real examples to demonstrate the findings of our study.

The marine diesel engine exhaust gas temperature baseline model based on particle swarm optimised generalised regression neural network

ABSTRACT This study addresses limitations in traditional condition monitoring for marine diesel engine (MDE) reliability and stability by proposing a hybrid machine learning and deep learning (DL) model called Particle Swarm Optimization-Generalized Regression Neural Network (PSO-GRNN) for real-time exhaust gas temperature (EGT) monitoring. The model integrates Mahalanobis distance (MD) calibration, wavelet packet denoising, and Pearson correlation analysis for comprehensive data preprocessing. Validation is conducted using historical '6L34DF' diesel engine data. Particle Swarm Optimization (PSO) optimizes the spread value (σ) of the Generalized Regression Neural Network (GRNN) to establish an optimal baseline model for EGT prediction. Experimental results show that PSO-GRNN outperforms Backpropagation Neural Network (BPNN), GRNN, Bidirectional Gated Recurrent Unit (BiGRU), Genetic Algorithm- Generalized Regression Neural Network (GA-GRNN), and Deep Belief Network-Support Vector Regression (DBN-SVR) in terms of training time and accuracy, demonstrating its suitability for MDE baseline modeling.

Enhancing cross-subject EEG emotion recognition through multi-source manifold metric transfer learning

Transfer learning (TL) has demonstrated its efficacy in addressing the cross-subject domain adaptation challenges in affective brain-computer interfaces (aBCI). However, previous TL methods usually use a stationary distance, such as Euclidean distance, to quantify the distribution dissimilarity between two domains, overlooking the inherent links among similar samples, potentially leading to suboptimal feature mapping. In this study, we introduced a novel algorithm called multi-source manifold metric transfer learning (MSMMTL) to enhance the efficacy of conventional TL. Specifically, we first selected the source domain based on Mahalanobis distance to enhance the quality of the source domains and then used manifold feature mapping approach to map the source and target domains on the Grassmann manifold to mitigate data drift between domains. In this newly established shared space, we optimized the Mahalanobis metric by maximizing the inter-class distances while minimizing the intra-class distances in the target domain. Recognizing that significant distribution discrepancies might persist across different domains even on the manifold, to ensure similar distributions between the source and target domains, we further imposed constraints on both domains under the Mahalanobis metric. This approach aims to reduce distributional disparities and enhance the electroencephalogram (EEG) emotion recognition performance. In cross-subject experiments, the MSMMTL model exhibits average classification accuracies of 88.83 % and 65.04 % for SEED and DEAP, respectively, underscoring the superiority of our proposed MSMMTL over other state-of-the-art methods. MSMMTL can effectively solve the problem of individual differences in EEG-based affective computing.

Digital dual test syphilis/HIV detection based on Fourier Descriptors of Cyclic Voltammetry curves

Background:Effective and timely detection is vital for mitigating the severe impacts of Sexually Transmitted Infections (STI), including syphilis and HIV. Cyclic Voltammetry (CV) sensors have shown promise as diagnostic tools for these STI, offering a pathway towards cost-effective solutions in primary health care settings. Objective:This study aims to pioneer the use of Fourier Descriptors (FDs) in analyzing CV curves as 2D closed contours, targeting the simultaneous detection of syphilis and HIV. Methods:Raw CV signals are filtered, resampled, and transformed into 2D closed contours for FD extraction. Essential shape characteristics are captured through selected coefficients. A complementary geometrical analysis further extracts features like curve areas and principal axes lengths from CV curves. A Mahalanobis Distance Classifier is employed for differentiation between patient and control groups. Results:The evaluation of the proposed method revealed promising results with classification performance metrics such as Accuracy and F1-Score consistently achieving values rounded to 0.95 for syphilis and 0.90 for HIV. These results underscore the potential efficacy of the proposed approach in differentiating between patient and control samples for STI detection. Conclusion:By integrating principles from biosensors, signal processing, image processing, machine learning, and medical diagnostics, this study presents a comprehensive approach to enhance the detection of both syphilis and HIV. This setts the stage for advanced and accessible STI diagnostic solutions.

An unsupervised machine learning approach for real-time damage detection in bridges

The bridge network is progressively aging, with an alarming proportion of bridges over 100 years. This situation engenders substantial risks to the overall reliability of transportation networks, requiring innovative methods for efficient management. Monitoring can provide a direct source of information about structural behavior generating alerts when changes occur. Real-time alerts enable effective infrastructure management and decision-making during damage or anomalous situations. However, monitoring can result in a large amount of data that is often difficult to convert into valuable information in real time. This paper presents an approach for real-time detection of abrupt damage occurrence in bridges using unsupervised anomaly detection algorithms and strain/acceleration measurements. The approach incorporates the separation of measurements into events having the same loading nature and the construction of three feature matrices based on statistical features, time-frequency features, and wavelet spectrum features. It includes the evaluation of five anomaly detection algorithms including Isolation Forest, One-Class Support Vector Machine, Robust Random Cut Forest, Local Outlier Factor, and Mahalanobis Distance. The approach is illustrated with a case study of a steel-bascule-railway bridge, that has experienced a brittle cracking event during monitoring. Results highlight the robustness of One-Class Support Vector Machine, Isolation Forest, and Local Outlier Factor algorithms in promptly detecting abrupt changes across different features. The separation of strain and acceleration data into loading-based events, coupled with the comparison of previous and new event features, provides robust feature matrices for effective damage detection. Enhanced detection and higher scores are particularly attributed to time-frequency domain features during damage occurrence. The presented approach can be used as a base on how to perform real-time anomaly detection within the context of bridge monitoring.

Design and validation of novel maize grain cleaning loss detection system based on classification models of particle time-domain signals

Quantitative evaluation of grain cleaning loss is a central concern in maize intelligent direct harvesting. This study integrates particle time-domain signals with machine learning models to develop a novel grain cleaning loss detection system and create modular embedded companion software. Specifically, collisional time-domain signals of grains and impurities with varying mass gradients are captured, and abnormal data are eliminated utilizing the Mahalanobis Distance (MD) algorithm. Signal classification models incorporating diverse preprocessing methods are trained using Naive Bayes (NB) and Support Vector Machine (SVM) algorithms. Model performance is evaluated through internal leave-one-out-cross-validation (LOOCV) and external validation sets. The best classification model is integrated into the grain loss detection software, and bench tests verify real-time cleaning loss rates for detection systems. Results demonstrate that the SVM model with Savitzky-Golay (S-G) smoothing + Second-Order Derivative (SOD) preprocessing achieves the highest predictive accuracy, with 97.44 % and 96.15 % in training and validation sets, respectively. When the feeding rate of maize mixtures is 5 kg/s, absolute grain loss rates for three measurements are 1.62 %, 1.72 % and 1.86 %, respectively. Compared to traditional loss detection systems with multifunctional circuits, the novel loss detection system enhances the average accuracy of grain loss rate by 6.54, 6.82 and 8.93 percentage points. Hence, the proposed method and apparatus can be applied to detect grain cleaning loss quantitatively.